We then apply our new formulas in chapter 6 to observe how we can manipulate the Majorana fermions in the Kitaev model. Topological quantum computation 6. Koga, Akihisa We investigate the anisotropic S = 1/2 Kitaev model on the honeycomb lattice with the ordered-flux structure. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Using the time-dependent thermal pure quantum state method, we examine finite-temperature spin dynamics in the Kitaev model. 20. M1 and M2 are the spanning vectors of the lattice, and A FIG. Floquet topological insulators (?) We will then derive the Schwinger-Dyson equations on the closed time contour, and in turn use them to derive the Kadano -Baym equations on the real time axis. Consider 1- dimensional tight binding chain with spinless fermions and p-orbital hopping. The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. Abstract We investigate the topological properties of a ladder model of the Kitaev superconductor chains with a periodically modulated chemical potential. [59] and which focuses on the Majorana signatures of the model.
In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev m Clearly by setting = 0 you have cut the first and last Majorana mode from the rest of the chain. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. The interest in studying Majorana end modes (MMs) was spurred on by a proposal by Kitaev and Preskill7 outlining a way to realise quantum com- A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. At this point you might however object: Unpaired Majoranas appear because you chose one particular, and perhaps even unreachable, set of parameters! 2010) Reflecting both of this peculiarity of the Majorana Special case: Topological regime: Majorana fermions (e= =0!!!) $\begingroup$ @RoderickLee My feeling is that your confusion is somehow related to what it means for "the Majorana mode to be localized". Employing an SO(6) Majorana representation of We discovered highly unusual Alexei Kitaev (Microsoft Research) Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point.
Majorana edge magnetization in the Kitaev honeycomb model.
Our circuits can be built using local ingredients in Majorana devices, namely
The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. So once again, here is our skeleton, the Kitaev model Hamiltonian written in momentum space: H K i t a e v = ( 2 t cos. . However, the Majorana representation enlarges the physical Hilbert space of the half spin by twice.
The ground state is topo-logically of our model indicate that the bulk-edge correspondence can be extended to a single-band system with hidden topological feature. H Katsura, Majorana excitations in Kitaev spin liquids, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-INV-3A-02 (2018). Intending to emulate Kitaev chain, we build a tight-binding model of a 3-site quantum dot chain. Kitaev chain is a theoretical model of a one-dimensional topological superconductor with Majorana zero modes at the two ends of the chain. the pure Kitaev model, how to solve it, and what types of Z2 QSLs can occur. Introduction Kitaev model Non-abelian statistics Hosting and detecting Majorana particles Conclusion and future directions Pairs of Majorana fermions can be combined into ordinary fermions c = 1 2 (1 + i 2);cy= 1 2 (1 i 2); form a single 2 level system If the Majorana fermions are spatially separated, implies fermion state is delocalised, The prototypical toy model possessing Majorana zero modes is the Kitaev chain with open boundaries [12], a one-dimensional tight-binding model for spinless fermions in the presence of p-wave superconducting pairing. At large magnetic elds the system enters a spin-polarized paramagnetic phase. To order 1/N, moments are given by those of the weight function of the Q-Hermite polynomials.Representing Wick contractions by rooted chord a model of N Majorana fermions This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (SYK) model, and obtain order 1/N 2 corrections for all moments, where N is the total number of Majorana fermions. 1Kitaev model Majorana Operators Exact Solution Spectrum and phase diagram 2Gapped Abelian Phase 3Magnetic Field: NonAbelian Phase Spectral Gap Edge Modes Non-Abelian Anyons Michele Burrello Kitaev Model Anyons and topological quantum computation Quantum phenomena do not occur in a Hilbert space. We also show that the flux fluctuations tend to open an energy gap in the Majorana spectrum near the gapless-gapped phase boundary. The Majorana bound states are located at domain walls between wire regions with a topological and normal superconducting phase - and this phase can be tuned The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z 2 gauge fields. 2. eld. 2.2 Quantum circuit constructions To illustrate how to construct the quantum circuit that prepares the ground states of Kitaev-inspired models, we focus on the original Kitaev model con-structed on the honeycomb lattice with 8 sites (result-ing in 2 2 unit cells) as shown in Fig.1(a). 1) Kitaev honeycomb model as Majorana fermions in Z2 gauge field (0 or flux) characterized by integer Chern number, modulo 16 2) Triangular vortex lattices : Chern = 0,1,,6,8 but not 7 3) Effective models in the dilute vortex limit function and conductance of a Kitaev model. In Section 3, we briey explain the symmetry properties of materials and how Kitaev interactions arise. The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. GENERAL INTRO In 1937 Ettore Majorana speculated that there could be a particle that is its own antiparticle. armadillo majorana nlohmann-json kitaev-model rashba-model Updated Mar 25, 2021; C++; Add a description, image, and links to the kitaev-model topic page so that developers can more easily learn about it. In the non-interacting case, a signal of topological order appears as zero-energy modes localized near the edges.
Majorana MF results for the [001] eld dependence of the magnetization Mz, the Majorana gap , and the magnetic susceptibility zz for (a) the FM Kitaev model and (b) the AFM one. honeycomb lattice square-octagon lattice (Kitaev 2006) (Yang et al. We rst study the present model from thedescription in terms of Majorana fermions. (ii) We investigate the Majorana bound states. The (localized) Majorana operator transforms you between different (degenerate) ground states. the fermionic operator squares to 1. It is the first result of its kind in nontrivial quantum spin models. Majorana fermions in Section II and compute the disorder averaged partition function for the SYK model with q= 2 and q= 4 interactions. Majorana Fermions ??
We propose an approach to detect the peculiarity of Majorana fermions at the edges of Kitaev magnets. tum computation. The aim will be to translate the Kitaev Chain Hamiltonian into a Matrix form to obtain energy spectrum and edge modes for an open chain. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting. At this point you might however object: Unpaired Majoranas appear because you chose one particular, and perhaps even unreachable, set of parameters! Clearly by setting = 0 you have cut the first and last Majorana mode from the rest of the chain. The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z 2 gauge field.
7,14 To this end, Kitaev, in a seminal paper, introduced a model of interacting spins on a honeycomb lat-tice which reduces to the problem of Majorana fermions coupled to a static Z 2 gauge eld. We study a Kitaev model on a square lattice, which describes topologically trivial superconductor when gap opens, while supports topological gapless phase when gap closes. Majorana states on TI edges 5. H Katsura, Majorana excitations in Kitaev spin liquids, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-INV-3A-02 (2018). Codes for Majorana zero modes identification in non-interacting systems. Majorana MF results for the [001] eld dependence of the magnetization Mz, the Majorana gap , and the magnetic susceptibility zz for (a) the FM Kitaev model and (b) the AFM one. Majroana and non-abelian statistics 7. In particular we focus on the models defined on the honeycomb, and square-octagon lattices. The red circles de-note the dierent, representative model parameter points that .
1. The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes.
(Color online) Kitaev model on the honeycomb lattice with xx coupling J1, yy coupling J2 and zz coupling J3. The magic stick rule still holds, but one Majorana species is free to hop in the presence of a static gauge eld. Bogoliubov de Gennes Theory 2. In contrast to previous studiesbased on Hermitian chains in the thermodynamic limit, we focus on the Kitaev model on a nite lattice system.This is motivated by the desire to get a clear physicalpicture of the edge mode through the investigation of asmall system. These results pave a new path to measurement of dynamical spinon or Majorana fermion spectroscopy of Kitaev and other spin-liquid materials. In the language of second quantization, this means that = y, i.e. In the year 1937, a new class of particles that are its own anti-particles were hypothesized by Ettore Majorana. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting. CM Seminar - Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model CM Seminar - Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model. k ) z + 2 y sin. Special case: What are Majorana fermions anyway? We show that the exact ground states can be obtained analytically even in the
The model exhibits two characteristic temperatures, ${T}_{L}$ and ${T}_{H}$, which correspond to energy Majorana bound states, Kitaev model 3. where. Majorana in wires 6. As is well known, a pair of Majorana edge modes is realized when a single complex fermion splits into real and imaginary parts which are, respectively, localized at the left and right edges of a sample magnet. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin c Majorana zero modes (MZMs) have attracted tremendous attention in condensed matter and materials physics communities due to the implications in topological quantum computation. By diagonalizing the Majorana Hamiltonian for the flux configuration, we find two distinct gapped quantum spin liquids. Kitaev used a simplied quantum wire model to show how Majorana modes might manifest as an emergent phenomena, which we will now discuss. Consider 1- dimensional tight binding chain with spinless fermions and p-orbital hopping. On the theoretical side, Kitaev introduced a celebrated model based upon the spinless p-wave superconductor in one dimension Kitaev , which is currently named as the Kitaev model, one of the simplest but highly nontrivial model to unveil MZM.
A Majorana fermion is a particle that is its own an-tiparticle.
It is the first result of its kind in non-trivial quantum spin models. In this chapter, we consider Kitaev's honeycomb lattice model (Kitaev, 2006). Majorana Fermions and Topological Quantum Computation 1. 2007 , Baskaran et al. This plays the same role as the NNN hopping inHaldane model [11] and opens a topological gap at theDirac cone of Majorana fermions. k = 2 J 1 + g 2 2 g cos ( k a) If we do Bogoliubov transformation of Fourier transformed Hamiltonian, we get.
Magnetic fields can give rise to a plethora of phenomena in Kitaev spin systems, such as the formation of non-trivial spin liquids in two and three spatial dimensions. Majorana edge states in the Kitaev model 4. The magnetic insulator -RuCl 3 is thought to realize a proximate KQSL. We calculate the resonant inelastic x-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model The Kitaev Model on the Honeycomb Lattice H = X K S i S j Superposition
One-dimensional (1D) dimerized Kitaev chain is a prototype model for MZMs, but its realization remains a challenge in material systems. lar kind of zero energy boundary mode called Majorana modes. Where. We will obtain these Majorana zero modes at the edges of an open chain.
Topological superconductor 4. 4B, solid and dashed orange arrows). Gapped: topological. The Kitaev model is ananisotropic spin- model with Ising interactions S xr S xr , S yr S yr and S zr S zr assigned to the three bonds in the hon-eycomb lattice. The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The BdG Hamiltonian acts on a set of basis states | n | , with = 1 corresponding to electron and hole states respectively. It has particle-hole symmetry, P H BdG P 1 = H BdG with P = x K. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting.
Authors: Petrova, Olga; Mellado, Paula; Tchernyshyov, Oleg Publication Date: 2014-10-01 NSF-PAR ID: 10009670 Journal Name: Physical Review B Volume: 90 Issue: 13 ISSN: 1098-0121 Publisher: American Physical Society The results of this thesis indicate that these Majorana acquire a relevant physical meaning. We used neutron scattering on single crystals of -RuCl 3 to reconstruct dynamical correlations in energy-momentum space.
See also the related analysis of Ref. Periodic Table of topological insulators and superconductors 5. Second, there is a gapless phase of (e ectively) free Majorana fermions. It is found that the system has two different topological classes, the class BDI characterized by the Z index and the class D characterized by the Z 2 index. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z 2 gauge fields. They occur in a laboratory Map into a chain of Majorana modes using: Majorana states in the Kitaev model. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. The key insight Kitaev provided is that this can be solved by \splitting" the fermionic site into two Majorana modes, which can then be spatially separated. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. which is not present in the ferromagnetically coupled model. 2020-11-26T15:00:00. We study how stable the Majorana-mediated spin transport in a quantum spin Kitaev model is against thermal fluctuations.
(a) Kitaevs model describes a two-dimensional system of spins S = 1 / 2 on a honeycomb lattice interacting through a strongly anisotropic exchange interaction. Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model at the edges of the chain! In this flux sector, the Majorana fermion system has linear dispersions and shows power-law behavior in In recent years, the Kitaev honeycomb model has been the focus of much attention, as it is a solvable example of a quantum spin liquid that hosts exotic Majorana excitations. Kitaevs toy-models key ingredient is spinless nearest neighbour p-wave superconductivity which has not been realised in real materials. In 2010, however, two seminal papers show how to map the Kitaev p-wave quantum wire to an s-wave quantum wire in the presence of strong spin orbit coupling and a magnetic eld. Our circuits can be built using local ingredients in Majorana devices, namely, 3).We mainly focus on the The latter should host propagating Majorana fermions, whose signatures could be measured, according to the work of Knolle et al. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. For hole, it is k / 2 and for electron it is k / 2. Honeycomb Lattice Model The honeycomb lattice is threefold coordinated. Kitaev model can be exactly solved by decomposing each spin into 4 Majorana fermions. 1) Kitaev honeycomb model as Majorana fermions in Z2 gauge field (0 or flux) characterized by integer Chern number, modulo 16 2) Triangular vortex lattices : Chern = 0,1,,6,8 but not 7 3) Effective models in the dilute vortex limit In recent years, the Kitaev honeycomb model has been the focus of much attention, as it is a solvable example of a quantum spin liquid that hosts exotic Majorana excitations. k = ( c k c k ) The energy spectrum for particle-hole symmetry is symmetric about zero. of \Kitaev" quantum spin liquids.
We use the exact solution to demonstrate several features of the Kitaev QSL both Technically, we adopt a Majorana mean-eld approach that was rst applied by Nasu et al. We also discuss the nite temperature behavior. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. 2. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. This is an analytically tractable spin model that gives rise to quasiparticles with Abelian as well as non-Abelian statistics. Now, we will calculate the differential conductance of the NS junction by means of the recursive Green's function method , .The model of NS junction is shown in Fig. The pure Kitaev model is solved by representing the half spin on each site with four Majorana fermions , , , as [ 16] or a JordanWigner transformation of half spins. The topological class of the system is determined by the The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model.
2009 , Kells et al. Review of Sachdev-Ye-Kitaev model Numerical studies of ETH in SYK model ETH in the Schwarzian sector of the SYK model ETH in the Conformal sector of the SYK model A few thoughts on the bulk duals Summary and conclusion!3.
We study a system of interacting spinless fermions in one dimension which, in the absence of interactions, reduces to the Kitaev chain [A. Yu Kitaev, Phys.-Usp.
Kitaev Materials Laboratory Sighting of Majorana Fermions ?? Our results indicate that the fractionalization is experimentally observable in the specific heat, spin correlations, and transport properties. (Majorana, 1937) and become increasingly important in the analysis of solid state phenomena (Wilczek, 2009). Title: Thermal Fractionalization of Quantum Spins in a Kitaev Model: Coherent Transport of Majorana Fermions and $T$-linear Specific Heat
In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev m Clearly by setting = 0 you have cut the first and last Majorana mode from the rest of the chain. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. The interest in studying Majorana end modes (MMs) was spurred on by a proposal by Kitaev and Preskill7 outlining a way to realise quantum com- A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. At this point you might however object: Unpaired Majoranas appear because you chose one particular, and perhaps even unreachable, set of parameters! 2010) Reflecting both of this peculiarity of the Majorana Special case: Topological regime: Majorana fermions (e= =0!!!) $\begingroup$ @RoderickLee My feeling is that your confusion is somehow related to what it means for "the Majorana mode to be localized". Employing an SO(6) Majorana representation of We discovered highly unusual Alexei Kitaev (Microsoft Research) Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point.
Majorana edge magnetization in the Kitaev honeycomb model.
Our circuits can be built using local ingredients in Majorana devices, namely
The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. So once again, here is our skeleton, the Kitaev model Hamiltonian written in momentum space: H K i t a e v = ( 2 t cos. . However, the Majorana representation enlarges the physical Hilbert space of the half spin by twice.
The ground state is topo-logically of our model indicate that the bulk-edge correspondence can be extended to a single-band system with hidden topological feature. H Katsura, Majorana excitations in Kitaev spin liquids, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-INV-3A-02 (2018). Intending to emulate Kitaev chain, we build a tight-binding model of a 3-site quantum dot chain. Kitaev chain is a theoretical model of a one-dimensional topological superconductor with Majorana zero modes at the two ends of the chain. the pure Kitaev model, how to solve it, and what types of Z2 QSLs can occur. Introduction Kitaev model Non-abelian statistics Hosting and detecting Majorana particles Conclusion and future directions Pairs of Majorana fermions can be combined into ordinary fermions c = 1 2 (1 + i 2);cy= 1 2 (1 i 2); form a single 2 level system If the Majorana fermions are spatially separated, implies fermion state is delocalised, The prototypical toy model possessing Majorana zero modes is the Kitaev chain with open boundaries [12], a one-dimensional tight-binding model for spinless fermions in the presence of p-wave superconducting pairing. At large magnetic elds the system enters a spin-polarized paramagnetic phase. To order 1/N, moments are given by those of the weight function of the Q-Hermite polynomials.Representing Wick contractions by rooted chord a model of N Majorana fermions This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (SYK) model, and obtain order 1/N 2 corrections for all moments, where N is the total number of Majorana fermions. 1Kitaev model Majorana Operators Exact Solution Spectrum and phase diagram 2Gapped Abelian Phase 3Magnetic Field: NonAbelian Phase Spectral Gap Edge Modes Non-Abelian Anyons Michele Burrello Kitaev Model Anyons and topological quantum computation Quantum phenomena do not occur in a Hilbert space. We also show that the flux fluctuations tend to open an energy gap in the Majorana spectrum near the gapless-gapped phase boundary. The Majorana bound states are located at domain walls between wire regions with a topological and normal superconducting phase - and this phase can be tuned The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z 2 gauge fields. 2. eld. 2.2 Quantum circuit constructions To illustrate how to construct the quantum circuit that prepares the ground states of Kitaev-inspired models, we focus on the original Kitaev model con-structed on the honeycomb lattice with 8 sites (result-ing in 2 2 unit cells) as shown in Fig.1(a). 1) Kitaev honeycomb model as Majorana fermions in Z2 gauge field (0 or flux) characterized by integer Chern number, modulo 16 2) Triangular vortex lattices : Chern = 0,1,,6,8 but not 7 3) Effective models in the dilute vortex limit function and conductance of a Kitaev model. In Section 3, we briey explain the symmetry properties of materials and how Kitaev interactions arise. The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. GENERAL INTRO In 1937 Ettore Majorana speculated that there could be a particle that is its own antiparticle. armadillo majorana nlohmann-json kitaev-model rashba-model Updated Mar 25, 2021; C++; Add a description, image, and links to the kitaev-model topic page so that developers can more easily learn about it. In the non-interacting case, a signal of topological order appears as zero-energy modes localized near the edges.
Majorana MF results for the [001] eld dependence of the magnetization Mz, the Majorana gap , and the magnetic susceptibility zz for (a) the FM Kitaev model and (b) the AFM one. honeycomb lattice square-octagon lattice (Kitaev 2006) (Yang et al. We rst study the present model from thedescription in terms of Majorana fermions. (ii) We investigate the Majorana bound states. The (localized) Majorana operator transforms you between different (degenerate) ground states. the fermionic operator squares to 1. It is the first result of its kind in nontrivial quantum spin models. Majorana fermions in Section II and compute the disorder averaged partition function for the SYK model with q= 2 and q= 4 interactions. Majorana Fermions ??
We propose an approach to detect the peculiarity of Majorana fermions at the edges of Kitaev magnets. tum computation. The aim will be to translate the Kitaev Chain Hamiltonian into a Matrix form to obtain energy spectrum and edge modes for an open chain. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting. At this point you might however object: Unpaired Majoranas appear because you chose one particular, and perhaps even unreachable, set of parameters! Clearly by setting = 0 you have cut the first and last Majorana mode from the rest of the chain. The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z 2 gauge field.
7,14 To this end, Kitaev, in a seminal paper, introduced a model of interacting spins on a honeycomb lat-tice which reduces to the problem of Majorana fermions coupled to a static Z 2 gauge eld. We study a Kitaev model on a square lattice, which describes topologically trivial superconductor when gap opens, while supports topological gapless phase when gap closes. Majorana states on TI edges 5. H Katsura, Majorana excitations in Kitaev spin liquids, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-INV-3A-02 (2018). Codes for Majorana zero modes identification in non-interacting systems. Majorana MF results for the [001] eld dependence of the magnetization Mz, the Majorana gap , and the magnetic susceptibility zz for (a) the FM Kitaev model and (b) the AFM one. Majroana and non-abelian statistics 7. In particular we focus on the models defined on the honeycomb, and square-octagon lattices. The red circles de-note the dierent, representative model parameter points that .
1. The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes.
(Color online) Kitaev model on the honeycomb lattice with xx coupling J1, yy coupling J2 and zz coupling J3. The magic stick rule still holds, but one Majorana species is free to hop in the presence of a static gauge eld. Bogoliubov de Gennes Theory 2. In contrast to previous studiesbased on Hermitian chains in the thermodynamic limit, we focus on the Kitaev model on a nite lattice system.This is motivated by the desire to get a clear physicalpicture of the edge mode through the investigation of asmall system. These results pave a new path to measurement of dynamical spinon or Majorana fermion spectroscopy of Kitaev and other spin-liquid materials. In the language of second quantization, this means that = y, i.e. In the year 1937, a new class of particles that are its own anti-particles were hypothesized by Ettore Majorana. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting. CM Seminar - Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model CM Seminar - Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model. k ) z + 2 y sin. Special case: What are Majorana fermions anyway? We show that the exact ground states can be obtained analytically even in the
The model exhibits two characteristic temperatures, ${T}_{L}$ and ${T}_{H}$, which correspond to energy Majorana bound states, Kitaev model 3. where. Majorana in wires 6. As is well known, a pair of Majorana edge modes is realized when a single complex fermion splits into real and imaginary parts which are, respectively, localized at the left and right edges of a sample magnet. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin c Majorana zero modes (MZMs) have attracted tremendous attention in condensed matter and materials physics communities due to the implications in topological quantum computation. By diagonalizing the Majorana Hamiltonian for the flux configuration, we find two distinct gapped quantum spin liquids. Kitaev used a simplied quantum wire model to show how Majorana modes might manifest as an emergent phenomena, which we will now discuss. Consider 1- dimensional tight binding chain with spinless fermions and p-orbital hopping. On the theoretical side, Kitaev introduced a celebrated model based upon the spinless p-wave superconductor in one dimension Kitaev , which is currently named as the Kitaev model, one of the simplest but highly nontrivial model to unveil MZM.
A Majorana fermion is a particle that is its own an-tiparticle.
It is the first result of its kind in non-trivial quantum spin models. In this chapter, we consider Kitaev's honeycomb lattice model (Kitaev, 2006). Majorana Fermions and Topological Quantum Computation 1. 2007 , Baskaran et al. This plays the same role as the NNN hopping inHaldane model [11] and opens a topological gap at theDirac cone of Majorana fermions. k = 2 J 1 + g 2 2 g cos ( k a) If we do Bogoliubov transformation of Fourier transformed Hamiltonian, we get.
Magnetic fields can give rise to a plethora of phenomena in Kitaev spin systems, such as the formation of non-trivial spin liquids in two and three spatial dimensions. Majorana edge states in the Kitaev model 4. The magnetic insulator -RuCl 3 is thought to realize a proximate KQSL. We calculate the resonant inelastic x-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model The Kitaev Model on the Honeycomb Lattice H = X
One-dimensional (1D) dimerized Kitaev chain is a prototype model for MZMs, but its realization remains a challenge in material systems. lar kind of zero energy boundary mode called Majorana modes. Where. We will obtain these Majorana zero modes at the edges of an open chain.
Topological superconductor 4. 4B, solid and dashed orange arrows). Gapped: topological. The Kitaev model is ananisotropic spin- model with Ising interactions S xr S xr , S yr S yr and S zr S zr assigned to the three bonds in the hon-eycomb lattice. The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The BdG Hamiltonian acts on a set of basis states | n | , with = 1 corresponding to electron and hole states respectively. It has particle-hole symmetry, P H BdG P 1 = H BdG with P = x K. The fact that the Kitaev model can have unpaired Majorana zero modes is certainly interesting.
Authors: Petrova, Olga; Mellado, Paula; Tchernyshyov, Oleg Publication Date: 2014-10-01 NSF-PAR ID: 10009670 Journal Name: Physical Review B Volume: 90 Issue: 13 ISSN: 1098-0121 Publisher: American Physical Society The results of this thesis indicate that these Majorana acquire a relevant physical meaning. We used neutron scattering on single crystals of -RuCl 3 to reconstruct dynamical correlations in energy-momentum space.
See also the related analysis of Ref. Periodic Table of topological insulators and superconductors 5. Second, there is a gapless phase of (e ectively) free Majorana fermions. It is found that the system has two different topological classes, the class BDI characterized by the Z index and the class D characterized by the Z 2 index. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z 2 gauge fields. They occur in a laboratory Map into a chain of Majorana modes using: Majorana states in the Kitaev model. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. The key insight Kitaev provided is that this can be solved by \splitting" the fermionic site into two Majorana modes, which can then be spatially separated. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. which is not present in the ferromagnetically coupled model. 2020-11-26T15:00:00. We study how stable the Majorana-mediated spin transport in a quantum spin Kitaev model is against thermal fluctuations.
(a) Kitaevs model describes a two-dimensional system of spins S = 1 / 2 on a honeycomb lattice interacting through a strongly anisotropic exchange interaction. Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model at the edges of the chain! In this flux sector, the Majorana fermion system has linear dispersions and shows power-law behavior in In recent years, the Kitaev honeycomb model has been the focus of much attention, as it is a solvable example of a quantum spin liquid that hosts exotic Majorana excitations. Kitaevs toy-models key ingredient is spinless nearest neighbour p-wave superconductivity which has not been realised in real materials. In 2010, however, two seminal papers show how to map the Kitaev p-wave quantum wire to an s-wave quantum wire in the presence of strong spin orbit coupling and a magnetic eld. Our circuits can be built using local ingredients in Majorana devices, namely, 3).We mainly focus on the The latter should host propagating Majorana fermions, whose signatures could be measured, according to the work of Knolle et al. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. For hole, it is k / 2 and for electron it is k / 2. Honeycomb Lattice Model The honeycomb lattice is threefold coordinated. Kitaev model can be exactly solved by decomposing each spin into 4 Majorana fermions. 1) Kitaev honeycomb model as Majorana fermions in Z2 gauge field (0 or flux) characterized by integer Chern number, modulo 16 2) Triangular vortex lattices : Chern = 0,1,,6,8 but not 7 3) Effective models in the dilute vortex limit In recent years, the Kitaev honeycomb model has been the focus of much attention, as it is a solvable example of a quantum spin liquid that hosts exotic Majorana excitations. k = ( c k c k ) The energy spectrum for particle-hole symmetry is symmetric about zero. of \Kitaev" quantum spin liquids.
We use the exact solution to demonstrate several features of the Kitaev QSL both Technically, we adopt a Majorana mean-eld approach that was rst applied by Nasu et al. We also discuss the nite temperature behavior. Through the representation of the Kitaev model in terms of quasi-particles an elegant description of a complex, strongly correlated system is possible. 2. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. This is an analytically tractable spin model that gives rise to quasiparticles with Abelian as well as non-Abelian statistics. Now, we will calculate the differential conductance of the NS junction by means of the recursive Green's function method , .The model of NS junction is shown in Fig. The pure Kitaev model is solved by representing the half spin on each site with four Majorana fermions , , , as [ 16] or a JordanWigner transformation of half spins. The topological class of the system is determined by the The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model.
2009 , Kells et al. Review of Sachdev-Ye-Kitaev model Numerical studies of ETH in SYK model ETH in the Schwarzian sector of the SYK model ETH in the Conformal sector of the SYK model A few thoughts on the bulk duals Summary and conclusion!3.
We study a system of interacting spinless fermions in one dimension which, in the absence of interactions, reduces to the Kitaev chain [A. Yu Kitaev, Phys.-Usp.
Kitaev Materials Laboratory Sighting of Majorana Fermions ?? Our results indicate that the fractionalization is experimentally observable in the specific heat, spin correlations, and transport properties. (Majorana, 1937) and become increasingly important in the analysis of solid state phenomena (Wilczek, 2009). Title: Thermal Fractionalization of Quantum Spins in a Kitaev Model: Coherent Transport of Majorana Fermions and $T$-linear Specific Heat