Majorana edge modes in the Kitaev model

Thakurathi, Manisha; Sengupta, K.; Sen, Diptiman

doi:10.1103/physrevb.89.235434

Cited by 78 publications

(75 citation statements)

References 105 publications

(77 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our approach is to start from Kitaev's honeycomb model 48 and make the exchange couplings time-dependent (as in Refs. [49][50][51][52]. The model can be solved by a mapping to free fermions coupled to a static Z 2 gauge field.…”

Section: Introductionmentioning

confidence: 99%

Topology and localization of a periodically driven Kitaev model

et al. 2019

View full text Add to dashboard Cite

Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be manybody localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form "vortex bands", which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.

show abstract

Section: Introductionmentioning

confidence: 99%

Topology and localization of a periodically driven Kitaev model

et al. 2019

View full text Add to dashboard Cite

show abstract

“…For example, new symmetry breaking phases with dynamical order parameters may arise [25,26], including the possibility of breaking of discrete time-translation invariance without any accompanying static symmetry breakinga (discrete) Floquet time-crystal [27][28][29][30], which was recently observed experimentally [31]. An additional possibility is that periodic driving enables fundamentally new topological phases [32][33][34][35], or symmetry protected topological phases of matter [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Dynamically enriched topological orders in driven two-dimensional systems

Potter

Morimoto

2017

Phys. Rev. B

View full text Add to dashboard Cite

Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry protected topological phases (FSPTs), and Floquet enriched topological orders (FETs). By constructing solvable lattice models for a complete set of 2D bosonic FSPT phases, we show that bosonic FSPTs can be understood as topological pumps which deposit loops of 1D SPT chains onto the boundary during each driving cycle, which protects a non-trivial edge state by dynamically tuning the edge to a self-dual point poised between the 1D SPT and trivial phases of the edge. By coupling these FSPT models to dynamical gauge fields, we construct solvable models of FET orders in which anyon excitations are dynamically transmuted into topologically distinct anyon types during each driving period. These bosonic FSPT and gauged FSPT models are classified by group cohomology methods. In addition, we also construct examples of "beyond cohomology" FET orders, which can be viewed as topological pumps of 1D topological chains formed of emergent anyonic quasi-particles. CONTENTS

show abstract

“…Such Floquet engineering has led to various applications in quantum optical contexts, such as the engineering of artificial gauge fields [1], as well as in solid-state contexts, e.g., to produce new Floquet-Bloch band structures [2,3] or understand nonlinear optical phenomena [4]. In addition to providing new tools to engineer phases that could arise as ground states of a different static Hamiltonian, periodic driving also opens up the possibility of engineering entirely new phases with no equilibrium analog [5][6][7][8][9][10][11][12][13][14]. In the context of noninteracting particles, various examples of new topological phases that arise from driving are known, including dynamical Floquet analogs of Majorana fermions in 1D [6] and phases with chiral edge modes but vanishing Chern number in 2D [5,7].…”

Section: Introductionmentioning

confidence: 99%

Classification of Interacting Topological Floquet Phases in One Dimension

2016

View full text Add to dashboard Cite

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper, we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that 1D bosonic and fermionic FSPT phases are classified by the same criteria as equilibrium phases but with an enlarged symmetry groupG, which now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group H 2 (G; Uð1Þ). We construct explicit lattice models for a variety of systems and then formalize the classification to demonstrate the completeness of this construction. We advocate that a prototypical Z 2 bosonic FSPT may be realized by very simple Hamiltonians of the type currently available in existing cold atoms and trapped ion experiments.

show abstract

Majorana edge modes in the Kitaev model

Cited by 78 publications

References 105 publications

Topology and localization of a periodically driven Kitaev model

Topology and localization of a periodically driven Kitaev model

Dynamically enriched topological orders in driven two-dimensional systems

Classification of Interacting Topological Floquet Phases in One Dimension

Contact Info

Product

Resources

About