Crossdimensional universality classes in static and periodically driven Kitaev models

Abstract

The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.

Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

“…[89]. We will show its importance in the band topology of pH phases by generalizing some of the results previously presented in the Hermitian cases [50,[90][91][92][93][94][95][96][97][98][99][100][101]. Importantly, we also show that the NH skin effects will appear after breaking the pseudo-Hermiticity in the original pH models [102].…”

A supervised learning algorithm for interacting topological insulators based on local curvature

“…To summarize, the phase diagram correctly captures all phases and phase boundaries, and moreover indicates the appearance of a multicritical point as a function of coupling u around M = −2.0, indicating that electron-phonon interaction can also serve as a mechanism to induce multicriticality. Thus, many-body interactions are added to the list of several recently uncovered mechanisms that can trigger topological multicriticality, including periodic driving or quantum walk protocols [17][18][19]58], long range hopping or pairing [12,13,59], spin-orbit coupling [11,60], topological insulator/topological superconductor hybridization [61], as well as more complicated mechanisms in the spin liquid [62] and toric code models [63]. We close this section by making a comparison between the CRG [8-15, 17, 18] and the ML scheme proposed here.…”

“…These aspects include the notion of critical exponents, scaling laws, universality classes, and correlation functions. These notions form the basis of the curvature renormalization group (CRG) method which can capture the TPTs solely based on the renormalization of the curvature function near the HSP [8], regardless of whether the system is noninteracting [9][10][11][12][13] or interacting [14,15] or periodically driven [16][17][18][19].…”

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

“…Recent advances have revealed the central role played by the Fubini-Study metric [1] in various fields of quantum sciences [2], with a direct impact on quantum technologies [3,4] and many-body quantum physics [2,5]. In condensed matter, the quantum metric generally defines a notion of distance over momentum space, and it was shown to provide essential geometric contributions to various phenomena, including exotic superconductivity [6][7][8] and superfluidity [9], orbital magnetism [10,11], the stability of fractional quantum Hall states [12][13][14][15][16][17], semiclassical wavepacket dynamics [18,19], topological phase transitions [20], and lightmatter coupling in flat-band systems [21]. Besides, the quantum metric plays a central role in the construction of maximally-localized Wannier functions in crystals [22,23], and it provides practical signatures for exotic momentum-space monopoles [24,25] and entanglement in topological superconductors [26,27].…”