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arXiv:2201.10884 · Journal of Physics Condensed Matter

Floquet topological phases with high Chern numbers in a periodically driven extended Su–Schrieffer–Heeger model

Aayushi Agrawal, Jayendra N. Bandyopadhyay

Published May 11, 2022• 19 citations
arXivHTMLPDF

Abstract

| > 1 are observed in this study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) model with a cyclic parameter. Besides the standard intra-dimer and the nearest-neighbor inter-dimer hopping of the SSH model, an additional next-nearest-neighbor hopping is considered in the E-SSH model. The cyclic parameter, which plays the role of a synthetic dimension, is invoked as a modulation of the hopping strengths. A rigorous analysis of different phase diagrams has shown multiple Floquet topological phase transitions among the high Chern number phases. These phase transitions can be controlled by the strength and frequency of the periodic driving. Instead of applying perturbation theory, the whole analysis is done by Floquet replica technique. This gives a freedom to study high as well as low-frequency effects on the system by considering less or more number of photon sectors. This system can be experimentally realized through a pulse sequence scheme in the optical lattice setup.

DOI
10.1088/1361-648x/ac6eac

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| > 1 are observed in this study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) model with a cyclic parameter. Besides the standard intra-dimer and the nearest-neighbor inter-dimer hopping of the SSH model, an additional next-nearest-neighbor hopping is considered in the E-SSH model. The cyclic parameter, which plays the role of a synthetic dimension, is invoked as a modulation of the hopping strengths. A rigorous analysis of different phase diagrams has shown multiple Floquet topological phase transitions among the high Chern number phases. These phase transitions can be controlled by the strength and frequency of the periodic driving. Instead of applying perturbation theory, the whole analysis is done by Floquet replica technique. This gives a freedom to study high as well as low-frequency effects on the system by considering less or more number of photon sectors. This system can be experimentally realized through a pulse sequence scheme in the optical lattice setup.
Recently, Floquet systems have attracted a great deal of interest as they offer the unprecedented ability to engineer topological states through the tuning of an external time-periodic drive. Consequentially, seeking new driving protocols that allow for more exotic topological phases and transitions becomes imperative for the Floquet engineer. In this paper, we study the Su-Schrieffer-Heeger model driven by two time-dependent periodic sources with commensurate frequencies and an amplitude modulation. Imposing more than one driving frequency allows us to realize even more exotic topological phases resulting from new couplings appearing in the Fourier space representation. Moreover, we find an experimentally practical method for sweeping the system through a topological phase transition by varying the amplitude mixture of the commensurate sources. We employ the local Chern marker, a real-space representation of the Chern number, to simulate topological phase diagrams of the two-drive Floquet Hamiltonian in a variety of driving cases.
The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work, we investigate the topological phase transition of the one-dimensional Floquet Su-Schrieffer-Heeger model using entanglement entropy, and construct the phase diagram based on entanglement entropy. The entanglement entropy exhibits pronounced peaks and follows the logarithmic scaling law at the phase transition points, from which we extract the central charge c=1c=1c=1. We further investigate the entanglement spectrum to accurately distinguish the different topological phases. In addition, the coupling between zero and πππ modes leads to characteristic splittings in the entanglement spectrum, signaling their hybridization under periodic driving. These results remain robust in non-Hermitian regimes and in the presence of next-nearest-neighbor hopping, demonstrating the reliability and universality of entanglement entropy as a diagnostic for topological phase transitions.
Abstract We propose a scheme to investigate the topological phase transition in the generalized one-dimensional Su–Schrieffer–Heeger (SSH) model based on a circuit quantum electrodynamics (QED) lattice with frequency modulation. We find that, if we keep the resonant counter rotating wave terms to map the p -wave superconducting pairing terms in the topological superconductor by dint of frequency modulation, the circuit QED lattice can be equivalent to the SSH model with p -wave superconducting pairing terms. The numerical results show that the existence of the superconducting pairing terms cannot close the energy gap of the SSH model within the feasible range of parameters, which means that the superconducting pairing terms cannot induce the topological phase transition. To induce the topological phase transition, we add the next-nearest-neighboring (NNN) interaction into the circuit QED-based SSH model simultaneously. We find that, for a given superconducting pairing strength, the appropriate selection of the NNN interaction can induce closing of the energy gap. It indicates that a new topological phase transition between the topologically nontrivial SSH phase and the topologically trivial SSH phase occurs in the SSH model. Our scheme provides a means to explore the topological SSH phase transition based on a circuit QED lattice with frequency modulation.
Despite extensive studies on the one-dimensional Su-Schrieffer-Heeger-Hubbard (SSHH) model, the variant incorporating second-nearest neighbor hopping remains largely unexplored. Here, the topological classification of the extended SSH model is analyzed within the framework of the BDI symmetry class, using the winding number as the corresponding topological invariant. We investigate the ground-state properties of this extended SSHH model using the constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) method. We show that this model exhibits rich topological phases, characterized by robust edge states against interaction. We quantify the properties of these edge states by analyzing spin correlation and second-order Rényi entanglement entropy. The system exhibits long-range spin correlation and near-zero Rényi entropy at half-filling. Besides, there is an anti-ferromagnetic order at quarter-filling. Interestingly, an external magnetic field disrupts this anti-ferromagnetic order, restoring long-range spin correlation and near-zero Rényi entropy. Furthermore, our work provides a paradigm for studying topological properties in large interacting systems via the CP-AFQMC algorithm.
Topological phases at quantum criticality have attracted much attention recently. Here we numerically study the interaction-induced phase transitions at around the topological quantum critical points of an extended Su-Schrieffer-Heeger (SSH) chain with next-nearest-neighbor hopping. This extended SSH model shows topological phase transitions between the topologically trivial and nontrivial critical phases when interaction is absent. So long as the interaction terms are turned on, the topologically nontrivial (trivial) critical phases are driven into topologically nontrivial (trivial) insulator phases with finite energy gaps. Particularly, we find the trivial insulator phase is further driven to the nontrivial insulator phase, through interaction-induced topological phase transition, although interaction generally is harmful to nontrivial topology. The stability of the trivial insulator phase against interaction tends to vanish at the multicritical point that separates the trivial and nontrivial critical phases. Our work provides a concrete example for manifesting the impact of interaction on topological quantum criticality.
Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion theories. We make this suggestion concrete by mapping the spectrum of a noninteracting (1+1)D Floquet insulator for certain drive parameters onto that of a discrete-time lattice fermion theory with a time-independent Hamiltonian. The resulting Hamiltonian is distinct from the Floquet Hamiltonian that generates stroboscopic dynamics. It can take the form of a discrete-time Su-Schrieffer-Heeger model with half the number of spatial sites of the original model, or of a (1+1)D Wilson-Dirac theory with one quarter of the spatial sites.