Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model

Abstract

We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupationdependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and density-matrix renormalization-group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides new insights into the topological phase transitions. What's more, we give an explanation of the statistically induced topological phase transition. The topological anyon-Mott phases can also appear in a variety of superlattice anyon-Hubbard models.

Topological end states in a one-dimensional spatially modulated interaction spinless fermion model

“…The K-theory and group theory have been used to classify topological insulators, semimetal, and superconductors under the internal (nonspatial) symmetry and space group [44][45][46][47]. On the other hand, the superlattice potential [20,21,23,25,26,28,[48][49][50][51], periodically modulated hopping [22,24,27,52,53], and periodically driven field [6,7,34,35,[54][55][56] have been the simple and elegant avenues towards realizing fascinating topological phases. The Su-Schrieffer-Heeger (SSH) model [52], diagonal and off-diagonal Aubry-Andre or Harper (AAH) model [48,53], and topological Floquet systems [54][55][56] with their counterpart interaction systems are object of considerable theoretical and experimental interest.…”

Statistically related many-body localization in the one-dimensional anyon Hubbard model

“…These proposals are based on the fractional Jordan-Wigner transformation by mapping anyons to bosons with a density-dependent tunneling parameter. Some exotic properties of one-dimensional anyons [29][30][31][32][33] closely related to the statistical angle have been revealed, such as the statistically induced ground state phase transition 26,34,35 , the asymmetry of two-body correlations in the momentum space 36 , and the spatially asymmetric particle transport of interacting anyons 37 . However, to the best of our knowledge, the MBL properties of anyons in disordered systems have not been studied in literature.…”

Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains

“…In this paper, we investigate the above issues in context of the paradigmatic Su-Schrieffer-Heeger (SSH) model for polyacetylene [10,11] that stabilises symmetry protected topological boundary modes. We examine an interesting tuning parameter that is of relevance in context of recent experimental [43,44] and theoretical [45][46][47] developments -the generalised algebra of the interacting fermions -and study it in context of two coupled SSH chains as shown in Fig. 1.…”

“…(1)), allows the degrees of freedom to smoothly transform from being fermionic to (hard core) bosonic and vice-versa in one spatial dimension. Such degrees of freedom, referred as pseudofermions [47], are generalizations of "anyons" in one dimension [45,. Quite remarkably, this anyonic physics has been recently realized experimentally in a cold atomic setting [44].…”