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

Abstract

The effect of spatially modulated interaction on quantum phase transition in one-dimensional interacting spinless fermion system is theoretically investigated by exact diagonalization and density matrix renormalization group method. Our calculations show that the periodically modulated interaction can drive the spinless fermion system into topological charge density wave state. The topological state is encoded by quasiparticle end states and the fractional quantized e/2 end charges, and characterized by Berry phase and Chern number. The quasiparticle energy spectra as a function of modulated interaction period appears a stunning fractal-like structure. For the quasi-periodic case, the topological phase transition can also occur. In a word, the spatially modulated interaction can be a new simple and elegant avenue towards realizing to interacting topological phases.

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

“…An interesting and important ongoing research is characterizing the interplay between the aperiodicity, manybody correlations and topology in quantum systems or between aperiodicity, non-linear effects and topology in classical systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. Quantum spin chains have been successfully used in the past to shed some light on this question, especially because they can be simulated with modest computational resources.…”

Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis

“…An interesting and important ongoing research is characterizing the interplay between the aperiodicity, manybody correlations and topology in quantum systems or between aperiodicity, non-linear effects and topology in classical systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70]. Quantum spin chains have been successfully used in the past to shed some light on this question, especially because they can be simulated with modest computational resources.…”

Mapping Chern numbers in quasi-periodic interacting spin chains

“…In these settings, most of the difficult questions such as the robustness of the topological invariants [51][52][53][54][55][56][57][58][59][60] or the bulk-boundary principles [61][62][63][64] in arbitrary dimensions and for arbitrary patterns of atomic configurations are now well understood and experimentally under control. A vigorous research is currently underway on the interplay between the aperiodicity, many-body correlations and topology in quantum systems or between aperiodicity, non-linear effects and topology in classical systems [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80]. At the mathematically rigorous level, there have been exciting new developments [81][82][83][84][85][86] on the formal definition and quantization of the linear transport coefficients.…”