Quantum phases in the interacting generalized Su-Schrieffer-Heeger model

TL;DR

This paper explores the rich quantum phase diagram of an interacting generalized Su-Schrieffer-Heeger model, revealing topological, symmetry-breaking, charge-density-wave, and gapless phases influenced by interactions.

Contribution

It extends the understanding of topological phases in the SSH model by including interactions and additional hopping terms, identifying new phases and phase transitions.

Findings

Noninteracting model hosts trivial and SPT phases with distinct degeneracies.

Interactions lead to new topological and symmetry-breaking phases.

Intermediate interactions produce Luttinger liquid, paired Luttinger liquid, and gSPT phases.

Abstract

We investigate the quantum phases of a half-filled generalized interacting Su-Schrieffer-Heeger model with intracell, nearest-neighbor, and next-nearest-neighbor intercell hoppings, together with an on-site inter-sublattice interaction. In the noninteracting limit, the model hosts one topologically trivial phase and two symmetry-protected topological (SPT) phases, distinguished under periodic boundary conditions by different winding numbers and under open boundary conditions by two-fold and four-fold entanglement-spectrum degeneracies, respectively. When interactions are introduced, these free-fermion SPT phases evolve into distinct interacting topological phases that retain characteristic signatures such as entanglement-spectrum degeneracy structures, boundary modes, and nonzero string order parameters. For strong repulsive interactions, a symmetry-breaking phase with unequal but spatially uniform sublattice densities appears between the trivial and topological regimes. For strong attractive interactions, period-2 and period-4 charge-density-wave phases emerge from particle clustering. At intermediate attractive interactions, the competition between interaction-induced localization and hopping-induced delocalization gives rise to a Luttinger liquid phase, a paired Luttinger liquid phase, and a gapless symmetry-protected topological (gSPT) phase. The gSPT phase is characterized by a gapless charge mode together with symmetry-protected current-carrying edge states. We further characterize the gapless phases and the associated quantum phase transitions through central charges and critical exponents.