We investigate the entanglement spectrum of the ground state of the Su-Schrieffer-Heeger-Hubbard model. The topological phases of the model can be identified by degeneracy of the largest eigenvalues of entanglement spectrum. The study of the periodic boundary condition is enough to obtain the phase diagram of the model, without the consideration of the open boundary condition case. By analyzing the states corresponding to the degenerate entanglement spectrum and showing the related edge states in real space, physical interpretation about the relation between bulk-edge correspondence and the entanglement spectrum is presented. The method of the entanglement spectrum can be applicable in studying other topological phases of matter.
We investigate the entanglement spectrum of the ground state of the Su-Schrieffer-Heeger-Hubbard model. The topological phases of the model can be identified by degeneracy of the largest eigenvalues of entanglement spectrum. The study of the periodic boundary condition is enough to obtain the phase diagram of the model, without the consideration of the open boundary condition case. By analyzing the states corresponding to the degenerate entanglement spectrum and showing the related edge states in real space, physical interpretation about the relation between bulk-edge correspondence and the entanglement spectrum is presented. The method of the entanglement spectrum can be applicable in studying other topological phases of matter.
Dramatically different from the Hermitian systems, the conventional bulk-boundary correspondence (BBC) is broken in the non-Hermitian systems. In this paper, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of the bulk-boundary correspondence, which eventually disappears at some critical value of interaction.
Recent studies of moiré physics have unveiled a wealth of opportunities for significantly advancing the field of quantum phase transitions. However, properties of reentrant phase transitions driven by moiré strength are poorly understood. Here, we investigate the reentrant sequence of phase transitions and the invariant of universality class in moiré-modulated extended Su-Schrieffer-Heeger (SSH) model. For the simplified case with intercell hopping w=0, we analytically derive renormalization relations of Hamiltonian parameters to explain the reentrant phenomenon. For the general case, numerical phase boundaries are calculated in the thermodynamic limit. The bulk boundary correspondence between zero-energy edge modes and entanglement spectrum is revealed from the degeneracy of both quantities. We also address the correspondence between the central charge obtained from entanglement entropy and the change in winding number during the phase transition. Our results shed light on the understanding of universal characteristics and bulk-boundary correspondence for moiré induced reentrant phase transitions in 1D condensed-matter systems.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
We investigate quantum correlations and entanglement in a non-Hermitian quantum system modeled by a 2D stacked Su–Schrieffer–Heeger (SSH) lattice incorporating nonreciprocal hopping amplitudes and balanced on-site gain and loss. Focusing on the interplay between non-Hermiticity, topology, and open-boundary conditions, we analyze how these factors shape bipartite entanglement properties, characterized through the entanglement spectrum and entanglement negativity ( E N ). By examining the complex energy spectrum under open boundary conditions, we identify critical points associated with the closing of complex energy gaps, which significantly influence entanglement structure and signal topological phase transitions. Our findings reveal that boundary-localized non-Bloch modes and nonreciprocal couplings can induce highly tunable and unconventional entanglement features, absent under periodic boundary conditions. These results highlight the breakdown of conventional bulk-boundary correspondence and underscore the utility of entanglement measures in diagnosing non-Hermitian topological phases. Beyond advancing the fundamental understanding of quantum correlations in open systems, our study suggests potential pathways to engineer quantum devices and topological materials where gain, loss, and nonreciprocity are intrinsic elements.
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.
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.