In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean-field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with free open-boundary conditions.
In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean-field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with free open-boundary conditions.
We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin S, which in the case of S=1/2 interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number N of spins, a semiclassical energy manifold is derived in the large-S limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multiconfigurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes---each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in 1/2S enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical $(S\ensuremath{\gg}1)$ limit, and quantum phase transitions, which are observed in the thermodynamic $(N\ensuremath{\rightarrow}\ensuremath{\infty})$ limit.
The Su--Schrieffer--Heeger (SSH) model is one of the simplest topological lattice models and is a promising candidate for quantum simulations of topological systems. In this study we investigate an interacting SSH model with nearest-neighbor interactions using mean field theory and an exact diagonalization method after the Jordan-Wigner transformation. We obtain a rich phase diagram with six different phases. Majorana bound states are found and confirmed by analyzing wave functions and Majorana number. In addition, we propose to use superconducting devices to construct a one-dimensional quantum circuit, where Cooper pair boxes and Josephson junctions are alternately connected in series, to theoretically simulate the interacting SSH model. This approach also provides us a toolkit to simulate correlated topological systems.
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.
We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V/t2 versus t1/t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and nontrivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a noninteracting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of edge states of topological origin in the equivalent chain can be readily identified, as well as their correspondence to the original two-hole states. Of these states only some, identified by us, are protected and, therefore, truly topological. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).
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.