In this work, we investigate the electronic, topological, and transport properties of a Creutz-Su-Schrieffer-Heeger (CSSH) ladder. Using a tight-binding model within the Green's function formalism, we calculate the energy spectrum, local density of states (LDOS), and electronic transmission. We first determine the energy spectrum of the CSSH ladder and analyze the different topological phases present in the system, identifying one trivial phase and three distinct nontrivial regions. We then study electronic transport and show that the transmission reproduces the different topological phases through characteristic transport signatures. Finally, we derive the conditions for the emergence of non-topological flat bands and demonstrate that these bands also provide the necessary conditions for the formation of bound states in the continuum (BICs). Our results establish a direct connection between the topological properties, flat-band formation, and electronic transport in the CSSH ladder.
In this work, we investigate the electronic, topological, and transport properties of a Creutz-Su-Schrieffer-Heeger (CSSH) ladder. Using a tight-binding model within the Green's function formalism, we calculate the energy spectrum, local density of states (LDOS), and electronic transmission. We first determine the energy spectrum of the CSSH ladder and analyze the different topological phases present in the system, identifying one trivial phase and three distinct nontrivial regions. We then study electronic transport and show that the transmission reproduces the different topological phases through characteristic transport signatures. Finally, we derive the conditions for the emergence of non-topological flat bands and demonstrate that these bands also provide the necessary conditions for the formation of bound states in the continuum (BICs). Our results establish a direct connection between the topological properties, flat-band formation, and electronic transport in the CSSH ladder.
The topological properties of the Su-Schrieffer-Heeger (SSH) model in the presence of nearest-neighbor interaction are investigated by means of a topological marker, generalized from a noninteracting one by utilizing the single-particle Green's function of the many-body ground state. We find that despite the marker not being perfectly quantized in the presence of interactions, it always remains finite in the topologically nontrivial phase while converging to zero in the trivial phase when approaching the thermodynamic limit, and hence correctly judges the topological phases in the presence of interactions. The marker also correctly captures the interaction-driven, second-order phase transitions between a topological phase and a Landau-ordered phase, which is a charge-density wave order in our model with a local-order parameter, as confirmed by the calculation of entanglement entropy and the many-body Zak phase. Our paper thus points to the possibility of generalizing topological markers to interacting systems through Green's function, which may be feasible for topological insulators in any dimension and symmetry class.
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.
Abstract The Su–Schrieffer–Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer trans -polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically protected, dispersionless boundary states. Here, using 87 Rb atoms in a momentum-space lattice, we realize fully tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation.
In strictly one-dimensional lattices, free fermions and hard-core bosons exhibit equivalent physical properties in many-particle systems. However, this statistical equivalence generally breaks down upon moving to higher dimensions. Our work investigates the significant effects of this difference on the topological phase transition in a minimal system lying away from one dimension: the two-leg Su-Schrieffer-Heeger (SSH) ladder. Starting in the limit of two decoupled SSH chains having opposite hopping dimerization patterns (staggered dimerization), we demonstrate that introducing inter-leg coupling drives a transition from a topological to a trivial phase for both spinless fermions and hard-core bosons. However, the topological to trivial phase transition boundary is strongly sensitive to the underlying particle statistics. We find that this intriguing effect favors a trivial phase sandwiched between the two topological phases with opposite characters for the case of hard-core bosons, resulting in a reentrant topological phase transition. In contrast, this reentrant phenomenon is absent for spinless fermions, with the topological phases being separated by a gapless line instead of an intervening trivial phase. This study demonstrates the interplay between particle statistics and topological features, revealing fundamentally different properties in an experimentally accessible set-up.
Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of the SSH model into four sublattices and thus is dubbed the SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from the topological insulator phase to the charge density wave (CDW) phase can be identified by analyzing the variations of the entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator, and CDW phases, respectively. In contrast to the interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial or nontrivial phases are shown to be continuous phase transitions. Finally, we also show the phase diagram of the interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.
This study explores the ground-state phase diagram and topological properties of the spinless 1D Su-Schrieffer-Heeger (SSH) model with nearest-neighbor (NN) interactions at quarter filling. We analyze key physical quantities such as the local electron density distribution, correlation functions for bond-order-wave (BOW) and charge-density-wave (CDW) -- by integrating twisted boundary conditions with the Lanczos technique and employing high-precision numerical diagonalization methods, complemented by a mean-field approximation (MFA) based on bond-order and charge-density modulation analysis. This approach enables precise identification of phase transition critical points. Our results indicate that the system exhibits a topologically trivial band insulating (BI) phase for strong attractive interactions, with its upper boundary forming a downward-opening curve peaking at V/t≃−2.3 and extending to V/t≃−2.6. Within −2.6≤V/t≤−0.5, a BOW phase emerges for ∣δt/t∣>0.45, with its boundaries converging as ∣δt/t∣ decreases, terminating at a single point at ∣δt/t∣≃0.45. In other parameter regions, a CDW phase is realized. Through this analysis, we elucidate the topological properties of the interacting spinless SSH model at quarter filling, highlighting the competition among CDW, BOW, and BI phases. By tuning V and δt, the system exhibits diverse correlated phenomena, offering new insights into one-dimensional quantum phase transitions and the interplay between topology and order.