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arXiv:2406.13878 · Physical review. B./Physical review. B

Role of bath-induced many-body interactions in the dissipative phases of the Su-Schrieffer-Heeger model

Brett Min, Kartiek Agarwal, Dvira Segal

Published Sep 10, 2024• 10 citations
arXivHTMLPDF

Abstract

The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. We also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.

DOI
10.1103/physrevb.110.125415

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The Su-Schrieffer-Heeger chain is a prototype example of a symmetry-protected topological insulator. Coupling it nonperturbatively to local thermal environments, either through the intercell or the intracell fermion tunneling elements, modifies the topological window. To understand this effect, we employ the recently developed reaction-coordinate polaron transform (RCPT) method, which allows treating system-bath interactions at arbitrary strengths. The effective system Hamiltonian, which is obtained via the RCPT, exposes the impact of the baths on the SSH chain through renormalization of tunneling elements and the generation of many-body interaction terms. By performing exact diagonalization and computing the ensemble geometric phase, a topological invariant, which is applicable even to systems at finite temperature, we distinguish the trivial band insulator (BI) from the topological insulator (TI) phases. Furthermore, through the RCPT mapping, we are able to pinpoint the main mechanism behind the extension of the parameter space for the TI or the BI phases (depending on the coupling scheme, intracell or intercell), which is the bath-induced, dimerized, many-body interaction. We also study the effect of on-site staggered potentials on the SSH phase diagram and discuss extensions of our method to higher dimensions.
Many-body interactions play a crucial role in quantum topological systems, being able to impact or alter the topological classifications of noninteracting fermion systems. In open quantum systems, where interactions with the environment cause dissipation and decoherence of the fermionic dynamics, the absence of Hermiticity in the subsystem Hamiltonian drastically reduces the stability of the topological phases of the corresponding closed systems. Here we investigate the nonperturbative effects induced by the environment on the prototype Su-Schrieffer-Heeger chain coupled to local harmonic oscillator baths through either intracell or intercell transfer integrals. Despite the common view, this type of coupling, if suitably engineered, can even induce a transition to topological phases. By using a world-line quantum Monte Carlo technique we determine the phase diagram of the model proving that the bimodality of the probability distribution of the polarization signals the emergence of the topological phase. We show that a qualitative description can be obtained by using an approach based on the cluster perturbation theory providing, in particular, a non-Hermitian Hamiltonian for the fermionic subsystem and insights on the dissipative dynamics. We prove that non-Hermitian effects disappear in the presence of classical heat baths.
A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of a one-dimensional system with a nontrivial band topology. An interplay of disorder and topological ordering in the SSH model is of great interest owing to experimental advancements in synthesized quantum simulators. In this paper, we investigate a special sort of a disorder when intercell hopping amplitudes are random. Using a definition for Z2{\mathbb{Z}}_{2}Z2​-topological invariant $\ensuremath{\nu}\ensuremath{\in}{0;1}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\rangle}$ averaged by random realizations. This allows to find: (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite-size fluctuations of $\ensuremath{\nu}$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for the finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green's function method for a thermodynamic limit.
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 the topological phase in a one-dimensional Su-Schrieffer-Heeger (SSH) chain in the presence of a finite concentration of non-Hermitian substitutional impurities. Our primary focus is the discovery of a deterministic mechanism to actively reconfigure the topological phase boundaries by introducing site-dependent, non-reciprocal intracell and intercell hopping amplitudes. Specifically, breaking the internal structural symmetry of the non-reciprocal impurity hoppings induces a targeted macroscopic displacement of the critical point. This mechanism allows for the controlled expansion or compression of the topological phase strictly via local defect asymmetry. We validate this boundary displacement through finite-size scaling analysis. The extracted correlation length critical exponents (ν≈1.455ν\approx 1.455ν≈1.455 and ν≈1.397ν\approx 1.397ν≈1.397 for symmetric and asymmetric configurations, respectively) confirm a disorder-induced departure from the pristine SSH universality class, with the exponent diverging at high defect densities. We also report an impurity-induced real-to-complex spectral transition geometrically characterized by the Non-Hermitian Skin Effect. Ultimately, our results establish how isolated non-Hermitian asymmetries cooperatively interact to deterministically shift macroscopic topological protection.
Topological phases at quantum criticality have attracted much attention recently. Here we numerically study the interaction-induced phase transitions at around the topological quantum critical points of an extended Su-Schrieffer-Heeger (SSH) chain with next-nearest-neighbor hopping. This extended SSH model shows topological phase transitions between the topologically trivial and nontrivial critical phases when interaction is absent. So long as the interaction terms are turned on, the topologically nontrivial (trivial) critical phases are driven into topologically nontrivial (trivial) insulator phases with finite energy gaps. Particularly, we find the trivial insulator phase is further driven to the nontrivial insulator phase, through interaction-induced topological phase transition, although interaction generally is harmful to nontrivial topology. The stability of the trivial insulator phase against interaction tends to vanish at the multicritical point that separates the trivial and nontrivial critical phases. Our work provides a concrete example for manifesting the impact of interaction on topological quantum criticality.
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.