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arXiv:2008.07224 · Physical Review A

Topological inheritance in two-component Hubbard models with single-component Su-Schrieffer-Heeger dimerization

Suman Mondal, Sebastian Greschner, Luis Santos, Tapan Mishra

Published Jul 22, 2021• 19 citations
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Abstract

The interplay between interparticle interactions and topological features may result in unusual phenomena. Interestingly, interactions may induce topological features in an originally trivial system, as we illustrate for the case of a one-dimensional two-component Hubbard model in which one component is subjected to Su-Schrieffer-Heeger dimerization, whereas the other one is not. We show that due to intercomponent interactions the topological properties of one component are induced in the originally trivial one. Although for large interactions topological inheritance may be readily explained by on-site pairing, we show that the threshold for full inheritance occurs at weak interactions, for which the components are not yet paired. We illustrate this inheritance by discussing both bulk and edge properties, as well as dynamical observables as mean chiral displacement and charge pumping.

DOI
10.1103/physreva.104.013315

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The interplay between interparticle interactions and topological features may result in unusual phenomena. Interestingly, interactions may induce topological features in an originally trivial system, as we illustrate for the case of a one-dimensional two-component Hubbard model in which one component is subjected to Su-Schrieffer-Heeger dimerization, whereas the other one is not. We show that due to intercomponent interactions the topological properties of one component are induced in the originally trivial one. Although for large interactions topological inheritance may be readily explained by on-site pairing, we show that the threshold for full inheritance occurs at weak interactions, for which the components are not yet paired. We illustrate this inheritance by discussing both bulk and edge properties, as well as dynamical observables as mean chiral displacement and charge pumping.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
We study the interplay of spontaneous symmetry breaking and topological properties in interacting one-dimensional models. We solve these models using bozonization and identify topologically non-trivial phases by counting the additional degeneracy (affiliated with the edge modes) of a finite-size system relative to the infinite one. We find even if the mean-field solution is topological, this may not be true when it arises from spontaneous symmetry breaking, including in the Su-Schrieffer-Heeger (SSH) model. This implies that the original SSH model, as presented by Su, Schrieffer, and Heeger, is topologically trivial, as opposed to its mean-field version. A spinful version, on the other hand, does exhibit a topologically non-trivial phase. In that state, both mean-field solutions are topologically non-trivial and correspond to non-interacting SSH chains in the opposite phases with the winding number ν=1ν=1ν=1. We show that this phase is protected by a chiral symmetry, similar to the non-interacting phases.
We study the topological properties of hardcore bosons on a two-leg ladder consisting of two Su-Schrieffer-Heeger chains that are coupled via hopping and interaction. We chart out the phase diagram for the system and show that based on the relative hopping dimerization pattern along the legs, distinctly different topological phases and phase transitions can occur. When the dimerization along the legs is uniform, we find that the topological nature vanishes for even the slightest rung hopping. For staggered dimerization, the system exhibits a well-defined topological character and a topological phase transition as a function of rung hopping. While the topological phase shows bond order character, the trivial phase shows the behavior of a rung-Mott insulator. For this case, the topological nature is found to survive even in the presence of finite interleg interactions. Moreover, we find that the critical point of the topological phase transition shifts to a higher or a lower rung hopping strength depending on the attractive or repulsive nature of the interaction. To highlight the marked effects of interactions, we propose a scheme involving a Thouless charge pump that provides insights for the topological phases characterized by a quantized particle transport through a periodic modulation of appropriate system parameters. In our studies, we show an interaction-induced charge pumping following specific pumping protocols in the case of staggered dimerization.
The interplay and competition of topology and electron--electron interactions have fascinated researchers since the discovery of topological insulators. The Su--Schrieffer--Heeger--Hubbard (SSH-Hubbard) model is a prototypical model which includes both nontrivial topology and interactions. Due to its simplicity, there are several artificial quantum systems which can realize such a model to a good approximation. Here we focus on the quarter-filled case, where interactions and dimerization open a charge gap. In particular, we study the single-particle spectral function for the extended SSH-Hubbard model with magnetic field and explore several parameter limits where effective model descriptions arise. In the strongly dimerized limit, we show that the low-energy excitations of the spectral function resemble a half-filled Hubbard model with effective dimer sites and renormalized couplings. For strong magnetic field and interactions, we find physics akin to the spinless Su--Schrieffer--Heeger model at half filling, featuring a noninteracting topological phase transition. Moreover, in light of the recent realization of this model in quantum dot simulation, we provide evidence for the stability of the topological phase towards moderate nonlocal interactions in the experimentally expected parameter range.
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 properties of one-dimensional weakly interacting topological insulators using bosonization. To do that we study the topological edge states that emerge at the edges of a model realized by a strong impurity or at the boundary between topologically distinct phases. In the bosonic model, the edge states are manifested as degenerate bosonic kinks at the boundaries. We first illustrate this idea on the example of the interacting Su-Schrieffer-Heeger (SSH) chain. We compute the localization length of the edge states as the width of an edge soliton that occurs in the SSH model in the presence of a strong impurity. Next, we examine models of two capacitively coupled SSH chains that can be either identical or in distinct topological phases. We find that weak Hubbard interaction reduces the ground-state degeneracy in the topological phase of identical chains. We then prove that, similarly to the noninteracting model, the degeneracy of the edge states in the interacting case is protected by chiral symmetry. We then study topological insulators built from two SSH chains with interchain hopping that represent models of different chiral symmetric universality classes. We demonstrate in bosonic language that the topological index of a weakly coupled model is determined by the type of interchain coupling, invariant under one of two possible chiral symmetry operators. Finally, we show that a general one-dimensional model in a phase with topological index $\ensuremath{\nu}$ is equivalent at low energies to a theory of at least $\ensuremath{\nu}$ SSH chains. We illustrate this idea on the example of an SSH model with longer-range hopping.