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arXiv:2208.03906 · Physical review. B./Physical review. B

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation

David Mikhail, B. Voisin, Dominique Didier St Medar, Gilles Buchs, Sven M. J. Rogge, Stephan Rachel

Published Nov 8, 2022• 11 citations
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Abstract

We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of ${U}_{c}\ensuremath{\approx}5t$ these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

DOI
10.1103/physrevb.106.195408

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We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of Uc\ensuremath≈5t{U}_{c}\ensuremath{\approx}5tUc​\ensuremath≈5t these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.
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.
Abstract Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.
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 present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using the interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a TTT-matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit.
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.
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≃−2.3V/t\simeq-2.3V/t≃−2.3 and extending to V/t≃−2.6V/t\simeq-2.6V/t≃−2.6. Within −2.6≤V/t≤−0.5-2.6 \leq V/t \leq -0.5−2.6≤V/t≤−0.5, a BOW phase emerges for ∣δt/t∣>0.45\left|δt/t\right| > 0.45∣δt/t∣>0.45, with its boundaries converging as ∣δt/t∣\left|δt/t\right|∣δt/t∣ decreases, terminating at a single point at ∣δt/t∣≃0.45\left|δt/t\right|\simeq0.45∣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 VVV and δtδtδt, the system exhibits diverse correlated phenomena, offering new insights into one-dimensional quantum phase transitions and the interplay between topology and order.