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Edge state behavior of interacting bosons in a Su-Schrieffer-Heeger lattice

A. Ghosh1,2 and A. M. Martin1

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Phys. Rev. Research 7, 013169 – Published 14 February, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.013169

Abstract

In the low-energy regime, the Su-Schrieffer-Heeger (SSH) model's key characteristics are encapsulated by a Dirac-type Hamiltonian in continuum space, i.e., localized states emerge at the boundaries. Building on this, we have developed an effective Hamiltonian to model ultracold interacting bosons on an SSH-like lattice through variational minimization under the mean-field approximation. To pinpoint the boundary states, we have developed an algorithm by generalizing the imaginary time propagator, where an initial state evolves under the squared Hamiltonian to converge to the targeted state. This algorithm has broader applicability, enabling the identification of specific eigenstates in various contexts. Furthermore, we draw a parallel to an experimentally physical setup involving a gas of ultracold bosons confined to an array of potential wells with alternating depths. By establishing the system's analogy with the SSH system, we apply our algorithm to investigate boundary states in the presence of interactions, demonstrating how these findings align with those of the continuous system.

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Phys. Rev. Research 7, 013169– Published 14 February, 2025
  • Received 23 October 2024
  • Accepted 22 January 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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