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arXiv:2001.09074 · Physical Review Research

Detecting topology through dynamics in interacting fermionic wires

Andreas Haller, Pietro Massignan, Matteo Rizzi

Published Aug 5, 2020• 11 citations
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Abstract

This work describe a dynamical method to characterize one dimensional chiral models, based on the direct observation of time-evolving bulk excitations. The protocol is tested on top of a readily-feasible experimental set-up of an interacting Su-Schrieffer-Heeger (SSH) chain which realizes both topological and symmetry-broken phases.
DOI
10.1103/physrevresearch.2.033200

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Probing the topological invariants of interacting systems stands as a grand and open challenge. Here we describe a dynamical method to characterize 1D chiral models, based on the direct observation of time-evolving bulk excitations. We present analytical and state-of-the-art numerical calculations on various flavors of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how measuring the mean chiral displacement allows us to distinguish between topological insulator, trivial insulator, and symmetry-broken phases. Finally, we provide a readily-feasible experimental blueprint for a model displaying these three phases and we describe how to detect those.
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 investigate the emergence of charge waves and their temporal dynamics in one-dimensional Su-Schrieffer-Heeger (SSH) topological chains. Contrary to the conventional view that charge oscillations are suppressed in gapped topological systems with preserved chiral symmetry, we show that such oscillations can indeed occur. The general condition for an arbitrary oscillation period is analysed, and we find that the charge waves propagating along the chain do not depend on its topology, except at the edges, where both topological phases exhibit essential differences. In chains with inequivalent atoms within the SSH unit cell, we observe regular long-period sublattice oscillations that appear simultaneously with even-odd charge oscillations. Furthermore, we study the nonequilibrium dynamics in SSH chains. After a quench, the time evolution of the local density of states and charge occupancies exhibits clear dynamical fingerprints that distinguish topologically trivial and nontrivial phases. Our results establish that transient charge dynamics can distinguish topologically trivial and nontrivial phases in real time by detecting the presence of topologically-protected edge states.
Abstract The Su–Schrieffer–Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higher-dimensional extension of the mean chiral displacement measurement, however, this has not yet been verified in experiment. Here, we report the realization of this model with ultracold atoms in a momentum lattice. We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary.
We develop an adiabatic quantum simulation framework on gate-based quantum computers to probe topological signatures of the one-dimensional fermionic Su--Schrieffer--Heeger--Hubbard (SSHH) model. We present explicit quantum-circuit constructions for initial-state preparation and time evolution, together with a practical measurement protocol and classical post-processing procedure for extracting the many-body Berry phase and the spatial profile of the sublattice polarization. Using classical simulations of the proposed circuits, we demonstrate -- for the first time within a genuine many-body framework -- that the topological characteristics of the SSH model remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component of the interaction exceeds a threshold. The required qubit number, gate complexity, measurement shots, and classical pre- and post-processing costs all scale polynomially with system size. Our results provide a proof-of-concept framework for probing topological properties of interacting many-body systems via adiabatic quantum simulation on future large-scale quantum computers.
We investigate the dynamics of entanglement in dissipative fermionic and bosonic Su-Schrieffer-Heeger (SSH) models and discover that they exhibit a revival dynamics of entanglement when the decoherence channel preserves the chiral symmetry. This behavior is only observable in the topological phase, and the visibility of the revival diminishes to zero at the phase boundary. Furthermore, the revival acquires a universal character, meaning that the entire time-evolution profile remains independent of system size, provided that the size exceeds the localization length of the edge modes associated with the topological phase. Our findings suggest that the universal entanglement revival originates from the topological properties of the SSH model. These dynamical properties may be experimentally accessible, for instance, by utilizing photonic quantum computers.