Topological Floquet Green's function zeros

TL;DR

This paper investigates topological Green's function zeros in Floquet systems, especially in interacting Kitaev-like chains, introducing new invariants and analyzing their properties both analytically and via quantum emulation.

Contribution

It introduces Floquet Green's-function-based topological invariants for symmetry class BDI and explores their behavior in interacting Floquet chains, including quantum emulator implementation.

Findings

Green's function zeros can exist without interactions in Floquet systems.

Topological invariants include contributions from Green's function zeros.

Quantum circuit implementation encodes interactions and detects boundary zeros.

Abstract

Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function zeros in topological Floquet systems. We concentrate on interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) and introduce Floquet Green's-function-based topological invariants for the corresponding symmetry class BDI. In the vicinity of special points in the free fermion phase diagram and using tailor-made interactions which lead to the Floquet version of symmetric mass generation, we analytically calculate both edge and bulk Green's functions. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.