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Strong Zero Modes in Integrable Quantum Circuits

Eric Vernier1, Hsiu-Chung Yeh2, Lorenzo Piroli3, and Aditi Mitra2

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Phys. Rev. Lett. 133, 050606 – Published 2 August, 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.050606

Abstract

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

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Outline

Information

Phys. Rev. Lett. 133, 050606– Published 2 August, 2024
  • Received 20 February 2024
  • Revised 7 May 2024
  • Accepted 28 June 2024
Article part of CHORUS
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