Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points

TL;DR

This paper develops an inverse method to construct dual-unitary quantum circuits with exceptional points, revealing unique polynomial-modified exponential decay in correlation functions and connecting Hamiltonian evolution to these special circuits.

Contribution

It introduces a novel inverse approach for creating dual-unitary circuits with exceptional points and analyzes their unique correlation decay behaviors.

Findings

Correlation functions show polynomial-modified exponential decay at exceptional points.

Hamiltonian evolution of a kicked XXZ chain can be approximated by such circuits.

Distinct behaviors of correlation functions are observed at and near exceptional points.

Abstract

Dual-unitary quantum circuits can provide analytic spatiotemporal correlation functions of local operators from transfer matrices, enriching our understanding of quantum dynamics with exact solutions. Nevertheless, a full understanding is still lacking as the case of a non-diagonalizable transfer matrix with exceptional points has less been investigated. In this paper, we give an inverse approach for constructing dual-unitary quantum circuits with exceptional points in the transfer matrices, by establishing relations between transfer matrices and local unitary gates. As a consequence of the coalesce of eigenvectors, the correlation functions exhibit a polynomial modified exponential decay, which is significantly different from pure exponential decay, especially at early stages. Moreover, we point out that the Hamiltonian evolution of a kicked XXZ spin chain can be approximately mapped to a dual-unitary circuit with exceptional points by Trotter decomposition. Finally, we investigate the dynamics approaching and at exceptional points, showing that behaviors of correlation functions are distinct by Laplace transformation.