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

• URL: http://arxiv.org/abs/2406.08338v2
• Date: Thu, 13 Jun 2024 03:17:59 GMT
• Title: Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Authors: Xi-Dan Hu, Dan-Bo Zhang,
• Abstract summary: We give an inverse approach for constructing dual-unitary quantum circuits with exceptional points. As a consequence of eigenvectors, correlation functions exhibit a modified exponential decay. We show that behaviors of correlation functions are distinct by Latemporalplace transformation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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