Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain

• URL: http://arxiv.org/abs/2005.12309v2
• Date: Wed, 19 Aug 2020 17:18:57 GMT
• Title: Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Authors: Marlon Brenes, John Goold and Marcos Rigol
• Abstract summary: We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain. We show that, at that size, the behavior of the variances of the off-diagonal matrix elements can be starkly different depending on the operator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain and of the quantum-chaotic model obtained by locally perturbing the XXZ chain with a magnetic impurity. We show that, at frequencies that are polynomially small in the system size, the behavior of the variances of the off-diagonal matrix elements can be starkly different depending on the operator. In the integrable model we find that, as the frequency $\omega\rightarrow0$, the variances are either nonvanishing (generic behavior) or vanishing (for a special class of operators). In the quantum-chaotic model, on the other hand, we find the variances to be nonvanishing as $\omega\rightarrow0$ and to indicate diffusive dynamics. We highlight which properties of the matrix elements of local operators are different between the integrable and quantum-chaotic models independently of the specific operator selected.

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