Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

Abstract

We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.

37 pages, 4 figures

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• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Correlations and diagonal entropy after quantum quenches in XXZ chains
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• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
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