We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the Néel and tilted Néel states. We apply the Quantum Transfer Matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM's. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t0, after which the integral equations have to be modified. In some regimes, t0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the Néel state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the Néel, tilted Néel and tilted ferromagnet states.

From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains / Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2017:2(2017), pp. 1-51. [10.1088/1742-5468/aa5d1e]

From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

Piroli, Lorenzo;Vernier, Eric
2017

Abstract

We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the Néel and tilted Néel states. We apply the Quantum Transfer Matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM's. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t0, after which the integral equations have to be modified. In some regimes, t0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the Néel state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the Néel, tilted Néel and tilted ferromagnet states.
2017
2
1
51
023106
http://stacks.iop.org/1742-5468/2017/i=2/a=023106
Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/85910
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