We study the dynamical fidelity F(t) and the Loschmidt echo L(t), following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after n periods tau. We show that [log F(n tau)]/L (the logarithm of the fidelity per site) reaches a steady value in the asymptotic limit n -> infinity, and we derive an exact analytical expression for this quantity. Remarkably, the steady-state value of [log F(n tau -> infinity)]/L shows memory of non-trivial phase information which is instead hidden in the case of thermodynamic quantities; this conclusion, moreover, is not restricted to 1-dimensional models.

Loschmidt echo and dynamical fidelity in periodically driven quantum systems

Russomanno, Angelo;Santoro, Giuseppe Ernesto;
2014-01-01

Abstract

We study the dynamical fidelity F(t) and the Loschmidt echo L(t), following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after n periods tau. We show that [log F(n tau)]/L (the logarithm of the fidelity per site) reaches a steady value in the asymptotic limit n -> infinity, and we derive an exact analytical expression for this quantity. Remarkably, the steady-state value of [log F(n tau -> infinity)]/L shows memory of non-trivial phase information which is instead hidden in the case of thermodynamic quantities; this conclusion, moreover, is not restricted to 1-dimensional models.
2014
106
6
1
6
67003
https://arxiv.org/abs/1402.0758v3
Sharma, S.; Russomanno, Angelo; Santoro, Giuseppe Ernesto; Dutta, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14243
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