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The European Physical Journal B

Quantum quenches in one-dimensional gapless systems

Emanuele Coira, Federico Becca, Alberto Parola

Published Feb 1, 2013• 25 citations
Publisher
DOI
10.1140/epjb/e2012-30978-y

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The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the non-monotonous behaviour of observables. In continuum non-interacting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favour of the robustness of the phenomenon in the cases of non-sudden quenches and higher dimensionality.
The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a generalized Gibbs ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, nonmonotonic response of steady-state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench information (light cone) for large quenches. We argue that this freezing is responsible for the nonmonotonous behavior of observables. In continuum noninteracting models, this freezing can be traced back to a Klein-Gordon equation in the presence of a source term. We conclude by arguing in favor of the robustness of the phenomenon in the cases of nonsudden quenches and higher dimensionality.
We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.