Quench in the 1D Bose-Hubbard model: topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics.

Jacek Dziarmaga,Wojciech H Zurek

doi:10.1038/srep05950

Jacek Dziarmaga, Wojciech H Zurek

Open Access

https://doi.org/10.1038/srep05950

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Abstract

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon.

Highlights

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics
We have seen that, in some cases, using Kibble-Zurek mechanism (KZM) requires more than just inserting critical exponents
To estimate the scale ^j one must make sure that the key idea behind KZM - the scaling of the sonic horizon that results from the critical slowing down - is accurately described by the critical exponents in the regime probed by the experiment

Summary

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Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics. Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. The study of the dynamics of second-order phase transitions started with the observation by Kibble[1,2] that, in the cosmological setting, as a result of relativistic causality, distinct domains of the nascent Universe will choose different broken symmetry vacua Their incompatibility, characterized by the relevant homotopy group, will typically lead to topological defects that may have observable consequences. Topological defects or other excitations left behind by the quench will approach the scaling predicted by the critical exponents, Eq (16), only asymptotically, and begin to conform with it only in the regime of extremely slow transitions that may be well out of the reach of laboratory experiments. In the regime of faster quenches that may be accessible to experiments a power law may still be locally a reasonable fit, its exponent will vary slowly, approaching the asymptotic prediction only very gradually

Results

Mott side of the transition is

Its solution is

Discussion

Additional information