Quench in 1D Bose-Hubbard Model: Topological Defects and Excitations from Kosterlitz-Thouless Phase Transition Dynamics

TL;DR

This paper examines how the Kibble-Zurek mechanism's predictions for defect formation during phase transitions can be inaccurate if critical exponents are used naively, especially in Kosterlitz-Thouless transitions like in the 1D Bose-Hubbard model.

Contribution

It highlights the importance of causality-based analysis over naive critical exponent application in predicting excitations during phase transitions.

Findings

Naive use of critical exponents can lead to inconsistent predictions.

Scaling exponents depend on quench rate, not just asymptotic critical exponents.

Kosterlitz-Thouless scaling shows rate-dependent behavior in defect formation.

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 KZM predictions can lead to results that are inconsistent with a more careful KZM-like 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.