Quantum Quench Across a Zero Temperature Holographic Superfluid Transition

TL;DR

This paper investigates the dynamics of a zero temperature holographic superfluid during a quantum quench across a phase transition, revealing a non-dissipative Landau-Ginsburg behavior with a fractional power expansion.

Contribution

It introduces a novel small-$v$ expansion near the critical point and derives a time-dependent Landau-Ginsburg equation with dynamical critical exponent $z=2$ for the holographic superfluid.

Findings

Adiabaticity breaks down near the critical point during the quench.

A fractional power expansion describes the critical dynamics for small quench rates.

The order parameter obeys a non-dissipative $z=2$ Landau-Ginsburg equation.

Abstract

We study quantum quench in a holographic model of a zero temperature insulator-superfluid transition. The model is a modification of that of arXiv:0911.0962 and involves a self-coupled complex scalar field, Einstein gravity with a negative cosmological constant, and Maxwell field with one of the spatial directions compact. In a suitable regime of parameters, the scalar field can be treated as a probe field whose backreaction to both the metric and the gauge field can be ignored. We show that when the chemical potential of the dual field theory lies between two critical values, the equilibrium background geometry is a AdS soliton with a constant gauge field, while the complex scalar condenses leading to broken symmetry. We then turn on a time dependent source for the order parameter which interpolates between constant values and crosses the order-disorder critical point. In the critical region adiabaticity breaks down, but for a small rate of change of the source $v$ there is a new small-$v$ expansion in fractional powers of $v$. The resulting critical dynamics is dominated by a zero mode of the bulk field. To lowest order in this small-$v$ expansion, the order parameter satisfies a time dependent Landau-Ginsburg equation which has $z=2$, but non-dissipative. These predictions are verified by explicit numerical solutions of the bulk equations of motion.