Equilibration and GGE in interacting-to-free Quantum Quenches in dimensions d>1

TL;DR

This paper demonstrates that in higher-dimensional quantum field theories, long-time evolution under free dynamics causes initial interacting ground states to effectively become Gaussian, with local observables described by a generalized Gibbs ensemble, extending previous 1D results.

Contribution

It generalizes the known 1D GGE results to higher dimensions, showing that interacting ground states evolve towards a Gaussian state characterized by initial two-point correlations.

Findings

Connected correlation functions decay over time.

Local observables equilibrate to Gaussian values.

GGE accurately describes asymptotic correlation behaviour.

Abstract

Ground states of interacting QFTs are non-gaussian states, i.e. their connected n-point correlation functions do not vanish for n>2, in contrast to the free QFT case. We show that when the ground state of an interacting QFT evolves under a free massive QFT for a long time (a scenario that can be realised by a Quantum Quench), the connected correlation functions decay and all local physical observables equilibrate to values that are given by a gaussian density matrix that keeps memory only of the two-point initial correlation function. The argument hinges upon the fundamental physical principle of cluster decomposition, which is valid for the ground state of a general QFT. An analogous result was already known to be valid in the case of d=1 spatial dimensions, where it is a special case of the so-called Generalised Gibbs Ensemble (GGE) hypothesis, and we now generalise it to higher dimensions. Moreover in the case of massless free evolution, despite the fact that the evolution may not lead to equilibration but unbounded increase of correlations with time instead, the GGE gives correctly the leading order asymptotic behaviour of correlation functions in the thermodynamic and large time limit. The demonstration is performed in the context of bosonic relativistic QFT, but the arguments apply more generally.