Time-evolution and dynamical phase transitions at a critical time in a system of one dimensional bosons after a quantum quench

TL;DR

This paper uses a renormalization group approach to demonstrate a finite-time dynamical phase transition in a one-dimensional bosonic system after a quantum quench, characterized by non-analytic growth of an order parameter.

Contribution

It introduces a novel renormalization group framework to analyze dynamical phase transitions at a critical time in quenched one-dimensional bosonic systems.

Findings

Identification of a finite-time dynamical phase transition.

Demonstration of non-analytic growth of the order parameter.

Analysis of the effects of simultaneous lattice and interaction quenches.

Abstract

A renormalization group approach is used to show that a one dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light-cone increases as a non-analytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time-dependent, crucially affecting the time-evolution of the system. Explicit results are presented for the time-evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.