Geometric phase contribution to quantum non-equilibrium many-body dynamics

TL;DR

This paper investigates how geometric phases influence the non-equilibrium dynamics of quantum many-body systems, revealing a transition between dynamical and topological regimes and their effects on defect formation.

Contribution

It demonstrates the significant role of geometric phase in quantum non-equilibrium dynamics and identifies a non-equilibrium phase transition driven by geometric effects.

Findings

Geometric phase impacts transition probabilities in quantum dynamics.

A non-equilibrium phase transition is identified between dynamical and topological regimes.

Geometric phase affects defect generation during quantum critical crossing.

Abstract

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, non-adiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. We show that this interplay can lead to a non-equilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum critical point.