Classical, semiclassical and quantum signatures of quantum phase transitions in a (pseudo) relativistic many-body system

TL;DR

This paper explores quantum phase transitions in a (pseudo) relativistic many-body system, identifying signatures through numerical and mean-field analyses, and characterizing dynamical exponents near the transition.

Contribution

It introduces a relativistic spin-dependent analogue of quantum phase transitions in bosonic gases, with an effective model and detailed numerical validation.

Findings

Identification of a relativistic quantum phase transition driven by bright soliton formation

Development of an effective model accurately predicting transition location

Numerical analysis of dynamical exponents near the transition

Abstract

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.