Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields

TL;DR

This paper uses continuous matrix product states to numerically analyze the mixing-demixing transition in one-dimensional quantum Bose mixtures, validating bosonization theory predictions and characterizing the transition through various physical quantities.

Contribution

It introduces a numerical approach with continuous matrix product states to study the transition, providing accurate Luttinger parameters and detailed physical characterizations.

Findings

Effective low-energy bosonization detects the transition with exact Luttinger parameters.

Ground-state energy density shows clear signatures of the transition.

Density correlations and field fluctuations characterize the transition behavior.

Abstract

We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory is able to detect the transition whenever the Luttinger parameters are exactly computed. We further characterize the transition by calculating the ground-state energy density, the field-field fluctuations and the density correlations.