Thermodynamics and renormalized quasi-particles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

TL;DR

This paper employs the functional renormalization group to derive analytical expressions for thermodynamic and single-particle properties of interacting bosons near the dilute Bose gas quantum critical point in two dimensions, validated by quantum Monte Carlo simulations.

Contribution

It extends previous RG calculations to finite chemical potentials and combines analytical FRG results with Monte Carlo simulations for validation.

Findings

FRG provides accurate thermodynamic predictions up to T ≈ 0.1 J for μ ≤ 0.

Analytical expressions match Monte Carlo data well in the quantum critical regime.

The approach captures the behavior of density, pressure, entropy, and effective mass near the critical point.

Abstract

We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wavefunction renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $\mu$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization group calculations for thermodynamic observables at $\mu =0$ to finite values of $\mu$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, the susceptibility, and the correlation length of the two-dimensional spin-$1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $\mu \leq 0$ rather accurately up to relatively high temperatures $T \lesssim 0.1 J$.