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

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 $\mu \le 0$ rather accurately up to relatively high temperatures $T\lesssim 0.1J$.

18 pages, 13 figures

References in corpus (7)

• Exact evolution equation for the effective potential
• Observation of scale invariance and universality in two-dimensional Bose gases
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Strongly Interacting Two-Dimensional Bose Gases
• Connecting Berezinskii-Kosterlitz-Thouless and BEC phase transitions by tuning interactions in a trapped gas
• Universal thermodynamics of a two-dimensional Bose gas
• Magneto-caloric effects, quantum critical points, and the Berezinsky-Kosterlitz-Thouless transition in 2D coupled spin dimer systems

Cited by in corpus (2)

• The nonperturbative functional renormalization group and its applications
• 2D dilute Bose mixture at low temperatures