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 $T\lesssim 0.1J$.

arXiv comment18 pages, 13 figures

References in corpus (24)

• Exact evolution equation for the effective potential
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Quantum Monte Carlo with Directed Loops
• Observation of scale invariance and universality in two-dimensional Bose gases
• Critical Point of a Weakly Interacting Two-Dimensional Bose Gas
• Observation of a 2D Bose-gas: from thermal to quasi-condensate to superfluid
• Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region
• Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
• Exploring the thermodynamics of a two-dimensional Bose gas
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Quantum critical behavior of ultracold atoms in two-dimensional optical lattices
• Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas
• Analytical and numerical study of hardcore bosons in two dimensions
• 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
• Quantum Monte Carlo simulation of a two-dimensional Bose gas
• Fit-free determination of scale invariant equations of state: application to the 2D Bose gas across the Berezinksii-Kosterlitz-Thouless transition
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Quantum critical dynamics of the two-dimensional Bose gas
• Finite temperature line-shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension
• Magneto-caloric effects, quantum critical points, and the Berezinsky-Kosterlitz-Thouless transition in 2D coupled spin dimer systems
• Hard-core boson approach to the spin-1/2 triangular-lattice antiferromagnet Cs${}_2$CuCl${}_4$ at finite temperatures in magnetic fields higher than the saturation field

Cited by in corpus (3)

• The nonperturbative functional renormalization group and its applications
• 2D dilute Bose mixture at low temperatures
• Entanglement of Hard-Core Bosons in Bipartite Lattices