二维稀玻色气体量子临界点附近的热力学和重整化准粒子
Thermodynamics and renormalized quasi-particles in the vicinity of the dilute Bose gas quantum critical point in two dimensions
摘要：
我们使用功能重整化群（FRG）推导出解析表达式的热力学观测值（密度，压力，熵，和压缩性），以及单粒子性质（波函数重整化和有效质量）的相互作用玻色子在二维温度$T$和化学势$μ$的函数。我们重点研究了在接近于稀玻色气体量子临界点的量子无序和量子临界区。我们的方法是基于截断顶点扩展的FRG流方程的层次和解耦的两体接触相互作用的粒子粒子通道中使用一个合适的Hubbard-Stratonovich变换。我们的解析FRG结果扩展了以前的解析重整化群计算的热力学观测量在$μ=0$的有限值的$μ$。为了证实我们的FRG方法的有效性，我们还进行了量子Monte Carlo模拟，以获得磁化强度，磁化率和相关长度的二维自旋$1/2$量子$XY$模型与耦合$J$在一个制度，其量子临界行为是由稀释玻色气体量子临界点控制。我们发现，我们的分析结果描述的Monte Carlo数据$μ\leq 0$相当准确的相对较高的温度$T \lesssim 0.1 J$。
英文摘要：
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 $μ$. 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 $μ=0$ to finite values of $μ$. 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 $μ\leq 0$ rather accurately up to relatively high temperatures $T \lesssim 0.1 J$.
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