$(2+1)$维量子临界点附近的Higgs振幅模：非微扰重整化群方法

Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group

We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fra…

Flowing bosonization in the nonperturbative functional renormalization-group approach

Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field $φ$ and its conjugate partner, the phase $\vartheta$ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for $\vartheta$ and $φ$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$…

强关联格点玻色子的非微扰重整化群方法

Nonperturbative renormalization-group approach to strongly-correlated lattice bosons

本文对玻色-哈伯德模型提出了一种非微扰的重整化群方法。通过将解耦点的（局部）极限作为重整化群流的初始条件，我们以非平凡的方式同时考虑了局部和长距离的涨落。这种方法产生的相图在很好的定量协议与量子蒙特卡罗模拟，并再现两个普适类的超流体-莫特绝缘体过渡。在多临界点附近的临界行为，即在恒定密度下发生转变的地方，与Fisher { \it et al.}的原始预测一致。[Phys. Rev. B { \bf 40}，546（1989）]基于简单的缩放参数。在一个通用的过渡点，临界行为是平均场的对数修正在二维。在弱关联超流相（远离Mott绝缘相），重整化群流受Bogoliubov不动点控制，降到特征（Ginzburg）动量尺度$k_G$，远小于逆愈合长度$k_h$ .在附近的多临界点，当密度是相称的，我们确定了一个尖锐的交叉从弱到强相关的超流相的凝聚体密度和超流刚度被强烈抑制和$k_G$和$k_h$的顺序的逆晶格间距。

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot--Mendéz-Galain--Wschebor approxim…

$(2+1)$维O（$N$）对称量子临界点附近输运的非微扰泛函重整化群方法

Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point

利用非微扰泛函重整化群方法对二维量子O（$N$）模型进行研究，计算了零温电导率在量子临界点附近的低频极限.我们的结果是从一个衍生的扩展到二阶的规模依赖的有效行动的存在下，外部（即，非动力学）非阿贝尔规范场。而在无序相的电导率张量$σ(ω)$是对角的，在有序相，它被定义，当$N\geq 3$，由两个独立的元素，$σ_{\rm A}(ω)$和$σ_{\rm B}(ω)$，分别与SO（$N$）旋转，做和不改变的顺序参数的方向。对于$N=2$，有序相中的电导率降低为单一组分$σ_{\rm A}(ω)$。我们表明，$\lim_{ω\to 0}σ(ω,δ)σ_{\rm A}(ω,-δ)/σ_q^2$是一个普适数，我们计算作为$N$的函数（$δ$措施的量子临界点的距离，$q$是电荷和$σ_q=q^2/h$的量子电导）。另一方面，我们认为，比例$σ_{\rm B}(ω\to 0)/σ_q$是通用的在整个有序相，独立于$N$，当$N\to\infty$，等于通用电导率$σ^*/σ_q$在量子临界点。

Nonperturbative renormalization group treatment of amplitude fluctuations for $|φ|^4$ topological phase transitions

The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional $|φ|^4$ models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the contribution of density fluctuations to nonuniversal quantities. We introduce a functional renormalization group scheme in AP representation where amplitude fluctuations are integrated first to yield an effective sine-Gordon model with renormalized superfluid stiffness. By a mapping between the lattice XY and continuum $|φ|^4$ models, our method applies to both on equal foot…