单个狄拉克锥的手征伊辛-格罗斯-涅韦临界性：一项量子蒙特卡罗研究

Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum Monte Carlo Study.

作者信息

Tabatabaei S Mojtaba, Negari Amir-Reza, Maciejko Joseph, Vaezi Abolhassan

机构信息

Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran.

Department of Physics & Theoretical Physics Institute (TPI), University of Alberta, Edmonton, Alberta T6G 2E1, Canada.

出版信息

Phys Rev Lett. 2022 Jun 3;128(22):225701. doi: 10.1103/PhysRevLett.128.225701.

DOI:10.1103/PhysRevLett.128.225701

PMID:35714234

Abstract

We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with N=2 spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength U_{c}=7.28±0.02 in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding N=2 chiral Ising Gross-Neveu universality class: the inverse correlation length exponent ν^{-1}=1.19±0.03, the order parameter anomalous dimension η_{ϕ}=0.31±0.01, and the fermion anomalous dimension η_{ψ}=0.136±0.005.

摘要

我们在具有单个狄拉克锥、(N = 2) 旋量分量且在位相互作用为排斥性的二维正方形晶格上，对半填充的斯坦福直线加速器中心（SLAC）费米子进行了大规模量子蒙特卡罗模拟。尽管存在符号问题，但对于顺磁狄拉克半金属和铁磁绝缘体之间的连续量子相变，我们以跳跃幅度为单位准确确定了临界相互作用强度 (U_{c}=7.28±0.02)。使用有限尺寸标度，我们提取了对应 (N = 2) 手征伊辛 - 格罗斯 - 内夫普遍性类的临界指数：逆关联长度指数 (ν^{-1}=1.19±0.03)，序参量反常维度 (η_{ϕ}=0.31±0.01)，以及费米子反常维度 (η_{ψ}=0.136±0.005)。