论文标题
在3D晶格上的扭转模型的对称性
Symmetries of Thirring models on 3d lattices
论文作者
论文摘要
我们回顾了一些有关在三个时空维度中强烈相互作用的相对论费米理论的最新发展。这些模型实现了渐近安全方案，并用于描述浓缩物理学中狄拉克材料的低能特性。我们首先讨论在任意维度上多品味费米系统的对称性。然后，我们回顾有关三个维度模型的关键风味$ n_ \ mathrm {crit} $的已知结果。只有低于$ n_ \ mathrm {crit} $的风味数模型才显示从对称折叠的强耦合阶段到对称弱耦合阶段的相变。手性费米子的最新模拟表明，$ n_ \ mathrm {crit} $比以前用各种非扰动方法提取的小。我们用手性slac费米子进行的模拟表明，对于四个成分的口味，$ n_ \ mathrm {crit} = 0.80（4）$。这意味着所有$ \ nr = 1,2,3，\ dots $均带有订单参数的相变。取而代之的是，我们发现没有顺序参数的相变的足迹。这些新的过渡可能是平稳的，可以用来将晶状体刺激模型与连续体中的扭转模型联系起来。对于单一的不可还原风味，我们为关键耦合和关键指数提供了以前未发表的值。
We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.
