论文标题
梅隆群集算法可解决的晶格费米顿模型
Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
论文作者
论文摘要
我们介绍了一个半填充的旋转晶格fermions的哈密顿量，可以通过在任何维度上使用有效的梅隆群集算法来研究，这些算法可以在任何维度上进行研究。与通常的双方半填充哈伯德型号一样，幼稚的$ u（2）$对称性增强到$（4）$。另一方面，我们的模型具有一种新颖的自旋电荷翻转$ {\ Mathbb z}^C_2 $对称性，这是免费的无质量费米子的重要组成部分。在这项工作中，我们专注于一个空间维度，并表明我们的模型可以被视为晶格调查的两种味道质量质量毛毛毛模型。在Hubbard耦合$ U $的情况下，我们的模型仍然可以解决，该耦合$ u $映射到一个尺寸的毛线和毛线耦合的组合。使用Meron-Cluster算法，我们发现模型的基态是$ u = 0 $时的价值固体。从我们的现场理论分析中，我们认为价值固体不可避免地是由于$ {\ Mathbb z}^C_2 $对称性强制实施的重新归一化组流量中的自旋和电荷扇区之间的挫败感。该状态自发地通过一个晶格单元打破了翻译对称性，可以用$ \ mathbb {z} _2 _2^χ$手性对称性在连续体中识别。我们表明，增加$ u $会导致量子相变为$ su（2）_1 $ wess-zumino-witten理论所描述的关键阶段。已知这两个阶段之间的量子临界点在自旋和二聚体之间表现出新颖的对称性增强。在这里，我们在数值上验证临界点附近这些相关函数的缩放关系。我们的研究开辟了使用Meron-Cluster算法在费米子晶格模型中，在较高维度中使用类似新型相变的数字访问的令人兴奋的可能性。
We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïve $U(2)$ symmetry is enhanced to $SO(4)$. On the other hand our model has a novel spin-charge flip ${\mathbb Z}^C_2$ symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension, and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling $U$, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when $U=0$. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the ${\mathbb Z}^C_2$ symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a $\mathbb{Z}_2^χ$ chiral symmetry in the continuum. We show that increasing $U$ induces a quantum phase transition to a critical phase described by the $SU(2)_1$ Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.
