Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
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DOI：
10.1103/physrevb.96.165133
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发表时间：
2017-03
影响因子：
3.7
通讯作者：
L. Mihaila;N. Zerf;Bernhard Ihrig;I. Herbut;M. Scherer
中科院分区：
文献类型：
--
作者：
L. Mihaila;N. Zerf;Bernhard Ihrig;I. Herbut;M. Scherer
狄拉克和韦尔费米子在许多不同的凝聚态系统中表现为准粒子激发。它们显示了各种量子跃迁，这些量子跃迁代表了与格罗斯-内沃模型的变体相关的非传统普适类。本文研究了标准格罗斯-奈夫模型的玻色化版本--格罗斯-奈夫-汤川理论--在三圈序下，计算了4个−e维费米子味的临界指数。我们的结果完全包含了已知的双圈计算，并且在理论的纯玻色子极限下与已知的三圈结果相一致。在单组分费米子的极限中，我们还找到了满足浮现超标度关系的指数，按序排列直到三圈。最后，我们将指数的计算级数和它们的Pade近似应用于当前感兴趣的几个相变：蜂窝晶格上自旋1/2和无自旋费米子的金属-绝缘体相变，拓扑相中的浮现超对称表面场理论，以及Weyl半金属中无序诱导的量子相变。并与其他解析方法和数值方法的结果进行了比较。
Dirac and Weyl fermions appear as quasiparticle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In this paper we study the bosonized version of the standard Gross-Neveu model—the Gross-Neveu-Yukawa theory—at three-loop order, and compute critical exponents in 4−e dimensions for a general number of fermion flavors. Our results fully encompass the previously known two-loop calculations, and agree with the known three-loop results in the purely bosonic limit of the theory. We also find the exponents to satisfy the emergent superscaling relations in the limit of a single-component fermion, order by order up to three loops. Finally, we apply the computed series for the exponents and their Pade approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods is discussed.