Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfuids
Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfuids
复制标题
多组分费米子超流体的非相对论Banks-Casher关系和随机矩阵理论
DOI：
10.1103/physrevd.93.016010
复制
发表时间：
2016
影响因子：
5
通讯作者：
Arata Yamamoto
中科院分区：
文献类型：
--
作者：
Takuya Kanazawa;Arata Yamamoto
我们应用QCD激发的技术来研究具有吸引相互作用的非相对论成分简并费米子。通过分析拉格朗日中费米子矩阵的奇值谱，我们得到了表征自发对称性突破双费米子凝聚的几个精确关系式。这是QCD中Banks-Casher关系和Smilga-Stern关系的非相对论类比。还引入了非局域有序参数，并导出了它们的谱表示，由此得到了相图上的一个非平凡约束。推导了软集体激发的有效理论，并证明了它与随机矩阵理论的等价性。我们在蒙特卡洛模拟中数值证实了上述分析预测。
We apply QCD-inspired techniques to study nonrelativistic-component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breakingthrough bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in theregime. We numerically confirm the above analytical predictions in Monte Carlo simulations.