论文标题
与配对相互作用的1D手性费米：从集成到混乱的过渡
Interacting 1D Chiral Fermions with Pairing: Transition from Integrable to Chaotic
论文作者
论文摘要
我们通过精确的对角线化研究了两种口味（伪短蛋白）手性复合物的通用一二维量量子模型，该模型可以具有局部互相相互作用和超导配对（忽略了所有不相关的术语）。从分析上讲，该模型在参数空间中具有两个可溶解（可以集成的）点：当fermion相互作用为零时，它是一个自由的费米子模型，并且当有一个全局u（1）$^{（\ uparrow）} \ times} \ times $ u（1）$ u（1）$^（1）$^{（\ downarrow）$ symementry时，是一个免费的玻色子luttinger液体。当通过打开对称性破坏参数来降低相互作用模型的全局对称性时，该模型经历了从量子积分模型到完全量子混沌模型的过渡，正如我们通过检查多体能量谱的水平间距统计量（LSS）所证明的那样。特别是，可能有一个具有中间全局对称性的可集成的态度，该模型既不是自由玻色子也不是免费的费米子，而是在每个全局对称性电荷部门中显示泊松LSS。这意味着隐藏的（准）局部保守数量的存在。当进一步降低全局对称性时，每个电荷扇区中的LSS变成Wigner-dyson，这意味着量子混乱。
We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization, which can have local interflavor interaction and superconducting pairings (with all irrelevant terms ignored). Analytically, the model has two solvable (integrable) points in the parameter space: it is a free fermion model when the fermion interaction is zero, and is a free boson Luttinger liquid when there is a global U(1)$^{(\uparrow)}\times$U(1)$^{(\downarrow)}$ symmetry (with nonzero interaction). When the global symmetry of the interacting model is lowered by turning on symmetry breaking parameters, the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model, as we demonstrate by examining the level spacing statistics (LSS) of the many-body energy spectrum. In particular, there is a possibly integrable regime with intermediate global symmetries, where the model is neither free bosons nor free fermions, but shows Poisson LSS in each global symmetry charge sector. This implies the existence of hidden (quasi)local conserved quantities. When the global symmetries are further lowered, the LSS in each charge sector becomes Wigner-Dyson, implying quantum chaos.
