SU($N$)费米子系统中识别无能隙的扭转变换算符方法
Twisting-operator approach to identifying gaplessness in SU($N$) fermionic systems
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中文总结 AI 辅助
研究提出SU(2)自旋旋转对称有自旋费米子链有能隙的必要条件，通过扭转变换算符期望值在热力学极限下是否为1来判断。用BCS哈密顿量和DQMC模拟证实，还扩展到SU($N$)对称费米子系统，为识别无能隙费米子链提供方法。
中文摘要 AI 辅助
我们提出了具有SU(2)自旋旋转对称性的有自旋费米子链为有能隙的一般必要条件。具体而言，我们证明在任何具有有限基态简并度的有能隙相中，适当定义的费米子扭转变换算符的期望值渐近趋近于1，有限尺寸修正由$\mathscr{O}(1/L)$界定。因此，在热力学极限下非单位值为识别无能隙费米子链提供了充分标准。我们用$s$波巴丁 - 库珀 - 施里弗（BCS）哈密顿量和相互作用哈伯德模型的行列式量子蒙特卡罗（DQMC）模拟证实了该标准。我们还将扭转变换算符方法扩展到SU($N$)对称费米子系统，其中有能隙基态扇区必须是SU($N$)单重态，且通过适当选择整数$M$的费米子扭转变换算符$\hat{\mathcal{U}}$，$\langle \hat{\mathcal{U}}^M\rangle=1+\mathscr{O}(1/L)$。
英文摘要
We propose a general necessary condition for a spinful fermion chain with SU(2) spin-rotation symmetry to be gapped. Specifically, we prove that the expectation value of a properly defined fermionic twisting operator asymptotically approaches unity in any gapped phase with finite ground-state degeneracy, with finite-size corrections bounded by $\mathscr{O}(1/L)$. Consequently, a non-unity value in the thermodynamic limit provides a sufficient criterion for identifying gapless fermion chains. We confirm this criterion using the $s$-wave Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and determinant quantum Monte Carlo (DQMC) simulations of interacting Hubbard models. We further extend the twisting-operator approach to SU($N$)-symmetric fermionic systems, where the gapped ground-state sector must be SU($N$)-singlet and $\langle \hat{\mathcal{U}}^M\rangle=1+\mathscr{O}(1/L)$ by a fermionic twisting operator $\hat{\mathcal{U}}$ with a suitably chosen integer $M$.
