两带自由费米子链中的北极曲线与有隙气态相
Arctic Curves and a Gapped Gas Phase in a Two-Band Free-Fermion Chain
- Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文系）
- School of Physics and Astronomy, University of Birmingham（伯明翰大学物理与天文学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究分析了交错自由费米子链中畴壁态的虚时演化，确定了由北极曲线分隔的冻结、液态和气态相，并给出了精确的返回振幅和关联核。
AI中文摘要：
我们研究了交错自由费米子链中受约束返回自身的畴壁态的虚时演化。由此产生的时空轮廓分为冻结相、液态相和气态相，它们由称为北极曲线的尖锐边界分隔。谱隙产生了一个不可压缩的半填充气态相，由内部北极曲线界定，此外还有外部冻结-液态边界。我们确定了这两条北极曲线、热力学返回振幅以及完整的等时关联核。关联在液态区域呈代数衰减，在气态区域呈指数衰减，而两条北极边界均作为自由准粒子轨迹的焦散出现。返回振幅和关联核分别由同一块Toeplitz算子的行列式和逆控制。我们通过将问题简化为椭圆谱曲线上的标量Riemann-Hilbert问题，获得了该算子的精确矩阵Wiener-Hopf分解。该分解还给出了精确的热力学返回振幅：其对数由具有显式间隙依赖的二次项和有界周期theta函数修正组成。所得的冻结-液态-气态结构是双周期二聚体模型中所发现结构的连续时间自由费米子对应物。
英文摘要：
We study the imaginary-time evolution of a domain-wall state constrained to return to itself in a staggered free-fermion chain. The resulting space-time profile separates into frozen, liquid, and gas phases divided by sharp boundaries known as arctic curves. The spectral gap produces an incompressible half-filled gas phase bounded by an inner arctic curve, in addition to the outer frozen-liquid boundary. We determine both arctic curves, the thermodynamic return amplitude, and the complete equal-time correlation kernel. Correlations decay algebraically in the liquid regions and exponentially in the gas, while both arctic boundaries arise as caustics of free quasiparticle trajectories. The return amplitude and correlation kernel are respectively controlled by the determinant and inverse of the same block-Toeplitz operator. We obtain an exact matrix Wiener-Hopf factorization of this operator by reducing the problem to a scalar Riemann-Hilbert problem on an elliptic spectral curve. The factorization also yields the exact thermodynamic return amplitude: its logarithm consists of a quadratic term with explicit gap dependence and a bounded periodic theta-function correction. The resulting frozen-liquid-gas structure is a continuous-time free-fermion counterpart of that found in doubly periodic dimer models.
