AI 中文总结
本文通过推广动量平均近似，求解二维、三维极化子相干性的温度演化，发现普适热崩溃尺度，结果与高精度数值方法吻合，拓展了Holstein的理论适用范围。
AI 中文摘要
极化子如何随温度升高失去其准粒子相干性是一个长期存在的开放问题。Holstein在1959年仅在极端反绝热、强耦合极限下对该问题进行了研究，而近期的数值精确方法大多局限于一维情形。本文在正方晶格和简单立方晶格上，针对弱耦合、中间耦合和强耦合 regimes（耦合 regime）求解了该问题。研究表明，极化子有效质量$m^*$和逆寿命$1/\tau$随温度单调增加，直至在$T \thicksim 0.5\\\\,\Omega$时，准粒子峰分解为宽的非相干热连续谱。因此，声子频率$\boldsymbol{\Omega}$定义了一个与维度和耦合强度无关的普适相干尺度，这验证了Holstein的预测在其推导的 regime 之外仍有效。这些结果源于动量平均（Momentum Average, MA）近似的有限温度推广，得到了一个通过图论推导的自能，该自能在所有温度下的强耦合极限中渐近精确。基准比较表明，所得一维谱函数与数值精确的变分精确对角化-有限温度 Lanczos 方法（Variational Exact Diagonalization-Finite-Temperature Lanczos Method, VED-FTLM）和有限温度密度矩阵重整化群（finite-$T$ Density Matrix Renormalization Group, DMRG）的结果具有出色的定量一致性。
英文摘要
How a polaron loses its quasiparticle coherence with increasing temperature is a long-standing open problem. Holstein addressed it in 1959 only in the extreme antiadiabatic, strong-coupling limit, while more recent numerically exact approaches are largely restricted to one dimension. Here we solve this problem on square and simple cubic lattices across the weak-, intermediate-, and strong-coupling regimes. We show that the polaron effective mass $m^*$ and inverse lifetime $1/τ$ increase monotonically with temperature until, at $T \sim 0.5\,Ω$, the quasiparticle peak dissolves into a broad incoherent thermal continuum. The phonon frequency $Ω$ therefore defines a universal coherence scale, independent of dimensionality and coupling strength, validating Holstein's prediction far beyond the regime in which it was derived. These results follow from a finite-temperature generalization of the Momentum Average (MA) approximation, yielding a closed-form, diagrammatically derived self-energy that is asymptotically exact in the strong-coupling limit at all temperatures. Benchmark comparisons demonstrate excellent quantitative agreement of the resulting 1D spectral functions with the numerically exact Variational Exact Diagonalization-Finite-Temperature Lanczos Method (VED-FTLM) and finite-$T$ Density Matrix Renormalization Group (DMRG).
Comments8 pages, 5 figures (main text, including End Matter); Supplemental Material: 14 pages, 17 figures. Dataset available at https://doi.org/10.5683/SP4/LYHBP7
