非抛物导带中极子的解析处理
Extending the Feynman variational principle and analytical methods to lattice polarons
AI总结：
本文提出了一种改进的费曼变分法，用于非抛物导带中极子的解析处理，展示了其在不同耦合强度下的准确性和适用性。
摘要：
我们开发并比较了几种解析近似方法，用于有限宽度、非抛物导带中的极子问题。本研究的重点是将费曼变分法扩展到紧束缚晶格中，其中有效质量近似不再适用。所得到的变分公式不局限于特定的声子色散或电子-声子相互作用，并为弱耦合、中等耦合和强耦合区域提供了统一的描述。我们重新审视并推广了传统用于连续极子的其他解析方法，包括规范变换和自洽的威格纳-布里渊型近似。对于晶格极子，这些方法表现出连续情况中没有的定性特征，如弱耦合和强耦合极限之间的非平凡联系。我们证明，改进的威格纳-布里渊方案产生了一个无谐振的动量依赖极子自能，并在布里渊区内的整个动量范围内与数值精确结果一致。所有方法都应用于霍尔stein模型，并与数值精确计算进行基准测试，包括图示蒙特卡洛（我们的计算和先前工作）、精确对角化和密度矩阵重整化群结果。解析方法被扩展到具有拉沙类型自旋-轨道耦合的极子，提供了对具有非平凡带结构系统适用性的严格测试。我们的结果表明，修改的费曼变分法得到的基态能量和色散关系的精度与，甚至在许多情况下超过，其他已建立的解析方法。所发展的框架为超越连续近似的晶格极子提供了灵活且可靠的解析描述。
英文摘要：
We develop and compare several analytical approximations for the ground state and zero-temperature polaron dispersion in finite-width, nonparabolic conduction bands. The main focus of the work is an extension of the Feynman variational method to a tight-binding lattice, where the effective-mass approximation is no longer applicable. The resulting variational formulation is not restricted to a specific phonon dispersion or electron-phonon interaction and provides a uniform description across weak-, intermediate-, and strong-coupling regimes. In addition, we revisit and generalize other analytical approaches traditionally formulated for continuum polarons, including canonical transformations and self-consistent Wigner-Brillouin-type approximations. For lattice polarons, these methods exhibit qualitative features absent in the continuum case, such as a nontrivial connection between weak- and strong-coupling limits. We show that an improved Wigner-Brillouin scheme yields a momentum-dependent polaron self-energy free of resonances and in good agreement with numerically exact results. All methods are applied to the Holstein model on a tight-binding lattice and are benchmarked against numerically exact calculations, including diagrammatic Monte Carlo (both our calculations and preceding works) and exact diagonalization results. Furthermore, the analytical approaches are extended to polarons with Rashba-type spin-orbit coupling, providing a stringent test of their applicability in systems with nontrivial band structure. Our results demonstrate that the modified Feynman variational method yields ground-state energies and dispersions with accuracy comparable to, and in many cases exceeding, that of other established analytical approaches. The developed framework offers a versatile and reliable analytical description of lattice polarons beyond the continuum approximation.
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