基于热场双的有限温度格林函数团簇展开：极化子图像的崩溃
Finite-temperature Green's function cluster expansion from thermofield doubles: Breakdown of the polaron picture
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中文总结 AI 辅助
本文提出基于热场双的有限温度格林函数团簇展开方法，数值精确计算有限温度极化子的动量频率分辨格林函数，经一维Holstein极化子基准测试，结果与有限温度密度矩阵重整化群定量一致，可直接在频率空间恢复动量分辨谱。
中文摘要 AI 辅助
我们提出了一种原则上数值精确的方法，用于计算有限温度下极化子的动量与频率分辨单粒子格林函数。该方法称为有限温度格林函数团簇展开，结合了两个要素：广义格林函数团簇展开，这是动量平均方法族的数值精确扩展，通过受限声子云构型的运动方程层级求解零温度下的极化子问题；以及热场双形式，其将热迹映射到双希尔伯特空间上的纯态期望值。所得运动方程具有与多玻色子零温度理论相同的代数结构，温度通过玻戈留波夫型混合角引入，该角度控制与一组虚构浴玻色子的耦合。我们在开源软件包中实现了该方法，并在一维Holstein极化子上进行基准测试，计算了从耦合 regime 到温度高达T/Ω ~ 1范围内的谱函数、色散、寿命和有效质量。在有有限温度密度矩阵重整化群结果的地方，我们以可承受的计算成本发现了定量一致性。该方法直接在频率空间恢复动量分辨谱，无需时间演化或解析延拓。我们还讨论了该方法的实际成本，特别是由于双声子希尔伯特空间具有真实云与虚构云竞争的非平凡构型结构，对应云参数的收敛需要谨慎处理。
英文摘要
We introduce a method, numerically exact in principle, for computing the momentum- and frequency-resolved single-particle Green's function of a polaron at finite temperature. The method, which we refer to as the finite-temperature Green's function cluster expansion, combines two ingredients: the generalized Green's function cluster expansion, a numerically exact extension of the momentum average family of methods that solves the polaron problem at zero temperature through a hierarchy of equations of motion for restricted phonon cloud configurations; and the thermofield double formalism, which maps the thermal trace onto a pure-state expectation value over a doubled Hilbert space. The resulting equations of motion have the same algebraic structure as those of the multi-boson zero-temperature theory, with the temperature entering through a Bogoliubov-type mixing angle that controls the coupling to a set of fictitious bath bosons. We implement the method in our open-source software package and benchmark it on the one-dimensional Holstein polaron, computing spectral functions, dispersions, lifetimes, and effective masses across coupling regimes and temperatures up to $T/Ω\sim 1$. Where finite-temperature density matrix renormalization group results are available, we find quantitative agreement at affordable computational cost. The method recovers momentum-resolved spectra directly in frequency space, with no time evolution or analytic continuation. We also discuss the practical costs of the approach. In particular, since the doubled phonon Hilbert space has a non-trivial configuration structure in which real and fictitious clouds compete, convergence in the corresponding cloud parameters requires care.
