In this work we propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of equilibrium density operator $e^{-βH}$ (with $H$ the total Hamiltonian and $β$ the imaginary time), and is thus Trotter-error free. We discover, through simulating XXZ spin chain and square-lattice quantum Ising models, that not only the Hamiltonian $H$, but also its powers $H^n$, can be efficiently expressed as matrix product operators, which enables us to calculate with high precision the equilibrium and dynamical properties of quantum lattice models at finite temperatures. Our SETTN method provides an alternative to conventional Trotter-Suzuki renormalization group (RG) approaches, and achieves an unprecedented standard of thermal RG simulations in terms of accuracy and flexibility.
Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion
球张量展开进行表示的共振非弹性散射截面的总和的产品的基本光谱与张量涉及波矢量和偏振矢量的入射和散射光子。本文提出的表达式不同于Carra等人的有影响力的文章（Phys. Rev. Lett. 74，3700，1995），因为当将每个光子耦合到其自身时，它没有省略电偶极子和四极贡献之间的干涉项。讨论了球面张量展开的一些特殊情况。例如，各向同性样品的情况下被认为是和横截面表示为只有三个基本光谱的组合的情况下，电偶极子或电四极跃迁的吸收过程中，其次是电偶极子跃迁的发射。这种情况包括无纹理粉末样品的情况，这对应于实验中遇到的最常见的情况。最后，它是预测，一些圆二色性可以观察到各向同性的样品提供的散射光束的圆偏振可以检测。
