论文标题
相对论密度矩阵重新归一化算法中的时间反转对称性适应
Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm
论文作者
论文摘要
在非递归的schrödinger方程中，总旋转$ S $和旋转投影$ m $是良好的量子数。相比之下，在存在自旋依赖性相互作用的情况下，诸如相对论汉密尔顿相对论的旋转耦合的存在，旋转对称性会丢失。相对论密度矩阵重新归一化算法（R-DMRG）的先前实现仅使用粒子数对称性比非依赖性DMRG贵得多。此外，在具有奇数电子的系统的处理中，Kramers变性的人工破裂可能会发生。为了克服这些问题，我们引入了R-DMRG的时间反转对称性适应。由于时间反转操作员是反独立的，因此不能简单地以通常的方式实现。我们定义了一个时间反向对称适应的重新归一化基础，并呈现策略，以维持扫描优化期间基础功能的结构。随着时间反转对称性的适应，仅需要一半的重新归一化操作员，并且哈密顿波功能乘法和重新归一化的计算成本减少了一半。当前的时间反转对称基准的构建也直接适用于没有循环的其他张量网络状态。
In the nonrelativistic Schrödinger equation, the total spin $S$ and spin projection $M$ are good quantum numbers. In contrast, spin symmetry is lost in the presence of spin-dependent interactions such as spin-orbit couplings in relativistic Hamiltonians. Previous implementations of relativistic density matrix renormalization group algorithm (R-DMRG) only employing particle number symmetry are much more expensive than nonrelativistic DMRG. Besides, artificial breaking of Kramers degeneracy can happen in the treatment of systems with odd number of electrons. To overcome these issues, we introduce time-reversal symmetry adaptation for R-DMRG. Since the time-reversal operator is antiunitary, this cannot be simply achieved in the usual way. We define a time-reversal symmetry-adapted renormalized basis and present strategies to maintain the structure of basis functions during the sweep optimization. With time-reversal symmetry adaptation, only half of the renormalized operators are needed and the computational costs of Hamiltonian-wavefunction multiplication and renormalization are reduced by half. The present construction of time-reversal symmetry-adapted basis also directly applies to other tensor network states without loops.
