论文标题
与对称性的计算浮动汉密尔顿人
Computing Floquet Hamiltonians with Symmetries
论文作者
论文摘要
单一矩阵在物理学上以许多方式出现，尤其是作为时间演化操作员。对于定期驱动的系统，人们经常希望计算一个应该是Hermitian操作员$ h $的floquet hamilonian，这样$ e^{ - ith} = u（t）$，其中$ u（t）$是与系统期间相关的时间演变运算符。也就是说，我们希望$ h $等于$ u（t）$的矩阵对数$ -i $ times。如果该系统具有对称性，例如时间逆转对称性，则可以期望$ h $具有对称性，而不仅仅是隐居。 我们在这里讨论具有某些对称性的矩阵对数计算矩阵对数的实用数值算法，这些算法可用于计算具有适当对称性的Floquet Hamiltonians。一路上，我们证明了一些结果，即Floquet Operator $ u（t）$中的对称性如何在Floquet Eigenstates的基础上导致对称性。
Unitary matrices arise in many ways in physics, in particular as a time evolution operator. For a periodically driven system one frequently wishes to compute a Floquet Hamilonian that should be a Hermitian operator $H$ such that $e^{-iTH}=U(T)$ where $U(T)$ is the time evolution operator at time corresponding the period of the system. That is, we want $H$ to be equal to $-i$ times a matrix logarithm of $U(T)$. If the system has a symmetry, such as time reversal symmetry, one can expect $H$ to have a symmetry beyond being Hermitian. We discuss here practical numerical algorithms on computing matrix logarithms that have certain symmetries which can be used to compute Floquet Hamiltonians that have appropriate symmetries. Along the way, we prove some results on how a symmetry in the Floquet operator $U(T)$ can lead to a symmetry in a basis of Floquet eigenstates.
