论文标题
量子旋转链的实时模拟：状态密度和重新加权方法
Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
论文作者
论文摘要
我们通过将其应用于最坏可能的符号问题的物理问题，将蒙特卡洛（MC）模拟的密度（DOS）方法置于压力测试下：不可综合的量子自旋链的实时演变。提出了针对数值精确对角度化和随机重新加权的基准。两种MC方法，即DOS方法和重新加权，都可以模拟旋转链的模拟，只要$ L = 40 $，远远超出了确切的对角度，尽管仅适用于短进化时间$ t \ lyssim 1 $。我们将状态密度的不连续性确定为MC模拟中的关键问题之一，并建议通过分析来计算一些主要贡献，从而将模拟的精度提高了几个数量级。即使在这些改进之后，状态的密度也被发现高度不平滑，因此DOS方法不能超过重新加权。我们从理论上证明了这一含义，并提供了数值证据，得出的结论是，DOS方法不太适合具有离散自由度的量子实时模拟。
We put the Density-of-States (DoS) approach to Monte-Carlo (MC) simulations under a stress test by applying it to a physical problem with the worst possible sign problem: the real time evolution of a non-integrable quantum spin chain. Benchmarks against numerical exact diagonalisation and stochastic reweighting are presented. Both MC methods, the DoS approach and reweighting, allow for simulations of spin chains as long as $L=40$, far beyond exact diagonalisability, though only for short evolution times $t\lesssim 1$. We identify discontinuities of the density of states as one of the key problems in the MC simulations and propose to calculate some of the dominant contributions analytically, increasing the precision of our simulations by several orders of magnitude. Even after these improvements the density of states is found highly non-smooth and therefore the DoS approach cannot outperform reweighting. We prove this implication theoretically and provide numerical evidence, concluding that the DoS approach is not well suited for quantum real time simulations with discrete degrees of freedom.
