发表机构
Leibniz Universität Hannover; University of Western Ontario（汉诺威莱布尼茨大学; 韦仕敦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出双正交含时变分原理，用于非厄米量子多体系统实时动力学，通过耦合截断避免配对奇异，并应用于远程非厄米Ising链，揭示双正交动力学量子相变及虚数场对临界时间的影响。
AI 中文摘要
我们为非厄米量子多体系统的实时动力学发展了一种双正交含时变分原理。独立的左、右矩阵乘积态满足耦合的双变分切空间方程，其交叉Gram矩阵定义了一个斜投影。一种无矩阵的缩放泰勒作用量传播了由此产生的非正规局部生成元，而无需组装稠密矩阵或存储Krylov基。我们区分了完全耦合算法（该算法解决交叉配对问题并联合截断两个键基）与用于大型系统的高效独立传播近似。独立截断可能使保留的左右配对近乎奇异；重叠漂移和键交叉矩阵的最小奇异值暴露了这一失败，而耦合截断则显著延迟了它。精确基准测试和收敛性测试验证了该方法。应用于相互作用的远程非厄米Ising链时，它解析了一个双正交动力学量子相变，并表明弱虚数场将主临界时间从$t^{\ast}|J|=1.84$移至$1.04$。
英文摘要
We develop a biorthogonal time-dependent variational principle for real-time dynamics of non-Hermitian quantum many-body systems. Independent left and right matrix-product states obey coupled bivariational tangent-space equations whose cross-Gram matrix defines an oblique projection. A matrix-free scaled Taylor action propagates the resulting non-normal local generators without assembling dense matrices or storing a Krylov basis. We distinguish the fully coupled algorithm, which solves the cross-pairing problem and truncates the two bond bases jointly, from an efficient independently propagated approximation used for large systems. Independent truncation can make the retained left-right pairing nearly singular; overlap drift and the smallest singular value of the bond cross matrix expose this failure, while coupled truncation substantially delays it. Exact benchmarks and convergence tests validate the method. Applied to an interacting long-range non-Hermitian Ising chain, it resolves a biorthogonal dynamical quantum phase transition and shows that a weak imaginary field shifts the leading critical time from $t^{\ast}|J|=1.84$ to $1.04$.
