论文标题
$ 1D $ lindbladians从操作员空间碎片化的集成性
Integrability of $1D$ Lindbladians from operator-space fragmentation
论文作者
论文摘要
我们介绍了一维Lindblad方程的家庭，描述了开放的多个粒子量子系统，这些系统可以从下面的意义上完全解决：$（i）$操作员的空间分散到指数的（系统大小）子空间中，这些子空间在耗散进化下剩下不变； $（ii）$ $（II）在每个不变子空间上密度矩阵的时间演变由一个可集成的哈密顿人描述。原型示例是不对称简单排除过程（ASEP）的量子版本，我们对此进行了详细分析。我们表明，在每个不变子空间中，动力学是用具有开放或扭曲边界条件的可集成的自旋1/2 XXZ海森贝格链来描述的。我们进一步证明，可以在具有任意局部物理维度的旋转链中找到具有可集成操作员空间碎片的lindbladians。
We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: $(i)$ the space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; $(ii)$ the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimension.
