Essler Fabian H L, Piroli Lorenzo
The Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3PU, United Kingdom.
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
Phys Rev E. 2020 Dec;102(6-1):062210. doi: 10.1103/PhysRevE.102.062210.
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 dimensions.
我们引入了一族描述开放多粒子量子系统的一维林德布拉德方程，这些方程在以下意义下是精确可解的：(i) 算符空间分解为指数级多个（与系统大小相关）在耗散演化下保持不变的子空间；(ii) 每个不变子空间上密度矩阵的时间演化由一个可积哈密顿量描述。典型例子是不对称简单排斥过程（ASEP）的量子版本，我们对其进行了详细分析。我们表明，在每个不变子空间中，动力学是根据具有开放或扭曲边界条件的可积自旋 - 1/2 XXZ 海森堡链来描述的。我们进一步证明，在具有任意局部物理维度的自旋链中都可以找到具有可积算符空间碎片化特征的林德布拉德算符。
