Integrable Trotterization: Local Conservation Laws and Boundary Driving
Integrable Trotterization: Local Conservation Laws and Boundary Driving
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DOI：
10.1103/physrevlett.121.030606
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发表时间：
2018-07-20
影响因子：
8.6
通讯作者：
Prosen, Tomaz
中科院分区：
文献类型：
--
作者：
Vanicat, Matthieu;Zadnik, Lenart;Prosen, Tomaz
我们讨论了构建交互晶格模型的可积实时 Trotterization 的一般过程。作为说明性示例，我们考虑一个自旋 1/2 链，其具有由各向同性 (XXX) 海森堡哈密顿量描述的连续时间动力学。对于周期性边界条件，从非齐次传递矩阵导出局部守恒定律，并构造boost算子。在连续时间限制内，这些局部电荷减少到海森堡链的已知运动积分。在简单的克劳斯表示中，我们还检查了非平衡设置，其中我们的可积元胞自动机由边界处的随机过程驱动。我们明确地展示了如何用交错矩阵乘积 ansatz 来编写精确的非平衡稳态密度矩阵，并且我们提出了具有周期性边界条件的模型的拟局域守恒定律。这种简单的 Trotterization 方案，特别是在开放系统框架中，可能被证明是在捕获离子和原子光学设置方面对晶格模型进行实验模拟的有用工具。
We discuss a general procedure to construct an integrable real-time Trotterization of interacting lattice models. As an illustrative example, we consider a spin-1/2 chain, with continuous time dynamics described by the isotropic (XXX) Heisenberg Hamiltonian. For periodic boundary conditions, local conservation laws are derived from an inhomogeneous transfer matrix, and a boost operator is constructed. In the continuous time limit, these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation, we also examine the nonequilibrium setting, where our integrable cellular automaton is driven by stochastic processes at the boundaries. We show explicitly how an exact nonequilibrium steady-state density matrix can be written in terms of a staggered matrix product ansatz, and we propose quasilocal conservation laws for the model with periodic boundary conditions. This simple Trotterization scheme, in particular in the open system framework, could prove to be a useful tool for experimental simulations of the lattice models in terms of trapped ion and atom optics setups.