Landa Haggai, Schiró Marco, Misguich Grégoire
Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France.
JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France.
Phys Rev Lett. 2020 Jan 31;124(4):043601. doi: 10.1103/PhysRevLett.124.043601.
We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the mean-field limit of these models manifests multistable parameter regions of coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to mean field by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product operators in one- and two-dimensional lattices. Correlations are shown to wash the mean-field bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible, provided the thermodynamic limit of an infinitely large lattice is taken first with respect to the longtime limit. Variation of the system parameters results in jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics.
我们研究了由相干驱动并受耗散作用的自旋为1/2的量子自旋晶格模型的动力学。一般来说，这些模型的平均场极限表现出具有不同磁化强度的共存稳态的多稳态参数区域。我们引入了一种有效的方案，通过领先阶的关联来考虑对平均场的修正，并使用基于一维和二维晶格中的矩阵乘积算符的高精度数值方法对该方案进行基准测试。结果表明，在一维中，关联消除了平均场双稳性，导致唯一的稳态。在二维及更高维度中，我们发现只要首先对无限大晶格取热力学极限相对于长时间极限，多稳态再次是可能的。系统参数的变化会导致不同稳态之间的跳跃，每个稳态在微扰向稳态收敛时都表现出临界减慢。捕获离子的实验可以实现该模型，并可能回答这些量子系统非平衡多体动力学中目前数值方法可及系统尺寸之外的开放性问题。
