Causer Luke, Garrahan Juan P, Lamacraft Austen
School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Phys Rev E. 2022 Jul;106(1-1):014128. doi: 10.1103/PhysRevE.106.014128.
The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground-state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPSs). The stochastic model displays slow dynamics, including power-law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations-which we compute accurately via numerical MPSs-including an active-inactive phase transition and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.
弗雷德金门自旋链是一个有趣的量子哈密顿量理论示例，其基态在三个不同相之间呈现相变，其中一个相违反面积律。在此，我们考虑弗雷德金模型的经典随机版本，它可被视为受附加动力学约束的简单排斥过程，并研究其经典随机动力学。量子链的基态相变意味着随机问题中的平衡相变，我们通过数值矩阵乘积态（MPS）对其性质进行量化。随机模型展现出缓慢动力学，包括幂律衰减自相关函数以及由于指数局域化导致的分层弛豫过程。与其他动力学约束模型一样，弗雷德金链在其动力学大偏差方面具有丰富结构——我们通过数值MPS精确计算——包括一个活跃 - 非活跃相变以及与模型特定平衡态相连的轨迹相层次结构。我们还通过其高度场表示，提出了弗雷德金模型在二维蜂窝晶格上的约束二聚体覆盖方面的推广。
