Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria.
Phys Rev Lett. 2011 Oct 21;107(17):170402. doi: 10.1103/PhysRevLett.107.170402. Epub 2011 Oct 19.
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum state such that the reduced density operator behaves as the thermal state of the classical system. We show that all these quantum states are unique ground states of a universal 5-body local quantum Hamiltonian acting on a (polynomially enlarged) qubit system on a 2D lattice. The only free parameters of the quantum Hamiltonian are coupling strengths of two-body interactions, which allow one to choose the type and dimension of the classical model as well as the interaction strength and temperature. This opens the possibility to study and simulate classical spin models in arbitrary dimension using a 2D quantum system.
我们建立了局域量子哈密顿量的基态和经典自旋系统的热态之间的联系。对于任意空间维度的离散经典统计力学模型，我们都找到了一个与之相关的量子态，使得约化密度算符表现为经典系统的热态。我们证明了所有这些量子态都是作用在二维格点上的（多项式扩大的）qubit 系统上的通用五体局域量子哈密顿量的唯一基态。量子哈密顿量的唯一自由参数是两体相互作用的耦合强度，这允许人们选择经典模型的类型和维度以及相互作用强度和温度。这为使用二维量子系统研究和模拟任意维度的经典自旋模型提供了可能性。
