2025/01/02 by Myung-Hoon Chung, Chung, Myung-Hoon
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2501.01098
openalex publication_date 2025/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network. The tensor has a different symmetry property for ferromagnets and antiferromagnets. The tensor network of the partition function is interpreted as a multiple product of the one-dimensional quantum Hamiltonian. We perform infinite density matrix renormalization group to contract the two-dimensional tensor network. We present the numerical result of magnetization and entanglement entropy for the Ising ferromagnet and antiferromagnet side by side. In order to determine the critical line in the parameter space of temperature and magnetic field, we use the half-chain entanglement entropy of the one-dimensional quantum state. The entanglement entropy precisely indicates the critical line forming the parabolic shape for the antiferromagnetic case, but shows the critical point for the ferromagnetic case.