Phase boundary location with information-theoretic entropy in tensor renormalization group flows

Abstract

We present a simple and efficient tensor network method to accurately locate phase boundaries of twodimensional classical lattice models. The method utilizes only the information-theoretic (von Neumann) entropy of quantities that automatically arise along tensor renormalization group [Phys. Rev. Lett. 12, 120601 (2007)] flows of partition functions. We benchmark the method against theoretically known results for the square-lattice q-state Potts models, which includes first-order, weakly first-order, and continuous phase transitions, and find good agreement in all cases. We also compare against previous Monte Carlo results for the frustrated square lattice J1 − J2 Ising model and find good agreement. arXiv:1901.08193v5 [cond-mat.stat-mech]

Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice

“…The tensor network algorithms we adopt can approach the thermodynamic limit. Recently, it was applied to calculate J 1 -J 2 frustrated model [31], and fix the Berezinskii-Kosterlitz-Thouless phase transition in the classical clock model [32]. The tensor renormalization group performed well in the spin glass model [33].…”