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 two-dimensional 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. \textbf{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 $J_1-J_2$ Ising model and find good agreement.

9 pages, 4 figures, 2 tables. v2: updated figure for clarity and fixed reference typos. v3: improved data. v4: expanded intro., more data/figures. v5: added appendix

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Cited by in corpus (2)

• Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model