Tensor network investigation of the hard-square model

Abstract

Using the corner-transfer matrix renormalization group to contract the tensor network that describes its partition function, we investigate the nature of the phase transitions of the hard-square model, one of the exactly solved models of statistical physics for which Baxter has found an integrable manifold. The motivation is twofold: assess the power of tensor networks for such models, and probe the 2D classical analog of a 1D quantum model of hard-core bosons that has recently attracted significant attention in the context of experiments on chains of Rydberg atoms. Accordingly, we concentrate on two planes in the 3D parameter space spanned by the activity and the coupling constants in the two diagonal directions. We first investigate the only case studied so far with Monte Carlo simulations, the case of opposite coupling constants. We confirm that, away and not too far from the integrable 3-state Potts point, the transition out of the period-3 phase appears to be unique in the Huse-Fisher chiral universality class, albeit with significantly different exponents as compared to Monte Carlo. We also identify two additional phase transitions not reported so far for that model, a Lifshitz disorder line, and an Ising transition for large enough activity. To make contact with 1D quantum models of Rydberg atoms, we then turn to a plane where the ferromagnetic coupling is kept fixed, and we show that the resulting phase diagram is very similar, the only difference being that the Ising transition becomes first-order through a tricritical Ising point, in agreement with Baxter's prediction that this plane should contain a tricritical Ising point, and in remarkable, almost quantitative agreement with the phase diagram of the 1D quantum version of the model.

References in corpus (15)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Corner Transfer Matrix Renormalization Group Method
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Competing density-wave orders in a one-dimensional hard-boson model
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Quantum field theory for the chiral clock transition in one spatial dimension
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Floating phase versus chiral transition in a 1D hard-boson model
• Critical Exponents of the Chiral Potts Model from Conformal Field Theory
• Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
• Commensurate-incommensurate transition in the chiral Ashkin-Teller model
• Identifying the Huse-Fisher universality class of the three-state chiral Potts model

Cited by in corpus (2)

• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• CTMRG study of the critical behavior of an interacting-dimer model