High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

TL;DR

The paper introduces a tensor renormalization-group method that accurately computes thermodynamic and critical properties of lattice models, achieving high precision and systematic convergence for the ferromagnetic triangular lattice Ising model.

Contribution

It presents a novel tensor RG approach that improves precision and convergence over previous methods for analyzing phase diagrams and critical phenomena.

Findings

Free energy calculated with high accuracy across all temperatures.

Systematic convergence achieved with tensor index range D=24.

Critical exponents and thermodynamic functions derived from tensor flows.

Abstract

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.