Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions

TL;DR

The paper introduces a novel tensor network renormalization method, TTNR, that accurately extracts conformal field theory data at thermal transitions in 2D quantum systems, offering an efficient phase transition analysis.

Contribution

It develops a global optimization-based TNR scheme and a new finite-temperature density matrix construction, forming the TTNR algorithm for improved thermal transition analysis.

Findings

Accurately extracts CFT data at thermal transition points.

Provides an efficient alternative to critical exponent analysis.

Enhances numerical identification of phase transitions.

Abstract

We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a new algorithm called thermal tensor network renormalization (TTNR), we obtain highly accurate conformal field theory (CFT) data at thermal transition points. This provides a new and efficient route for numerically identifying phase transitions, offering an alternative to the conventional analysis via critical exponents.