Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain

TL;DR

This paper enhances the Matrix Product Operator Renormalization Group method to improve accuracy and applicability, enabling better analysis of phase transitions in complex disordered quantum spin chains.

Contribution

The authors propose two simple, fast improvements to MPO-RG, significantly increasing accuracy and revealing phase transition types in the N-color random Ashkin-Teller chain.

Findings

Ground state energy accuracy improved by at least a factor of 4.

MPO-RG can distinguish between first- and second-order phase transitions.

Enhanced MPO-RG yields results consistent with a second-order transition in the Ashkin-Teller chain.

Abstract

Strong-Disorder Renormalization Group (SDRG), despite being a relatively simple real-space renormalization procedure, provides in principle exact results on the critical properties at the infinite-randomness fixed point of random quantum spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities of finite chains that are inaccessible to SDRG. In this work, the accuracy of this approach is studied and two simple and fast improvements are proposed. The accuracy on the ground state energy is improved by a factor at least equal to 4 for the random Ising chain in a transverse field. Finally, the proposed algorithms are shown to yield Binder cumulants of the 3-color random Ashkin-Teller chain that are compatible with a second-order phase transition while a first-order one is predicted by the original MPO-RG algorithm.