Probing universal critical scaling with scan-DMRG

TL;DR

This paper demonstrates that scan-DMRG effectively captures universal critical scaling in quantum chains, providing high-quality data collapses and revealing universal behaviors with lower computational costs.

Contribution

It introduces the application of scan-DMRG to extract universal critical signatures across various quantum models and transitions, showing its efficiency and broad applicability.

Findings

Successful data collapse for order parameter and entanglement entropy in three models

Universal scaling of lowest excitation energy with gradient rate

Scan-DMRG captures critical behavior across multiple quantum phase transitions

Abstract

We explore the universal signatures of quantum phase transitions that can be extracted with the density matrix renormalization group (DMRG) algorithm applied to quantum chains with a gradient. We present high-quality data collapses for the order parameter and for the entanglement entropy for three minimal models: transverse-field Ising, 3-state Potts and Ashkin-Teller. Furthermore, we show that scan-DMRG successfully captures the universal critical scaling when applied across the magnetic Wess-Zumino-Witten and non-magnetic Ising transitions in the frustrated Haldane chain. In addition, we report a universal scaling of the lowest excitation energy as a function of a gradient rate. Finally, we argue that the scan-DMRG approach has significantly lower computational cost compare to the conventional DMRG protocols to study quantum phase transitions.