Adaptive Density Matrix Renormalization Group for Disordered Systems

TL;DR

This paper introduces an adaptive DMRG method tailored for strongly disordered quantum spin chains, enabling larger system sizes and more accurate analysis of disordered ground states, including novel findings on SU(3) chains.

Contribution

The paper presents a simple adaptive modification to DMRG that improves performance on disordered systems and extends understanding of universal properties in SU(N) random-singlet states.

Findings

The adaptive DMRG reaches larger system sizes in disordered regimes.

The mean correlation function in SU(3) chains decays algebraically with exponent 2.

Numerical and analytical RG confirm the universality of the decay exponent.

Abstract

We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach larger system sizes in the strong disorder limit by avoiding most of the metastable configurations which hinder the performance of the standard DMRG method. We benchmark our adaptive method by revisiting the random antiferromagnetic XXZ spin-1/2 chain for which we compute the random-singlet ground-state average spin-spin correlation functions and von Neumann entanglement entropy. We then apply our method to the bilinear-biquadratic random antiferromagnetic spin-1 chain tuned to the antiferromagnet and gapless highly symmetric SU(3) point. We find the new result that the mean correlation function decays algebraically with the same universal exponent $\phi=2$ as the spin-1/2 chain. We then perform numerical and analytical strong-disorder renormalization-group calculations which confirm this finding and generalize it for any highly symmetric SU($N$) random-singlet state.