Density matrix renormalization on random graphs and the quantum spin-glass transition

TL;DR

This paper extends the density matrix renormalization group method to analyze quantum phase transitions on random graphs, specifically applying it to the quantum spin-glass transition in a disordered transverse-field Ising model, revealing low entanglement and measurable spin-glass behavior.

Contribution

It introduces a novel application of DMRG to random graphs and demonstrates its effectiveness in studying quantum spin-glass transitions with manageable computational complexity.

Findings

Low number of retained states even for large sizes

Successful tracing of the quantum spin-glass transition

Measured key observables like correlations and entanglement entropy

Abstract

The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the couplings are random, the number of retained states remains reasonably low even for large sizes. The resulting quantum spin-glass transition has been traced down for a few disorder realizations, through the careful measurement of selected observables: spatial correlations, entanglement entropy, energy gap and spin-glass susceptibility, among others.