Renormalization group study of random quantum magnets

TL;DR

This paper introduces an efficient numerical algorithm for the strong disorder renormalization group method, enabling large-scale studies of the critical behavior in random quantum magnets like the transverse-field Ising model, revealing infinite disorder fixed points.

Contribution

The authors developed a fast N*log(N) algorithm for the strong disorder RG, allowing analysis of large systems and diverse topologies, confirming the universal critical behavior of random quantum magnets.

Findings

Quantum critical behavior is governed by an infinite disorder fixed point.

Disorder dominates over quantum fluctuations at criticality.

The algorithm is applicable to various graph topologies and large system sizes.

Abstract

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time N*log(N), independently of the topology of the graph and we went up to N~4*10^6. We have studied regular lattices with dimension D<=4 as well as Erdos-Renyi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and the ferromagnetic phases and generalized the numerical algorithm for another random quantum systems.