Infinite-randomness quantum Ising critical fixed points

TL;DR

This paper investigates the ground state of the random quantum Ising model in a transverse field, demonstrating that at strong randomness, the critical point exhibits an infinite-randomness fixed point in two and possibly three dimensions, with implications for quantum critical scaling.

Contribution

It extends the understanding of quantum critical points in disordered systems by showing the presence of an infinite-randomness fixed point in higher dimensions using a generalized RG approach.

Findings

In 2D, the RG flow leads to an infinite-randomness fixed point at strong disorder.

Critical exponents from RG agree with quantum Monte Carlo results.

The fixed point likely governs both ferromagnetic and spin-glass quantum critical points.

Abstract

We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG flow for the quantum critical point is towards an infinite-randomness fixed point, as in one-dimension. This is consistent with the results of a recent quantum Monte Carlo study by Pich, et al., including estimates of the critical exponents from our RG that agree well with those from the quantum Monte Carlo. The same qualitative behavior appears to occur for three-dimensions; we have not yet been able to determine whether or not it persists to arbitrarily high d. Some consequences of the infinite-randomness fixed point for the quantum critical scaling behavior are discussed. Because frustration is irrelevant in the infinite-randomness limit, the same fixed point should govern both ferromagnetic and spin-glass quantum critical points. This RG maps the random quantum Ising model with strong disorder onto a novel type of percolation/aggregation process.