Quantum multicritical point in the two- and three-dimensional random transverse-field Ising model

TL;DR

This paper investigates the quantum multicritical point in the random transverse-field Ising model across two and three dimensions, revealing universal, ultraslow scaling behavior governed by an infinite disorder fixed point.

Contribution

It provides the first detailed numerical characterization of the quantum multicritical point in the random transverse-field Ising model, demonstrating universality and infinite disorder scaling.

Findings

Quantum multicritical points exhibit ultraslow, activated dynamic scaling.

Multicritical exponents tend to exact universal values at large scales.

The results are robust against different forms of disorder.

Abstract

Quantum multicritical points (QMCPs) emerge at the junction of two or more quantum phase transitions due to the interplay of disparate fluctuations, leading to novel universality classes. While quantum critical points have been well characterized, our understanding of QMCPs is much more limited, even though they might be less elusive to study experimentally than quantum critical points. Here, we characterize the QMCP of an interacting heterogeneous quantum system in two and three dimensions, the ferromagnetic random transverse-field Ising model (RTIM). The QMCP of the RTIM emerges due to both geometric and quantum fluctuations, studied here numerically by the strong disorder renormalization group method. The QMCP of the RTIM is found to exhibit ultraslow, activated dynamic scaling, governed by an infinite disorder fixed point. This ensures that the obtained multicritical exponents tend to the exact values at large scales, while also being universal -- i.e. independent of the form of disorder -- , providing a solid theoretical basis for future experiments.