A Quantum Monte Carlo Study of the Random Field Ising Model in a Transverse Field

Recently a surprisingly broad region of critical behavior was found in the charge modulations of single-layer BSCO [Nature Communications (2023)14:2622], in which the critical fluctuations extend across the entire superconducting doping range, in contrast with the narrow doping range expected for quantum critical fluctuations. The observed criticality was found to be consistent with the classical criticality of the random field Ising model.

There have been numerous studies about the random field Ising model at zero temperature since the criticality of the random field Ising model is controlled by a zero temperature random field fixed point. In contrast, the interplay between thermal fluctuations, quantum fluctuations and quenched randomness is not well understood.

We study the random field Ising model in a transverse field, using the continuous-time quantum Monte Carlo method with a Wolff cluster update. Our calculations show the interplay between thermal fluctuations, quantum fluctuations and quenched randomness, and pave the way toward understanding random field effects in quantum systems.