Quantum Monte Carlo study of the bond- and site-diluted transverse-field Ising model

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram and critical behavior of the bond- and site-diluted transverse-field Ising model, revealing new insights into quantum phase transitions and Griffiths phases.

Contribution

It provides the first finite-size scaling analysis of critical exponents at the quantum phase transitions in diluted transverse-field Ising models.

Findings

Identified quantum critical points with high accuracy using Binder ratios.

Determined critical exponents $eta$ and $ u_{av}$ along critical lines and at multicritical points.

Discovered activated scaling occurs at both percolation and phase transition lines for $p < p_c$.

Abstract

We study the transverse-field Ising model on a square lattice with bond- and site-dilution at zero temperature by stochastic series expansion quantum Monte Carlo simulations. Tuning the transverse field $h$ and the dilution $p$, the quantum phase diagram of both models is explored. Both quantum phase diagrams show long-range order for small $h$ and small $p$. The ordered phase of each is separated from the disordered (quantum) Griffiths phase by second-order phase transitions on two critical lines touching at a multi-critical point. Using Binder ratios we locate quantum critical points with high accuracy. The order-parameter critical exponent $\beta$ and the average correlation-length exponent $\nu_{\mathrm{av}}$ are determined along the critical lines and at the multi-critical points for the first time via finite-size scaling. We find three internally consistent sets of critical exponents and compare them with potentially connected universality classes. The quantum Griffiths phase in the vicinity of the phase transition lines is analyzed through the local susceptibility. Our results indicate that activated scaling occurs not only at the percolation transition, but also at the phase transition line for $p$ smaller than the percolation threshold $p_c$.