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

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 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 $p_c$.

arXiv comment11 pages, 6 figures

References in corpus (31)

• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Critical Phenomena and Renormalization-Group Theory
• Precision Islands in the Ising and $O(N)$ Models
• Computational Studies of Quantum Spin Systems
• Efficient Monte Carlo algorithm and high-precision results for percolation
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• The critical probability for random Voronoi percolation in the plane is 1/2
• Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet
• Griffiths Singularities in the Disordered Phase of a Quantum Ising Spin Glass
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Disorder in quantum many-body systems
• Strong Disorder RG approach - a short review of recent developments
• Higher dimensional realizations of activated dynamic scaling at random quantum transitions
• Evidence of a magnetic Bose glass in IPA-Cu(Cl0.95Br0.05)3 from neutron diffraction
• $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ as a random field Ising ferromagnet
• Exponent relations at quantum phase transitions, with applications to metallic quantum ferromagnets
• Quantum Griffiths phase inside the ferromagnetic phase of Ni${}_{1-x}$V${}_x$
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice
• Signatures of a quantum Griffiths phase in a d-metal alloy close to its ferromagnetic quantum critical point
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Phase diagram of diluted Ising ferromagnet LiHo${}_x$Y${}_{1-x}$F${}_4$
• Persistence of magnons in a site-diluted dimerized frustrated antiferromagnet
• Random Transverse Field Ising model in $d=2$ : analysis via Boundary Strong Disorder Renormalization
• Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet