Validity of Harris criterion for two-dimensional quantum spin systems with quenched disorder

Abstract

Inspired by the recent results regarding whether the Harris criterion is valid for quantum spin systems, we have simulated a two-dimensional spin-1/2 Heisenberg model on the square lattice with a specific kind of quenched disorder using the quantum Monte Carlo (QMC) calculations. In particular, the considered quenched disorder has a tunable parameter $0\le p\le 1$ which can be considered as a measure of randomness. Interestingly, when the magnitude of $p$ increases from 0 to 0.9, at the associated quantum phase transitions the numerical value of the correlation length exponent $\nu$ grows from a number compatible with the $O(3)$ result 0.7112(5) to a number slightly greater than 1. In other words, by varying $p$, $\nu$ can reach an outcome between 0.7112(5) and 1 (or greater). Furthermore, among the studied values of $p$, all the associated $\nu$ violate the Harris criterion except the one corresponding to $p=0.9$. Considering the form of the employed disorder here, the above described scenario should remain true for other randomness if it is based on the similar idea as the one used in this study. This is indeed confirmed by our preliminary results stemming from investigating another disorder distribution.

arXiv comment8 pages, 8 figures, 7 tables

References in corpus (36)

• emcee: The MCMC Hammer
• Critical Phenomena and Renormalization-Group Theory
• Stochastic series expansion method with operator-loop update
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Infinite-randomness quantum Ising critical fixed points
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Bose glass and Mott glass of quasiparticles in a doped quantum magnet
• Disorder in quantum many-body systems
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Revisiting the Theory of Finite Size Scaling in Disordered Systems: νCan Be Less Than 2/d
• Bose glass and Mott insulator phase in the disordered boson Hubbard model
• Criticality and quenched disorder: rare regions vs. Harris criterion
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Low-energy fixed points of random Heisenberg models
• Multi-critical point in a diluted bilayer Heisenberg quantum antiferromagnet
• Random-exchange quantum Heisenberg antiferromagnets on the square lattice
• Exotic vs. conventional scaling and universality in a disordered bilayer quantum Heisenberg antiferromagnet
• Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet
• Two-particle decay and quantum criticality in dimerized antiferromagnets
• Quantum percolation in two-dimensional antiferromagnets
• Protecting clean critical points by local disorder correlations
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Kernel method for corrections to scaling
• Quantum-criticality and percolation in dimer-diluted 2D antiferromagnets
• Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
• Direct Mott Insulator-to-Superfluid Transition in the Presence of Disorder
• Quantum critical scaling at a Bose-glass/superfluid transition: theory and experiment on a model quantum magnet
• Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion
• A violation of the Harris-Barghathi-Vojta criterion
• Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution
• Evidence for impurity-induced frustration in La2CuO4
• Criticality and Mott-glass phase in a disordered 2D quantum spin systems

Cited by in corpus (4)

• Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice
• Quantum criticality at finite temperature for two-dimensional $J{Q}_3$ models on the square and the honeycomb lattices
• Disordered purification phase transition in hybrid random circuits
• Ground state energy density, susceptibility, and Wilson ratio of a two-dimensional disordered quantum spin system