Quantum Critical Scaling of Dirty Bosons in Two Dimensions

Abstract

We determine the dynamical critical exponent, $z$, appearing at the Bose glass to superfluid transition in two dimensions by performing large scale numerical studies of two microscopically different quantum models within the universality class; The hard-core boson model and the quantum rotor (soft core) model, both subject to strong on-site disorder. By performing many simulations at different system size, $L$, and inverse temperature, $\beta$, close to the quantum critical point, the position of the critical point and the critical exponents, $z$, $\nu$ and $\eta$ can be determined independently of any prior assumptions of the numerical value of $z$. This is done by a careful scaling analysis close to the critical point with a particular focus on the temperature dependence of the scaling functions. For the hard-core boson model we find $z=1.88(8),\nu =0.99(3)$ and $\eta =-0.16(8)$ with a critical field of $h_c=4.79(3)$, while for the quantum rotor model we find $z=1.99(5),\nu =1.00(2)$ and $\eta =-0.3(1)$ with a critical hopping parameter of $t_c=0.0760(5)$. In both cases do we find a correlation length exponent consistent with $\nu =1$, saturating the bound $\nu \ge 2/d$ as well as a value of $z$ significantly larger than previous studies, and for the quantum rotor model consistent with $z=d$.

arXiv comment7 pages, 10 figures

References in corpus (37)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Monte Carlo with Directed Loops
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• The superconductor-insulator transition in 2D dirty boson systems
• Strongly interacting bosons in a disordered optical lattice
• Disordered insulator in an optical lattice
• Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
• Thickness-Magnetic Field Phase Diagram at the Superconductor-Insulator Transition in 2D
• 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
• Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations
• Phase diagram of the disordered Bose-Hubbard model
• The dynamics of quantum criticality via Quantum Monte Carlo and holography
• Bose glass and Mott insulator phase in the disordered boson Hubbard model
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates
• Quantum simulations of the superfluid-insulator transition for two-dimensional, disordered, hard-core bosons
• Dirty-boson physics with magnetic insulators
• Particle-hole symmetry and the dirty boson problem
• Universal Conductivity in the Two dimensional Boson Hubbard Model
• Quantum glass phases in the disordered Bose-Hubbard model
• Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions
• Directed geometrical worm algorithm applied to the quantum rotor model
• Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons
• The superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model
• Bose-glass to Superfluid transition in the three-dimensional Bose-Hubbard Model
• Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions
• Quantum Phase Transitions of Hard-Core Bosons in Background Potentials
• Quantum Critical Dynamics Simulation of Dirty Boson Systems
• Dirty Bosons: Twenty Years Later
• Quantum critical scaling at a Bose-glass/superfluid transition: theory and experiment on a model quantum magnet
• Universal phase diagram of disordered bosons from a doped quantum magnet
• Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder
• Magnetic Field Tuned Quantum Phase Transition in the Insulating Regime of Ultrathin Amorphous Bi Films
• Destruction of diagonal and off-diagonal long range order by disorder in two-dimensional hard core boson systems
• Anomalous quantum glass of bosons in a random potential in two dimensions
• Ensemble dependence in the Random transverse-field Ising chain

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• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
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• Quantum critical behavior of a three-dimensional superfluid-Mott glass transition
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• Quantum crystallography of Rydberg-dressed Bose gases on a square lattice
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