Solving quantum rotor model with different Monte Carlo techniques

Abstract

We systematically test the performance of several Monte Carlo update schemes for the $(2+1)$d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) scheme, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z${}_2$ topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.

12 pages, 8 figures

References in corpus (21)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The critical exponents of the superfluid transition in He4
• Self-Learning Monte Carlo Method
• Carving out OPE space and precise $O(2)$ model critical exponents
• Monte Carlo study of an improved clock model in three dimensions
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Evidence of the Berezinskii-Kosterlitz-Thouless Phase in a Frustrated Magnet
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Superconductivity and charge density wave order in the 2D Holstein model
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Langevin Simulations of a Long Range Electron Phonon Model
• Consistent scaling exponents at the deconfined quantum-critical point
• Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots
• Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Fermi-surface reconstruction without symmetry breaking
• Metal to Orthogonal Metal Transition
• The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study
• Fermi arcs and pseudogap in a lattice model of a doped orthogonal metal

Cited by in corpus (4)

• Evidence of the Berezinskii-Kosterlitz-Thouless Phase in a Frustrated Magnet
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Variational quantum dynamics of two-dimensional rotor models
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems