Critical behavior in the presence of an order-parameter pinning field

Abstract

We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte Carlo approach, we show that for this model, the pinning-field approach allows to locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be hard since the pinning field introduces strong corrections to scaling. In order to further elucidate the scaling behavior in this situation, we also study an improved classical lattice model in the three-dimensional Ising universality class by means of Monte Carlo simulations on large lattice sizes, which allow us to employ refined finite-size scaling considerations. A renormalization group analysis exhibits the presence of an important crossover effect from the zero pinning-field to a critical adsorption fixed point. In line with field-theoretical results, we find that at the critical adsorption fixed point the short-distance expansion of the order-parameter profile exhibits a new universal critical exponent. This result also implies the presence of slowly decaying scaling corrections, which we analyze in detail.

arXiv comment20 pages, 7 figs; v2: 21 pages, 7 figs, added discussion on experimental realization, added new appendix, new refs

References in corpus (38)

• Critical Phenomena and Renormalization-Group Theory
• Quantum Monte Carlo with Directed Loops
• Stochastic series expansion method with operator-loop update
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Neel order in square and triangular lattice Heisenberg models
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• The Theory of Boundary Critical Phenomena
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Spin Gaps and Spin Dynamics in La_{2-x}Sr_xCuO_4 and YBa_2Cu_3O7_δ
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• Relativistic Mott criticality in graphene
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Finite-size scaling at quantum transitions
• Phase Transition, Longitudinal Spin Fluctuations and Scaling in a Two-Layer Antiferromagnet
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Spin Gaps and Bilayer Coupling in YBa${}_2$Cu${}_3$O${}_{7-\delta }$ and YBa${}_2$Cu${}_4$O${}_8$
• Susceptibility of the 2D S=1/2 Heisenberg antiferromagnet with an impurity
• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• Critical adsorption on curved objects
• Parallel multicanonical study of the three-dimensional Blume-Capel model
• Critical adsorption near edges
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Spin 1/2 Magnetic Impurity in a 2D Magnetic System Close to Quantum Critical Point
• Critical adsorption and Casimir torque in wedges and at ridges
• Critical Casimir force in the presence of random local adsorption preference
• Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• Applications of lattice QCD techniques for condensed matter systems
• Magnetic defect line in a critical Ising bath

Cited by in corpus (18)

• Localized magnetic field in the $O(N)$ model
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Spin Impurities, Wilson Lines and Semiclassics
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Bootstrapping line defects with $O(2)$ global symmetry
• Broken global symmetries and defect conformal manifolds
• Notes on a Surface Defect in the $O(N)$ Model
• Analytic bootstrap for the localized magnetic field
• Phases of Wilson Lines in Conformal Field Theories
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Line Defect RG Flows in the $\epsilon$ Expansion
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• The ordinary surface universality class of the three-dimensional O($N$) model
• Phase diagram of the SU($N$) antiferromagnet of spin $S$ on a square lattice
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Surface critical behavior of the three-dimensional O(3) model
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere