Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions

Abstract

The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional $|\phi {|}^4$ models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the contribution of density fluctuations to nonuniversal quantities. We introduce a functional renormalization group scheme in AP representation where amplitude fluctuations are integrated first to yield an effective sine-Gordon model with renormalized superfluid stiffness. By a mapping between the lattice XY and continuum $|\phi {|}^4$ models, our method applies to both on equal footing. Our approach correctly reproduces the existence of a line of fixed points and of universal thermodynamics and it allows to estimate universal and nonuniversal quantities of the two models, finding good agreement with available Monte Carlo results. The presented approach is flexible enough to treat parameter ranges of experimental relevance.

arXiv comment18 pages, 6 figures; published version

References in corpus (47)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Functional renormalization group approach to correlated fermion systems
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• On solving quantum many-body problems by experiment
• Critical Point of a Weakly Interacting Two-Dimensional Bose Gas
• The transition temperature of the dilute interacting Bose gas
• Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region
• Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas
• Observation of pair condensation in the quasi-2D BEC-BCS crossover
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Vortex proliferation in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional lattice of Bose-Einstein condensates
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Kosterlitz-Thouless Phase Transition In The Two Dimensional Linear Sigma Model
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• Universal equation of state and pseudogap in the two-dimensional Fermi gas
• O(N)-Universality Classes and the Mermin-Wagner Theorem
• Critical temperature of interacting Bose gases in two and three dimensions
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Two Definitions of Superfluid Density
• Critical exponents of O(N) models in fractional dimensions
• Ultracold atoms and the Functional Renormalization Group
• Functional renormalization group approach to the sine-Gordon model
• On the renormalization of periodic potentials
• Finite-Size Scaling in Two-Dimensional Superfluids
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Universal thermodynamics of a two-dimensional Bose gas
• Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
• Space-time vortex driven crossover and vortex turbulence phase transition in one-dimensional driven open condensates
• Anisotropic Long-Range Spin Systems
• Comparison of renormalization group schemes for sine-Gordon type models
• Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Rapidly Quenched Kosterlitz-Thouless Superfluid Transitions
• Functional renormalization group for d-wave superconductivity in Hubbard type models
• Generalized universality in the massive sine-Gordon model
• Effective Action and Phase Structure of Multi-Layer Sine-Gordon Type Models
• Core structure of two-dimensional Fermi gas vortices in the BEC-BCS crossover region
• Phase Structure and Compactness
• $c$-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow
• Exact renormalisation group flow for ultracold Fermi gases in unitary limit

Cited by in corpus (23)

• The nonperturbative functional renormalization group and its applications
• Long-range interacting quantum systems
• Criticality of Spin Systems with Weak Long-Range Interactions
• Coupled superfluidity of binary Bose mixtures in two dimensions
• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
• BKT-paired phase in coupled XY models
• Indications of isotropic Lifshitz points in four dimensions
• The low-temperature phase in the two-dimensional long-range diluted XY model
• Application of the functional renormalization group to Bose gases: from linear to hydrodynamic fluctuations
• Topological phase transitions in four dimensions
• Vortex confinement transitions in the modified Goldstone model
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Melting of the two-dimensional solid phase in the Gaussian-core model
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Renormalization group for the ${\phi }^4$-theory with long-range interaction and the critical exponent $\eta$ of the Ising model
• Isotropic Lifshitz Scaling in four dimensions
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Helicity modulus in the bilayer XY model by worm algorithm
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• Amplitude, phase, and topological fluctuations shaping the complex phase diagram of two-dimensional superconductors