Flow equation approach to the sine-Gordon model

Abstract

A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for β^2\in(2π,\infty). This approach can be understood as an extension of perturbative scaling theory since it links weak- to strong-coupling behavior in a systematic expansion: a small expansion parameter is identified and this parameter remains small throughout the entire flow unlike the diverging running coupling constant of perturbative scaling. Our approximation consists in neglecting higher orders in this small parameter. We find very accurate results for the single-particle/hole spectrum in the strong-coupling phase and can describe the full crossover from weak to strong-coupling. The integrable structure of the sine-Gordon model is not used in our approach. Our new method should be of interest for the investigation of nonintegrable perturbations and for other strong-coupling problems.

38 pages, 7 figures

References in corpus (2)

• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model

Cited by in corpus (29)

• An exactly solvable model of the BCS-BEC crossover
• Commensurate-incommensurate transition of cold atoms in an optical lattice
• Scaling and Decoherence in the Out-of-Equilibrium Kondo Model
• Lectures on renormalization and asymptotic safety
• Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• Flow Equations and Normal Ordering. A Survey
• Non-Equilibrium Kondo Model with Voltage Bias in a Magnetic Field
• Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
• Renormalizable parameters of the sine-Gordon model
• Non-Equilibrium Scaling Analysis of the Kondo Model with Voltage Bias
• Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling
• Non-perturbative flow equations from continuous unitary transformations
• Non-perturbative flow equations from continuous unitary transformations
• Landau's quasi-particle mapping: Fermi liquid approach and Luttinger liquid behavior
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Energy Correlations In Random Transverse Field Ising Spin Chains
• Charge Gap in the One-Dimensional Extended Hubbard Model at Quarter Filling
• Efficient flow equations for dissipative systems
• Strongly interacting bosons in a 1D optical lattice at incommensurate densities
• Exact Renormalization Group and Sine Gordon Theory
• Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model
• Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model
• Semi-analytical solution of the Kondo model in a magnetic field
• Entanglement Continuous Unitary Transformations
• Holographic Beta functions for the Generalized Sine Gordon Theory
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models