Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model

Abstract

A continuous sequence of infinitesimal unitary transformations, combined with an operator product expansion for vertex operators, is used to diagonalize the quantum sine-Gordon model for 2 pi < beta^2 < infinity. The leading order of this approximation already gives very accurate results for the single-particle gap in the strong-coupling phase. This approach can be understood as an extension of perturbative scaling theory since it links weak to strong-coupling behavior in a systematic expansion. The approach should also be useful for other strong-coupling problems that can be formulated in terms of vertex operators.

4 pages, 1 figure, minor changes (typo in Eq. (3) corrected, references added), published version

References in corpus (1)

• Bosonization and Strongly Correlated Systems

Cited by in corpus (37)

• Entanglement renormalization for quantum fields
• 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
• Unifying variational methods for simulating quantum many-body systems
• Functional renormalization group approach to the sine-Gordon model
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• Non-linear feedback effects in coupled Boson-Fermion systems
• Flow Equations and Normal Ordering. A Survey
• Flow equation approach to the sine-Gordon model
• 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
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Renormalizable parameters of the sine-Gordon model
• Flow equation analysis of the anisotropic Kondo model
• Combined Analysis of Numerical Diagonalization and Renormalization Group methods for the One-Dimensional $U$-$V$ Model at Quarter filling
• Quantum creep and quantum creep transitions in 1D sine-Gordan chains
• Non-Equilibrium Scaling Analysis of the Kondo Model with Voltage Bias
• Structure of the broken phase of the sine-Gordon model using functional renormalization
• Dynamic scaling in the vicinity of the Luttinger liquid fixed point
• Interplay of fixed points in scalar models
• Landau's quasi-particle mapping: Fermi liquid approach and Luttinger liquid behavior
• Feshbach resonance described by the boson fermion coupling
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Charge Gap in the One-Dimensional Extended Hubbard Model at Quarter Filling
• Strongly interacting bosons in a 1D optical lattice at incommensurate densities
• Efficient flow equations for dissipative systems
• Flow Equations for the Ionic Hubbard Model
• Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond
• Semi-analytical solution of the Kondo model in a magnetic field
• Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation
• Entanglement Continuous Unitary Transformations
• Lattice sine-Gordon model
• Crystalline phase for one-dimensional ultra-cold atomic bosons
• Renormalization of the bilocal sine-Gordon model
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models