Some aspects of jump-defects in the quantum sine-Gordon model

Abstract

The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where the conditions relating the fields on either side of a defect are Backlund transformations frozen at the defect location. The purpose of this article is to explore the extent to which this idea may be extended to the quantum sine-Gordon model and how the striking features of the classical model may translate to the quantum version. Assuming a positive defect parameter there are two types of defect. One type, carrying even charge, is stable, but the other type, carrying odd charge, is unstable and may be considered as a resonant bound state of a soliton and a stable defect. The scattering of solitons with defects is considered in detail, as is the scattering of breathers, and in all cases the jump-defect is purely transmitting. One surprising discovery concerns the lightest breather. Its transmission factor is independent of the bulk coupling - a property susceptible to a perturbative check, but not shared with any of the other breathers. It is argued that classical jump-defects can move and some comments are made concerning their quantum scattering matrix.

33 pages; a few typos have been corrected and two references added

References in corpus (23)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Boundary energy and boundary states in integrable quantum field theories
• Scattering Theory and Correlation Functions in Statistical Models with a Line of Defect
• Bound State Boundary S-matrix of the sine-Gordon Model
• Classically integrable field theories with defects
• Purely Transmitting Defect Field Theories
• Statistical Models with a Line of Defect
• Scattering in the Presence of a Reflecting and Transmitting Impurity
• Affine Toda field theories with defects
• From Defects to Boundaries
• Integrable Quantum Field Theories with Unstable Particles
• Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model
• The quantum non-linear Schrodinger model with point-like defect
• On the absence of simultaneous reflection and transmission in integrable impurity systems
• From integrability to conductance, impurity systems
• Aspects of sine-Gordon solitons, defects and gates
• A Quantum Field Theory with Infinite Resonance States
• Boundary breathers in the sinh-Gordon model
• Finite Temperature Quantum Field Theory with Impurities
• Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry
• Aspects of the Homogeneous Sine-Gordon models
• Boundary sine-Gordon model
• Bosonic Theory with a Random Defect Line

Cited by in corpus (44)

• Exact Solutions to the Sine-Gordon Equation
• Quantum and classical integrable sine-Gordon model with defect
• Solving topological defects via fusion
• On purely transmitting defects in affine Toda field theory
• Equivalences between spin models induced by defects
• Liouville integrable defects: the non-linear Schrodinger paradigm
• A transmission matrix for a fused pair of integrable defects in the sine-Gordon model
• A new class of integrable defects
• Semiclassical analysis of defect sine-Gordon theory
• Comments on defects in the a_r Toda field theories
• Integrablility of a Classical $N=2$ Super Sinh-Gordon Model with Jump Defects
• Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
• The sine-Gordon model with integrable defects revisited
• Sigma models in the presence of dynamical point-like defects
• Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices
• Defects in the discrete non-linear Schrodinger model
• Form factors in the presence of integrable defects
• An Algebraic Setting for Defects in the XXZ and Sine-Gordon Models
• Folding defect affine Toda field theories
• Exact g-function flows from the staircase model
• Defect scaling Lee-Yang model from the perturbed DCFT point of view
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• Finite volume form factors in the presence of integrable defects
• Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
• Defects in the supersymmetric mKdV hierarchy via Backlund transformations
• Jumps and twists in affine Toda field theories
• Defect fusing rules in affine Toda field theory
• Type-I integrable quantum impurities in the Heisenberg model
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Transmission amplitudes from Bethe ansatz equations
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Aspects of defects in integrable quantum field theory
• Defects and Dressed Boundaries in Complex Sine-Gordon Theory
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Purely transmitting integrable defects
• The sine-Gordon model in the presence of defects
• Integrable Defects at Junctions within a Network
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Lee-Yang Model in Presence of Defects
• Type II defects revisited
• Entanglement Entropy in Integrable Field Theories with Line Defects II. Non-topological Defect
• Aspects of Purely Transmitting Defects in Integrable Field Theories
• Time-dependent defects in integrable soliton equations
• Defects in affine Toda field theories