Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian

Abstract

Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We modify the KZ equations by replacing these Gaudin operators with constants of motion of the closely-related Richardson pairing Hamiltonian and reconstruct a deformed WZNW model, whose correlators satisfy these equations. This modified theory, dubbed here the boundary WZNW model, contains a term that breaks translational symmetry and therefore represents a generalized boundary operator. The corresponding correlators of the boundary WZNW model are calculated and are shown to acquire exponential prefactors, in contrast to the bulk WZNW theories. The solution also establishes a connection between correlation functions of the WZNW model and the spectrum of the reduced pairing Hamiltonian.

arXiv comment7 pages, 1 figure

References in corpus (16)

• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Gate-Voltage Studies of Discrete Electronic States in Al Nanoparticles
• Integrability of the pairing hamiltonian
• Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
• Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations
• Algebraic Bethe Ansatz for a discrete-state BCS pairing model
• Exact mesoscopic correlation functions of the pairing model
• Conformal Field Theory and the Exact Solution of the BCS Hamiltonian
• BCS theory for finite size superconductors
• Finite Size Corrections for the Pairing Hamiltonian
• Exact correlation functions of the BCS model in the canonical ensemble
• Normal and anomalous solitons in the theory of dynamical Cooper pairing
• The BCS model and the off shell Bethe ansatz for vertex models
• On phase transitions in two-dimensional disordered systems
• High-gradient operators in perturbed Wess-Zumino-Witten field theories in two dimensions

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• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• Exact out-of-equilibrium central spin dynamics from integrability
• Integrability of an extended d+id-wave pairing Hamiltonian
• Quantum nonequilibrium dynamics from Knizhnik-Zamolodchikov equations
• Majorana path integral for nonequilibrium dynamics of two-level systems
• Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models