Dynamical response functions in the quantum Ising chain with a boundary

2007/09/12 by Dirk Schuricht, Fabian H. L. Essler, Fabian H L Essler
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Chain (unit) #Ising model #Periodic boundary conditions #Quantum #Quantum many-body systems #Scaling #Scaling limit #Theoretical and Computational Physics #cond-mat.str-el #hep-th

paper · pdf · doi:10.1088/1742-5468/2007/11/p11004

published as J. Stat. Mech.: Theor. Exp. P11004 (2007). · 32 pages

arxiv created 2007/09/12 · openalex publication_date 2007/11/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We determine dynamical response functions in the scaling limit of the quantum Ising chain on the half-line in the presence of a boundary magnetic field. Using a spectral representation in terms of infinite volume form factors and a boundary state, we derive an expansion for the correlator that is found to be rapidly convergent as long as , where ξ is the correlation length. At sufficiently late times we observe oscillatory behaviour of the correlations arbitrarily far away from the boundary. We investigate the effects of the boundary bound state that is present for a range of boundary magnetic fields.

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