2007/05/18 by Herman E. Boos, Herman E Boos, Frank Göhmann +2 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chain (unit) #Conjecture #Constant (computer programming) #Correlation function (quantum field theory) #Exponential function #Factorization #Monodromy #Operator (biology) #Quantum many-body systems #TRACE (psycholinguistics) #Theoretical and Computational Physics #Transcendental number #cond-mat.str-el #hep-th
paper · pdf · doi:10.1088/1751-8113/40/35/001
published as J.Phys.A40:10699-10728,2007 · 35 pages
arxiv created 2007/05/18 · openalex publication_date 2007/08/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density matrix, conceived as a map which associates with every local operator its thermal expectation value, can be written as the trace of the exponential of an operator constructed from weighted traces of the elements of certain monodromy matrices related to and only two transcendental functions pertaining to the one-point function and the neighbour correlators, respectively. Our conjecture implies that all static correlation functions of the XXZ chain are polynomials in these two functions and their derivatives with coefficients of purely algebraic origin.