Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

Abstract

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 $U_q({\widehat{\mathfrak{sl}}}_2)$ 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.

35 pages

References in corpus (4)

• Hidden Grassmann structure in the XXZ model
• Algebraic representation of correlation functions in integrable spin chains
• Holonomy of the Ising model form factors
• High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

Cited by in corpus (18)

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• Current operators in integrable models: A review
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• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
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• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Current mean values in the XYZ model
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• The Hilbert-space structure of free fermions in disguise
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• On correlation functions in models related to the Temperley-Lieb algebra
• Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach