Correlation functions of the open XXZ chain II

Abstract

We derive compact multiple integral formulas for several physical spin correlation functions in the semi-infinite XXZ chain with a longitudinal boundary magnetic field. Our formulas follow from several effective re-summations of the multiple integral representation for the elementary blocks obtained in our previous article (I). In the free fermion point we compute the local magnetization as well as the density of energy profiles. These quantities, in addition to their bulk behavior, exhibit Friedel type oscillations induced by the boundary; their amplitudes depend on the boundary magnetic field and decay algebraically in terms of the distance to the boundary.

38 pages

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• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
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• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Surface free energy of the open XXZ spin-1/2 chain
• The open XXX spin chain in the SoV framework: scalar product of separate states
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• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
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• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
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• The open XXZ spin chain in the SoV framework: scalar product of separate states
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• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Open XXZ chain and boundary modes at zero temperature
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
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• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Reflection algebra and functional equations
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