Short distance correlators in the XXZ spin chain for arbitrary string distributions

Abstract

In this letter we consider expectation values of local correlators in highly excited states of the spin-1/2 XXZ chain. Assuming that the string hypothesis holds we formulate the following conjecture: The correlation functions can be computed using the known factorized formulas of the finite temperature situation, if the building blocks are computed via certain linear integral equations using the string densities only. We prove this statement for the nearest neighbour z-z correlator for states with arbitrary string densities. Also, we check the conjecture numerically for other correlators in the finite temperature case. Our results pave the way towards the computation of the stationary values of correlators in non-equilibrium situations using the so-called quench-action approach.

arXiv comment15 pages, v2: minor modifications, v3: minor modifications

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• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
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• General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
• Popcorn Drude weights from quantum symmetry
• Correlation and entanglement spreading in nested spin chains
• The equilibrium landscape of the Heisenberg spin chain
• Correlation functions by Separation of Variables: the XXX spin chain
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• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
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