Overlaps with arbitrary two-site states in the XXZ spin chain

Pozsgai, Balázs (2018) Overlaps with arbitrary two-site states in the XXZ spin chain. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2018 (5). ISSN 1742-5468

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Abstract

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no O(1) term in the quench action.

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