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

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, where existing methods can not be applied. 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 $\mathcal{O}(1)$ piece in the Quench Action.

22 pages, v2: references added

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