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

TL;DR

This paper conjectures an exact formula for overlaps between Bethe states and two-site states in the XXZ spin chain, confirmed numerically, and highlights the role of Gaudin-like determinants in the thermodynamic limit.

Contribution

It introduces a conjectured exact overlap formula for the XXZ chain with two-site states, extending previous results and confirming it with numerical data.

Findings

The formula involves Gaudin-like determinants and single-particle overlap functions.

Numerical data supports the conjecture for chains of various lengths.

The ratio of determinants ensures no O(1) term in the thermodynamic limit.

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.