# Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the N\'eel state

## TL;DR

This paper investigates universal finite-size scaling terms in the overlap between the N9el state and the ground state of the spin-1/2 XXZ chain, connecting boundary conformal field theory predictions with exact asymptotic calculations.

## Contribution

It provides an exact asymptotic analysis of the overlap's order one term using a finite-size determinant formula, confirming boundary CFT predictions and extracting finite-size correction exponents.

## Key findings

- Confirmed boundary conformal field theory predictions for the overlap.
- Derived exact asymptotic expressions for the order one term.
- Determined the exponent of the leading finite-size correction.

## Abstract

We analyze universal terms that appear in the large system size scaling of the overlap between the N\'eel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of $g$-factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction.