Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet

TL;DR

This paper provides exact analytical expressions for third neighbor and four-spin correlators in the ground state of the spin-1/2 Heisenberg XXX antiferromagnet, matching numerical results precisely.

Contribution

It presents the first exact evaluation of third neighbor and four-spin correlators in the ground state of the spin-1/2 Heisenberg XXX model, expressed through special mathematical constants.

Findings

Exact formulas for third neighbor correlator involving ln2 and zeta functions.

All correlators match numerical results from DMRG and diagonalization.

Provides a comprehensive analytical approach to spin correlators in this model.

Abstract

We exactly evaluate the third neighbor correlator <S_j^z S_{j+3}^z> and all the possible non-zero correlators <S^{alpha}_j S^{beta}_{j+1} S^{gamma}_{j+2} S^{delta}_{j+3}> of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.