Spin operator matrix elements in the quantum Ising chain: fermion approach

TL;DR

This paper develops a modified fermion technique to derive factorized formulas for spin operator matrix elements in the finite quantum Ising chain, aligning with results from the Separation of Variables Method.

Contribution

It introduces a new fermion-based approach to compute spin operator matrix elements in the quantum Ising chain, extending previous methods to finite systems.

Findings

Derived explicit factorized formulas for matrix elements.

Confirmed consistency with Separation of Variables results.

Applicable to finite-length quantum Ising chains.

Abstract

Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite length. The derivation is based on the approach recently used to derive factorized formula for Z_N-spin operator matrix elements between ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable chiral Potts quantum chain. The obtained factorized formulas for the matrix elements of Ising chain coincide with the corresponding expressions obtained by the Separation of Variables Method.