Hamiltonian Determination with Restricted Access in Transverse Field Ising Chain

TL;DR

This paper introduces a method to determine Hamiltonian parameters in a transverse field Ising chain by measuring only one edge spin, using spectral analysis of time-evolved expectation values, applicable under mild assumptions.

Contribution

It presents a novel approach to Hamiltonian parameter estimation with restricted access, specifically for a transverse field Ising chain, using spectral analysis of edge spin measurements.

Findings

Exact evaluation of eigenvalues and time evolution for a 3-spin chain

Parameters identified from Fourier transform peak positions

Method relies on four mild assumptions

Abstract

We propose a method to evaluate parameters in the Hamiltonian of the Ising chain under site-dependent transverse fields, with a proviso that we can control and measure one of the edge spins only. We evaluate the eigenvalues of the Hamiltonian and the time-evoultion operator exactly for a 3-spin chain, from which we obtain the expectation values of $\sigma_x$ of the first spin. The parameters are found from the peak positions of the Fourier transform of the expectation value. There are four assumptions in our method, which are mild enough to be satisfied in many physical systems.