Non-local quench spectroscopy of fermionic excitations in 1D quantum spin chains

TL;DR

This paper demonstrates that quench spectroscopy in quantum simulators can directly measure fermionic quasiparticle dispersions in 1D spin chains, overcoming the limitations of local probes due to non-local spin-fermion mappings.

Contribution

It introduces a theoretical framework showing how non-local correlation measurements can reconstruct fermionic excitation spectra in spin chains.

Findings

Quench spectroscopy accurately reconstructs fermionic dispersion relations.

Non-local correlation functions are key to observing fermionic quasiparticles.

The approach opens new avenues for probing excitations in synthetic quantum systems.

Abstract

The elementary excitations of quantum spin systems have generally the nature of weakly interacting bosonic quasi-particles, generated by local operators acting on the ground state. Nonetheless in one spatial dimension the nature of the quasiparticles can change radically, since many relevant one-dimensional $S=1/2$ Hamiltonians can be exactly mapped onto models of spinless fermions with local hopping and interactions. Due to the non-local nature of the spin-to-fermion mapping, observing directly the fermionic quasiparticle excitations is impossible using local probes, which are at the basis of all the forms of spectroscopy (such as neutron scattering) traditionally available in condensed matter physics. Here we show theoretically that \emph{quench spectroscopy} for synthetic quantum matter -- which probes the excitation spectrum of a system by monitoring the nonequilibrium dynamics of its correlation functions -- can reconstruct accurately the dispersion relation of fermionic quasiparticles in spin chains. This possibility relies on the ability of quantum simulation experiments to measure non-local spin-spin correlation functions, corresponding to elementary fermionic correlation functions. Our analysis is based on new exact results for the quench dynamics of quantum spin chains; and it opens the path to probe arbitrary quasiparticle excitations in synthetic quantum matter.