Optimal quasi-free approximation:reconstructing the spectrum from ground state energies

TL;DR

This paper introduces a method to reconstruct quasi-particle spectra from finite-size ground state energies, enabling insights into the nature of excitations and effective boundary conditions in quantum many-body systems.

Contribution

The authors develop a novel approach to approximate quasi-particle dispersion relations using only finite-size ground state energies, with a validity criterion and applications to various spin models.

Findings

Successfully reconstructs quasi-particle spectra for spin models

Accurately reproduces known fermionic and bosonic spectra

Provides a criterion to validate quasi-free approximations

Abstract

The sequence of ground state energy density at finite size, e_{L}, provides much more information than usually believed. Having at disposal e_{L} for short lattice sizes, we show how to re-construct an approximate quasi-particle dispersion for any interacting model. The accuracy of this method relies on the best possible quasi-free approximation to the model, consistent with the observed values of the energy e_{L}. We also provide a simple criterion to assess whether such a quasi-free approximation is valid. As a side effect, our method is able to assess whether the nature of the quasi-particles is fermionic or bosonic together with the effective boundary conditions of the model. When applied to the spin-1/2 Heisenberg model, the method produces a band of Fermi quasi-particles very close to the exact one of des Cloizeaux and Pearson. The method is further tested on a spin-1/2 Heisenberg model with explicit dimerization and on a spin-1 chain with single ion anisotropy. A connection with the Riemann Hypothesis is also pointed out.