Universal witnesses of vanishing energy gap

TL;DR

The paper introduces a method to estimate the energy gap of a Hamiltonian using expectation values, providing a practical criterion for identifying gapless systems, exemplified by the XY model.

Contribution

A new technique to bound the energy gap of Hamiltonians using expectation values and auxiliary Hamiltonians, aiding the detection of gapless quantum systems.

Findings

Method successfully applied to the XY model.

Provides an effective criterion for gaplessness.

Offers a practical tool for quantum phase transition analysis.

Abstract

Energy gap, the difference between the energy of the ground state of a given Hamiltonian and the energy of its first excited state, is a parameter of a critical importance in analysis of phase transitions and adiabatic quantum computation. We present a concrete technique to determine the upper bound for the energy gap of a Hamiltonian $H_0$ based on properties of the set of expectation values of $H_0$ and an additional auxiliary Hamiltonian $V$. This formalism can be applied to obtain an effective criterion of gaplessness, which we illustrate with a concrete example of the XY model -- a physical system with vanishing energy gap.