On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains

TL;DR

This paper explores how a spectral gap in quantum spin chains ensures the split property of subsystems and discusses implications for gapless excitations in spinless Fermion systems.

Contribution

It establishes a link between spectral gap presence and the split property, and analyzes gapless excitations in gauge-invariant ground states.

Findings

Spectral gap implies split property in quantum spin chains.

Presence of spectral gap correlates with subsystem independence.

Gapless excitations exist under certain conditions in Fermion systems.

Abstract

We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As a corollary, we show that gapless excitation exists for spinless Fermion if the pure gauge invariant ground state is non-trivial and translationally invariant.