Energy gap of neutral excitations implies vanishing charge susceptibility

TL;DR

This paper demonstrates that in quantum many-body systems with U(1) symmetry, a finite neutral excitation gap guarantees vanishing charge susceptibility, explaining quantization conditions at magnetization plateaus.

Contribution

It establishes a direct link between neutral excitation gaps and charge susceptibility, providing a new understanding of incompressibility in strongly correlated systems.

Findings

Finite neutral excitation gap implies zero charge susceptibility.

Charge susceptibility vanishes when all charged excitations are gapped.

Supports the quantization condition at magnetization plateaus in higher dimensions.

Abstract

In quantum many-body systems with a U(1) symmetry, such as the particle number conservation and the axial spin conservation, there are two distinct types of excitations: charge-neutral excitations and charged excitations. The energy gaps of these excitations may be independent with each other in strongly correlated systems. The static susceptibility of the U(1) charge vanishes when the charged excitations are all gapped, but its relation to the neutral excitations is not obvious. Here we show that a finite excitation gap of the neutral excitations is, in fact, sufficient to prove that the charge susceptibility vanishes (i.e. the system is incompressible). This result gives a partial explanation on why the celebrated quantization condition $n(S-m_z)\in\mathbb{Z}$ at magnetization plateaus works even in spatial dimensions greater than one.