Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems

TL;DR

This paper derives recursive spectral relations for quantum lattice Hamiltonians, showing that symmetries enforce the charge gap to dominate the neutral gap in fractional quantum Hall systems, and introduces a new method for analyzing spectral gaps.

Contribution

It introduces recursive spectral relations and an induction-on-particle-number method, revealing universal symmetry-imposed gap domination in fractional quantum Hall systems.

Findings

Charge gap dominates neutral gap under symmetry conditions

Recursive spectral relations connect particle sectors

Method applies to both bosons and fermions

Abstract

We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.