The charge gap is greater than the neutral gap in fractional quantum Hall systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913974840197120 |
|---|---|
| author | Lemm, Marius Nachtergaele, Bruno Warzel, Simone Young, Amanda |
| author_facet | Lemm, Marius Nachtergaele, Bruno Warzel, Simone Young, Amanda |
| contents | Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any Hamiltonian that satisfies a few simple structural properties: translation-invariance, charge conservation, dipole conservation, and a fractionally filled ground state. The result applies to both fermions and bosons. Our main tool is a new mathematical scheme, the gap comparison method, which provides a sequence of inequalities that relate the spectral gaps in successive particle number sectors. Our finding sheds new light on dipole conservation's profound effects on many-body physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The charge gap is greater than the neutral gap in fractional quantum Hall systems Lemm, Marius Nachtergaele, Bruno Warzel, Simone Young, Amanda Strongly Correlated Electrons Mathematical Physics 81V70 Past studies of fractional quantum Hall systems have found that the charge gap dominates the neutral gap for all relevant parameter choices. We report a wide-ranging proof that this domination is in fact a universal property of any Hamiltonian that satisfies a few simple structural properties: translation-invariance, charge conservation, dipole conservation, and a fractionally filled ground state. The result applies to both fermions and bosons. Our main tool is a new mathematical scheme, the gap comparison method, which provides a sequence of inequalities that relate the spectral gaps in successive particle number sectors. Our finding sheds new light on dipole conservation's profound effects on many-body physics. |
| title | The charge gap is greater than the neutral gap in fractional quantum Hall systems |
| topic | Strongly Correlated Electrons Mathematical Physics 81V70 |
| url | https://arxiv.org/abs/2410.11645 |