Hall-like behaviour of higher rank Chern-Simons theory of fractons
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_ | 1866913568740343808 |
|---|---|
| author | Bertolini, Erica Blasi, Alberto Maggiore, Nicola Shaikh, Daniel Sacco |
| author_facet | Bertolini, Erica Blasi, Alberto Maggiore, Nicola Shaikh, Daniel Sacco |
| contents | Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless ``electric'' field and a ``magnetic'' vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial ``flux-attachment'' relation for dipoles. This gives a possible starting point for a fracton - vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hall-like behaviour of higher rank Chern-Simons theory of fractons Bertolini, Erica Blasi, Alberto Maggiore, Nicola Shaikh, Daniel Sacco High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless ``electric'' field and a ``magnetic'' vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial ``flux-attachment'' relation for dipoles. This gives a possible starting point for a fracton - vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model. |
| title | Hall-like behaviour of higher rank Chern-Simons theory of fractons |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2405.19446 |