Fractonic Fractional Quantum Hall Effect
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916930533720064 |
|---|---|
| author | Schirmann, Justin d'Ornellas, Peru Stahl, Charles Grushin, Adolfo G. |
| author_facet | Schirmann, Justin d'Ornellas, Peru Stahl, Charles Grushin, Adolfo G. |
| contents | In non-interacting systems, disorder can drive a trivial phase into a topological one. However little is known how to construct a fractional quantum Hall ground-state, a paradigmatic topologically ordered state, that exists both in crystalline and disordered lattices and is qualitatively different to known topological phases. Here, we propose a general method for building such a phase. This is done by coupling quantum wires placed aperiodically in real-space, where the spatial positioning allows us to tune the inter-wire couplings. We call the emergent phase the Fractonic Fractional Quantum Hall Effect as it displays a rich interplay of fractional quantum Hall physics with fractonic constraints, formed by coupling differently-fractionalised wires into a globally gapped phase. The ground state has an exponential degeneracy in system size, a signature of the emergence of fractons. It displays a rich phenomenology of excitations, which can either behave like anyons confined to move in one dimension (lineons), multiples of which can then hop between two wires (s-lineons) or be free to travel across the system (C-anyons), depending on the multiplicity. Both the ground state degeneracy and mutual statistics are directly determined by the real-space positions of the wires, which can be disordered. Our method provides an analytically solvable pathway to non-crystalline fractional quantum Hall effects and fractonic theories in two-dimensions, examples of which were lacking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractonic Fractional Quantum Hall Effect Schirmann, Justin d'Ornellas, Peru Stahl, Charles Grushin, Adolfo G. Strongly Correlated Electrons Mesoscale and Nanoscale Physics In non-interacting systems, disorder can drive a trivial phase into a topological one. However little is known how to construct a fractional quantum Hall ground-state, a paradigmatic topologically ordered state, that exists both in crystalline and disordered lattices and is qualitatively different to known topological phases. Here, we propose a general method for building such a phase. This is done by coupling quantum wires placed aperiodically in real-space, where the spatial positioning allows us to tune the inter-wire couplings. We call the emergent phase the Fractonic Fractional Quantum Hall Effect as it displays a rich interplay of fractional quantum Hall physics with fractonic constraints, formed by coupling differently-fractionalised wires into a globally gapped phase. The ground state has an exponential degeneracy in system size, a signature of the emergence of fractons. It displays a rich phenomenology of excitations, which can either behave like anyons confined to move in one dimension (lineons), multiples of which can then hop between two wires (s-lineons) or be free to travel across the system (C-anyons), depending on the multiplicity. Both the ground state degeneracy and mutual statistics are directly determined by the real-space positions of the wires, which can be disordered. Our method provides an analytically solvable pathway to non-crystalline fractional quantum Hall effects and fractonic theories in two-dimensions, examples of which were lacking. |
| title | Fractonic Fractional Quantum Hall Effect |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2504.18337 |