Dihedral twist liquid models from emergent Majorana fermions
We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-03-30-967/pdf/ |
| _version_ | 1797855933196402688 |
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| author | Jeffrey C. Y. Teo Yichen Hu |
| author_facet | Jeffrey C. Y. Teo Yichen Hu |
| author_sort | Jeffrey C. Y. Teo |
| collection | DOAJ |
| description | We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the $SO(N)$ Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral $D_k$ symmetry of $SO(2n)_1$, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the $\mathcal{C}/G$ twist liquids, where $G=\mathbb{Z}_2$ for $\mathcal{C}=U(1)_l$, $SU(n)_1$, and $G=\mathbb{Z}_2$, $\mathbb{Z}_k$, $D_k$ for $\mathcal{C}=SO(2n)_1$. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in $SO(2n)_1/G$ by identifying the non-chiral components of the twist liquids with discrete gauge theories. |
| first_indexed | 2024-04-09T20:32:11Z |
| format | Article |
| id | doaj.art-3e1dda6bd727437ab1bdc133424491d4 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-09T20:32:11Z |
| publishDate | 2023-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-3e1dda6bd727437ab1bdc133424491d42023-03-30T12:38:28ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-03-01796710.22331/q-2023-03-30-96710.22331/q-2023-03-30-967Dihedral twist liquid models from emergent Majorana fermionsJeffrey C. Y. TeoYichen HuWe present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute the $SO(N)$ Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedral $D_k$ symmetry of $SO(2n)_1$, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates the $\mathcal{C}/G$ twist liquids, where $G=\mathbb{Z}_2$ for $\mathcal{C}=U(1)_l$, $SU(n)_1$, and $G=\mathbb{Z}_2$, $\mathbb{Z}_k$, $D_k$ for $\mathcal{C}=SO(2n)_1$. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern in $SO(2n)_1/G$ by identifying the non-chiral components of the twist liquids with discrete gauge theories.https://quantum-journal.org/papers/q-2023-03-30-967/pdf/ |
| spellingShingle | Jeffrey C. Y. Teo Yichen Hu Dihedral twist liquid models from emergent Majorana fermions Quantum |
| title | Dihedral twist liquid models from emergent Majorana fermions |
| title_full | Dihedral twist liquid models from emergent Majorana fermions |
| title_fullStr | Dihedral twist liquid models from emergent Majorana fermions |
| title_full_unstemmed | Dihedral twist liquid models from emergent Majorana fermions |
| title_short | Dihedral twist liquid models from emergent Majorana fermions |
| title_sort | dihedral twist liquid models from emergent majorana fermions |
| url | https://quantum-journal.org/papers/q-2023-03-30-967/pdf/ |
| work_keys_str_mv | AT jeffreycyteo dihedraltwistliquidmodelsfromemergentmajoranafermions AT yichenhu dihedraltwistliquidmodelsfromemergentmajoranafermions |