Topological order in spin nematics from the quantum melting of a disclination lattice
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866917870699544576 |
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| author | Nikolić, Predrag |
| author_facet | Nikolić, Predrag |
| contents | The topological defects of Spin($n+1$) nematics in two spatial dimensions, known as disclinations, are characterized by the $π_1(\mathbb{R}P^n) = \textrm{Z}_2$ homotopy group for $n\ge2$. We argue that incompressible quantum liquids of disclinations can exist as stable low-temperature phases and host composite quasiparticles which combine a fractional amount of fundamental Z$_2$ charge with a unit of topological charge. The four-fold topological ground state degeneracy on a torus admits a fermionic or semionic quasiparticle exchange statistics. The topological non-triviality of these states is visible in the existence of protected gapless edge modes. While the fermionic nematic and gapped Z$_2$ spin liquids have equivalent topological orders, they are still thermodynamically distinct due to having different edge modes, in analogy to the topologically non-trivial and trivial states of quantum spin-Hall systems. The analysis proceeds by recasting the Z$_2$ gauge theory of spin nematics as a continuum limit theory with a larger gauge structure. Nematic fractionalization parallels that of a quantum Hall liquid, but the large gauge symmetry restores the time-reversal symmetry and restricts the quasiparticle fusion rules and statistics. The conclusions from field theory analysis are complemented with the construction of plausible host microscopic models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological order in spin nematics from the quantum melting of a disclination lattice Nikolić, Predrag Strongly Correlated Electrons The topological defects of Spin($n+1$) nematics in two spatial dimensions, known as disclinations, are characterized by the $π_1(\mathbb{R}P^n) = \textrm{Z}_2$ homotopy group for $n\ge2$. We argue that incompressible quantum liquids of disclinations can exist as stable low-temperature phases and host composite quasiparticles which combine a fractional amount of fundamental Z$_2$ charge with a unit of topological charge. The four-fold topological ground state degeneracy on a torus admits a fermionic or semionic quasiparticle exchange statistics. The topological non-triviality of these states is visible in the existence of protected gapless edge modes. While the fermionic nematic and gapped Z$_2$ spin liquids have equivalent topological orders, they are still thermodynamically distinct due to having different edge modes, in analogy to the topologically non-trivial and trivial states of quantum spin-Hall systems. The analysis proceeds by recasting the Z$_2$ gauge theory of spin nematics as a continuum limit theory with a larger gauge structure. Nematic fractionalization parallels that of a quantum Hall liquid, but the large gauge symmetry restores the time-reversal symmetry and restricts the quasiparticle fusion rules and statistics. The conclusions from field theory analysis are complemented with the construction of plausible host microscopic models. |
| title | Topological order in spin nematics from the quantum melting of a disclination lattice |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2409.16352 |