Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry
Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS sta...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2013-04-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2073-8994/5/2/119 |
| _version_ | 1817990217596928000 |
|---|---|
| author | Keisuke Totsuka Kazuki Hasebe |
| author_facet | Keisuke Totsuka Kazuki Hasebe |
| author_sort | Keisuke Totsuka |
| collection | DOAJ |
| description | Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS) states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU(2) and SO(5) VBS states, i.e., UOSp(N|2) and UOSp(N|4) SVBS states, whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (super)spins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (super)spin states. |
| first_indexed | 2024-04-14T00:56:25Z |
| format | Article |
| id | doaj.art-903c36e60815422c9fd5188ee9c7de3d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T00:56:25Z |
| publishDate | 2013-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-903c36e60815422c9fd5188ee9c7de3d2022-12-22T02:21:35ZengMDPI AGSymmetry2073-89942013-04-015211921410.3390/sym5020119Topological Many-Body States in Quantum Antiferromagnets via Fuzzy SupergeometryKeisuke TotsukaKazuki HasebeRecent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS) states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU(2) and SO(5) VBS states, i.e., UOSp(N|2) and UOSp(N|4) SVBS states, whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (super)spins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (super)spin states.http://www.mdpi.com/2073-8994/5/2/119quantum antiferromagnetsupersymmetryfuzzy spherematrix product statequantum entanglementtopological order |
| spellingShingle | Keisuke Totsuka Kazuki Hasebe Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry Symmetry quantum antiferromagnet supersymmetry fuzzy sphere matrix product state quantum entanglement topological order |
| title | Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry |
| title_full | Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry |
| title_fullStr | Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry |
| title_full_unstemmed | Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry |
| title_short | Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry |
| title_sort | topological many body states in quantum antiferromagnets via fuzzy supergeometry |
| topic | quantum antiferromagnet supersymmetry fuzzy sphere matrix product state quantum entanglement topological order |
| url | http://www.mdpi.com/2073-8994/5/2/119 |
| work_keys_str_mv | AT keisuketotsuka topologicalmanybodystatesinquantumantiferromagnetsviafuzzysupergeometry AT kazukihasebe topologicalmanybodystatesinquantumantiferromagnetsviafuzzysupergeometry |