Quantum and classical localization and the Manhattan lattice
We consider a network model, embedded on the Manhattan lattice, of a quantum localization problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A map...
| Principais autores: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
2003
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| _version_ | 1826268979002343424 |
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| author | Beamond, E Owczarek, A Cardy, J |
| author_facet | Beamond, E Owczarek, A Cardy, J |
| author_sort | Beamond, E |
| collection | OXFORD |
| description | We consider a network model, embedded on the Manhattan lattice, of a quantum localization problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A mapping exists between problems belonging to this symmetry class and certain classical random walks which are self-avoiding and have attractive interactions; we exploit this equivalence, using a study of the classical random walks to gain information about the corresponding quantum problem. In a field-theoretic approach, we show that the interactions may flow to one of two possible strong-coupling regimes separated by a transition: however, using Monte Carlo simulations we show that the walks are in fact always compact two-dimensional objects with a well-defined one-dimensional surface, indicating that the corresponding quantum system is localized. |
| first_indexed | 2024-03-06T21:17:50Z |
| format | Journal article |
| id | oxford-uuid:4065170b-cb15-4688-b951-b8664d322311 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:17:50Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:4065170b-cb15-4688-b951-b8664d3223112022-03-26T14:37:39ZQuantum and classical localization and the Manhattan latticeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4065170b-cb15-4688-b951-b8664d322311EnglishSymplectic Elements at Oxford2003Beamond, EOwczarek, ACardy, JWe consider a network model, embedded on the Manhattan lattice, of a quantum localization problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A mapping exists between problems belonging to this symmetry class and certain classical random walks which are self-avoiding and have attractive interactions; we exploit this equivalence, using a study of the classical random walks to gain information about the corresponding quantum problem. In a field-theoretic approach, we show that the interactions may flow to one of two possible strong-coupling regimes separated by a transition: however, using Monte Carlo simulations we show that the walks are in fact always compact two-dimensional objects with a well-defined one-dimensional surface, indicating that the corresponding quantum system is localized. |
| spellingShingle | Beamond, E Owczarek, A Cardy, J Quantum and classical localization and the Manhattan lattice |
| title | Quantum and classical localization and the Manhattan lattice |
| title_full | Quantum and classical localization and the Manhattan lattice |
| title_fullStr | Quantum and classical localization and the Manhattan lattice |
| title_full_unstemmed | Quantum and classical localization and the Manhattan lattice |
| title_short | Quantum and classical localization and the Manhattan lattice |
| title_sort | quantum and classical localization and the manhattan lattice |
| work_keys_str_mv | AT beamonde quantumandclassicallocalizationandthemanhattanlattice AT owczareka quantumandclassicallocalizationandthemanhattanlattice AT cardyj quantumandclassicallocalizationandthemanhattanlattice |