An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System
We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a nove...
| Main Authors: | , , , , |
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| Format: | Journal article |
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2014
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| _version_ | 1797062558584143872 |
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| author | Giscard, P Choo, Z Mitchison, M Mendoza-Arenas, J Jaksch, D |
| author_facet | Giscard, P Choo, Z Mitchison, M Mendoza-Arenas, J Jaksch, D |
| author_sort | Giscard, P |
| collection | OXFORD |
| description | We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a novel form of the fractional moment criterion, which we establish, together with a generalisation of the self-avoiding walk representation of the system Green's functions, called path-sums. These techniques are not specific to the XYZ model and hold in a much more general setting. We further present bounds for two observable quantities in the localised regime: the magnetisation of any sublattice of the system as well as the linear magnetic response function of the system. We confirm our results through numerical simulations. |
| first_indexed | 2024-03-06T20:47:14Z |
| format | Journal article |
| id | oxford-uuid:36527157-e67e-46f5-b10d-03233be0cc96 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:47:14Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:36527157-e67e-46f5-b10d-03233be0cc962022-03-26T13:37:10ZAn Explicit Bound for Dynamical Localisation in an Interacting Many-Body SystemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:36527157-e67e-46f5-b10d-03233be0cc96Symplectic Elements at Oxford2014Giscard, PChoo, ZMitchison, MMendoza-Arenas, JJaksch, DWe characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a novel form of the fractional moment criterion, which we establish, together with a generalisation of the self-avoiding walk representation of the system Green's functions, called path-sums. These techniques are not specific to the XYZ model and hold in a much more general setting. We further present bounds for two observable quantities in the localised regime: the magnetisation of any sublattice of the system as well as the linear magnetic response function of the system. We confirm our results through numerical simulations. |
| spellingShingle | Giscard, P Choo, Z Mitchison, M Mendoza-Arenas, J Jaksch, D An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System |
| title | An Explicit Bound for Dynamical Localisation in an Interacting Many-Body
System |
| title_full | An Explicit Bound for Dynamical Localisation in an Interacting Many-Body
System |
| title_fullStr | An Explicit Bound for Dynamical Localisation in an Interacting Many-Body
System |
| title_full_unstemmed | An Explicit Bound for Dynamical Localisation in an Interacting Many-Body
System |
| title_short | An Explicit Bound for Dynamical Localisation in an Interacting Many-Body
System |
| title_sort | explicit bound for dynamical localisation in an interacting many body system |
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