Analytic solution of the domain-wall nonequilibrium stationary state
We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetizations. We study the stationary state which emerges by the unitary evolution via the spin-1/2 XXZ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Usin...
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| Format: | Journal article |
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American Physical Society
2018
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| _version_ | 1826302760249720832 |
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| author | Collura, M De Luca, A Viti, J |
| author_facet | Collura, M De Luca, A Viti, J |
| author_sort | Collura, M |
| collection | OXFORD |
| description | We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetizations. We study the stationary state which emerges by the unitary evolution via the spin-1/2 XXZ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Using the generalized hydrodynamic approach, we present a simple formula for the space-time profile of the spin current and the magnetization exact in the limit of long times. As a remarkable effect, we show that the stationary state has a strongly discontinuous dependence on the strength of interaction as confirmed by the exact analytic expression of the Drude weight that we compute. These features allow us to give a qualitative estimation for the transient behavior of the current which is in good agreement with numerical simulations. Moreover, we analyze the behavior around the edge of the magnetization profile, and we argue that, unlike the XX free-fermionic point, interactions always prevent the emergence of a Tracy-Widom scaling. |
| first_indexed | 2024-03-07T05:52:24Z |
| format | Journal article |
| id | oxford-uuid:e9577eaf-6e75-4d4c-93c5-1ecfb60b8549 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:52:24Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:e9577eaf-6e75-4d4c-93c5-1ecfb60b85492022-03-27T10:53:33ZAnalytic solution of the domain-wall nonequilibrium stationary stateJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e9577eaf-6e75-4d4c-93c5-1ecfb60b8549Symplectic Elements at OxfordAmerican Physical Society2018Collura, MDe Luca, AViti, JWe consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetizations. We study the stationary state which emerges by the unitary evolution via the spin-1/2 XXZ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Using the generalized hydrodynamic approach, we present a simple formula for the space-time profile of the spin current and the magnetization exact in the limit of long times. As a remarkable effect, we show that the stationary state has a strongly discontinuous dependence on the strength of interaction as confirmed by the exact analytic expression of the Drude weight that we compute. These features allow us to give a qualitative estimation for the transient behavior of the current which is in good agreement with numerical simulations. Moreover, we analyze the behavior around the edge of the magnetization profile, and we argue that, unlike the XX free-fermionic point, interactions always prevent the emergence of a Tracy-Widom scaling. |
| spellingShingle | Collura, M De Luca, A Viti, J Analytic solution of the domain-wall nonequilibrium stationary state |
| title | Analytic solution of the domain-wall nonequilibrium stationary state |
| title_full | Analytic solution of the domain-wall nonequilibrium stationary state |
| title_fullStr | Analytic solution of the domain-wall nonequilibrium stationary state |
| title_full_unstemmed | Analytic solution of the domain-wall nonequilibrium stationary state |
| title_short | Analytic solution of the domain-wall nonequilibrium stationary state |
| title_sort | analytic solution of the domain wall nonequilibrium stationary state |
| work_keys_str_mv | AT colluram analyticsolutionofthedomainwallnonequilibriumstationarystate AT delucaa analyticsolutionofthedomainwallnonequilibriumstationarystate AT vitij analyticsolutionofthedomainwallnonequilibriumstationarystate |