Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models
Isotropic but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, nonintegrable, as well as disordered examples, and not necessarily restricted to one dimension or short-range interactions. Taking for granted tha...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043040 |
| _version_ | 1797210381744078848 |
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| author | Peter Reimann Patrick Vorndamme Jürgen Schnack |
| author_facet | Peter Reimann Patrick Vorndamme Jürgen Schnack |
| author_sort | Peter Reimann |
| collection | DOAJ |
| description | Isotropic but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, nonintegrable, as well as disordered examples, and not necessarily restricted to one dimension or short-range interactions. Taking for granted that the nonequilibrium initial condition and the spectrum of the field-free model satisfy some very weak requirements, expectation values of generic observables are analytically shown to exhibit permanent long-time oscillations, thus ruling out equilibration. If the model (but not necessarily the initial condition) is translationally invariant, the long-time oscillations are moreover shown to exhibit synchronization in the long run, meaning that they are invariant under arbitrary translations of the observable. Analogous long-time oscillations are also recovered for temporal correlation functions when the system is already at thermal equilibrium from the outset, thus realizing a so-called time crystal. |
| first_indexed | 2024-04-24T10:09:42Z |
| format | Article |
| id | doaj.art-814ac7e38ec5461aa962cb3105388a80 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:09:42Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-814ac7e38ec5461aa962cb3105388a802024-04-12T17:34:58ZengAmerican Physical SocietyPhysical Review Research2643-15642023-10-015404304010.1103/PhysRevResearch.5.043040Nonequilibration, synchronization, and time crystals in isotropic Heisenberg modelsPeter ReimannPatrick VorndammeJürgen SchnackIsotropic but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, nonintegrable, as well as disordered examples, and not necessarily restricted to one dimension or short-range interactions. Taking for granted that the nonequilibrium initial condition and the spectrum of the field-free model satisfy some very weak requirements, expectation values of generic observables are analytically shown to exhibit permanent long-time oscillations, thus ruling out equilibration. If the model (but not necessarily the initial condition) is translationally invariant, the long-time oscillations are moreover shown to exhibit synchronization in the long run, meaning that they are invariant under arbitrary translations of the observable. Analogous long-time oscillations are also recovered for temporal correlation functions when the system is already at thermal equilibrium from the outset, thus realizing a so-called time crystal.http://doi.org/10.1103/PhysRevResearch.5.043040 |
| spellingShingle | Peter Reimann Patrick Vorndamme Jürgen Schnack Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models Physical Review Research |
| title | Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models |
| title_full | Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models |
| title_fullStr | Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models |
| title_full_unstemmed | Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models |
| title_short | Nonequilibration, synchronization, and time crystals in isotropic Heisenberg models |
| title_sort | nonequilibration synchronization and time crystals in isotropic heisenberg models |
| url | http://doi.org/10.1103/PhysRevResearch.5.043040 |
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