Strongly correlated non-equilibrium steady states with currents – quantum and classical picture
In this minireview we will discuss recent progress in the analytical study of current-carrying non-equilibrium steady states (NESS) that can be constructed in terms of a matrix product ansatz. We will focus on one-dimensional exactly solvable strongly correlated cases, and will study both quantum mo...
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| Format: | Journal article |
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EDP Sciences
2018
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| _version_ | 1826287817815228416 |
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| author | Buca, B Prosen, T |
| author_facet | Buca, B Prosen, T |
| author_sort | Buca, B |
| collection | OXFORD |
| description | In this minireview we will discuss recent progress in the analytical study of current-carrying non-equilibrium steady states (NESS) that can be constructed in terms of a matrix product ansatz. We will focus on one-dimensional exactly solvable strongly correlated cases, and will study both quantum models, and classical models which are deterministic in the bulk. The only source of classical stochasticity in the time-evolution will come from the boundaries of the system. Physically, these boundaries may be understood as Markovian baths, which drive the current through the system. The examples studied include the open XXZ Heisenberg spin chain, the open Hubbard model, and a classical integrable reversible cellular automaton, namely the Rule 54 of A. Bobenko et al. [A. Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] with stochastic boundaries. The quantum NESS can be at least partially understood through the Yang–Baxter integrability structure of the underlying integrable bulk Hamiltonian, whereas for the Rule 54 model NESS seems to come from a seemingly unrelated integrability theory. In both the quantum and the classical case, the underlying matrix product ansatz defining the NESS also allows for construction of novel conservation laws of the bulk models themselves. In the classical case, a modification of the matrix product ansatz also allows for construction of states beyond the steady state (i.e., some of the decay modes – Liouvillian eigenvectors of the model). We hope that this article will help further the quest to unite different perspectives of integrability of NESS (of both quantum and classical models) into a single unified framework. |
| first_indexed | 2024-03-07T02:04:21Z |
| format | Journal article |
| id | oxford-uuid:9e73dd0a-c379-4d16-911e-b3af3ca8d9e1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:04:21Z |
| publishDate | 2018 |
| publisher | EDP Sciences |
| record_format | dspace |
| spelling | oxford-uuid:9e73dd0a-c379-4d16-911e-b3af3ca8d9e12022-03-27T00:50:08ZStrongly correlated non-equilibrium steady states with currents – quantum and classical pictureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9e73dd0a-c379-4d16-911e-b3af3ca8d9e1Symplectic Elements at OxfordEDP Sciences2018Buca, BProsen, TIn this minireview we will discuss recent progress in the analytical study of current-carrying non-equilibrium steady states (NESS) that can be constructed in terms of a matrix product ansatz. We will focus on one-dimensional exactly solvable strongly correlated cases, and will study both quantum models, and classical models which are deterministic in the bulk. The only source of classical stochasticity in the time-evolution will come from the boundaries of the system. Physically, these boundaries may be understood as Markovian baths, which drive the current through the system. The examples studied include the open XXZ Heisenberg spin chain, the open Hubbard model, and a classical integrable reversible cellular automaton, namely the Rule 54 of A. Bobenko et al. [A. Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] with stochastic boundaries. The quantum NESS can be at least partially understood through the Yang–Baxter integrability structure of the underlying integrable bulk Hamiltonian, whereas for the Rule 54 model NESS seems to come from a seemingly unrelated integrability theory. In both the quantum and the classical case, the underlying matrix product ansatz defining the NESS also allows for construction of novel conservation laws of the bulk models themselves. In the classical case, a modification of the matrix product ansatz also allows for construction of states beyond the steady state (i.e., some of the decay modes – Liouvillian eigenvectors of the model). We hope that this article will help further the quest to unite different perspectives of integrability of NESS (of both quantum and classical models) into a single unified framework. |
| spellingShingle | Buca, B Prosen, T Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title | Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title_full | Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title_fullStr | Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title_full_unstemmed | Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title_short | Strongly correlated non-equilibrium steady states with currents – quantum and classical picture |
| title_sort | strongly correlated non equilibrium steady states with currents quantum and classical picture |
| work_keys_str_mv | AT bucab stronglycorrelatednonequilibriumsteadystateswithcurrentsquantumandclassicalpicture AT prosent stronglycorrelatednonequilibriumsteadystateswithcurrentsquantumandclassicalpicture |