Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver
The accurate characterization of nonequilibrium strongly correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043052 |
| _version_ | 1797211238857441280 |
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| author | Matan Lotem Andreas Weichselbaum Jan von Delft Moshe Goldstein |
| author_facet | Matan Lotem Andreas Weichselbaum Jan von Delft Moshe Goldstein |
| author_sort | Matan Lotem |
| collection | DOAJ |
| description | The accurate characterization of nonequilibrium strongly correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, they feature correlated phenomena, including small emergent energy scales and non-Fermi-liquid physics, requiring renormalization group treatment. This has typically been at odds with the description of their nonequilibrium steady state under finite bias, which exposes their nature as open quantum systems. We present a numerically exact method for obtaining the nonequilibrium state of a general quantum impurity coupled to metallic leads at arbitrary voltage or temperature bias, which we call “RL-NESS” (renormalized Lindblad-driven nonequilibrium steady state). It is based on coherently coupling the impurity to discretized leads which are treated exactly. These leads are furthermore weakly coupled to reservoirs described by Lindblad dynamics which impose voltage or temperature bias. Going beyond previous attempts, we exploit a hybrid discretization scheme for the leads together with Wilson's numerical renormalization group, in order to probe exponentially small energy scales. The steady state is then found by evolving a matrix-product density operator via real-time Lindblad dynamics, employing a dissipative generalization of the time-dependent density matrix renormalization group. In the long-time limit, this procedure successfully converges to the steady state at finite bond dimension due to the introduced dissipation, which bounds the growth of entanglement. We thoroughly test the method against the exact solution of the noninteracting resonant level model. We then demonstrate its power using an interacting two-level model, for which it correctly reproduces the known limits, and gives the full I-V curve between them. |
| first_indexed | 2024-04-24T10:23:19Z |
| format | Article |
| id | doaj.art-f455f4c45cb74edc8269205a4e141063 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:23:19Z |
| publishDate | 2020-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f455f4c45cb74edc8269205a4e1410632024-04-12T17:02:08ZengAmerican Physical SocietyPhysical Review Research2643-15642020-10-012404305210.1103/PhysRevResearch.2.043052Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solverMatan LotemAndreas WeichselbaumJan von DelftMoshe GoldsteinThe accurate characterization of nonequilibrium strongly correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, they feature correlated phenomena, including small emergent energy scales and non-Fermi-liquid physics, requiring renormalization group treatment. This has typically been at odds with the description of their nonequilibrium steady state under finite bias, which exposes their nature as open quantum systems. We present a numerically exact method for obtaining the nonequilibrium state of a general quantum impurity coupled to metallic leads at arbitrary voltage or temperature bias, which we call “RL-NESS” (renormalized Lindblad-driven nonequilibrium steady state). It is based on coherently coupling the impurity to discretized leads which are treated exactly. These leads are furthermore weakly coupled to reservoirs described by Lindblad dynamics which impose voltage or temperature bias. Going beyond previous attempts, we exploit a hybrid discretization scheme for the leads together with Wilson's numerical renormalization group, in order to probe exponentially small energy scales. The steady state is then found by evolving a matrix-product density operator via real-time Lindblad dynamics, employing a dissipative generalization of the time-dependent density matrix renormalization group. In the long-time limit, this procedure successfully converges to the steady state at finite bond dimension due to the introduced dissipation, which bounds the growth of entanglement. We thoroughly test the method against the exact solution of the noninteracting resonant level model. We then demonstrate its power using an interacting two-level model, for which it correctly reproduces the known limits, and gives the full I-V curve between them.http://doi.org/10.1103/PhysRevResearch.2.043052 |
| spellingShingle | Matan Lotem Andreas Weichselbaum Jan von Delft Moshe Goldstein Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver Physical Review Research |
| title | Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver |
| title_full | Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver |
| title_fullStr | Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver |
| title_full_unstemmed | Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver |
| title_short | Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver |
| title_sort | renormalized lindblad driving a numerically exact nonequilibrium quantum impurity solver |
| url | http://doi.org/10.1103/PhysRevResearch.2.043052 |
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