Keldysh nonlinear sigma model for a free-fermion gas under continuous measurements
Quantum entanglement phase transitions have provided new insights into quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their in...
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Published in | Physical review research Vol. 5; no. 3; p. 033174 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
American Physical Society
01.09.2023
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Online Access | Get full text |
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Summary: | Quantum entanglement phase transitions have provided new insights into quantum many-body dynamics. Both disorders and measurements are found to induce similar entanglement transitions. Here, we provide a theoretical framework that unifies these two seemingly disparate concepts and discloses their internal connections. Specifically, we analytically analyze a d-dimensional free-fermion gas subject to continuous projective measurements. By mapping the Lindblad master equation to the functional Keldysh field theory, we develop an effective theory termed as the time-local Keldysh nonlinear sigma model, which enables us to analytically describe the physics of the monitored system. Our effective theory resembles that used to describe the disordered fermionic systems. As an application of the effective theory, we study the transport property and obtain a Drude-form conductivity where the elastic scattering time is replaced by the inverse measurement strength. According to these similarities, two different concepts, measurements and disorders, are unified in the same theoretical framework. A numerical verification of our theory and predictions is also provided. |
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ISSN: | 2643-1564 2643-1564 |
DOI: | 10.1103/PhysRevResearch.5.033174 |