Nonlinear Sigma Models for Monitored Dynamics of Free Fermions
We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginar...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-12-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.13.041045 |
| _version_ | 1797400505142476800 |
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| author | Michele Fava Lorenzo Piroli Tobias Swann Denis Bernard Adam Nahum |
| author_facet | Michele Fava Lorenzo Piroli Tobias Swann Denis Bernard Adam Nahum |
| author_sort | Michele Fava |
| collection | DOAJ |
| description | We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal N×N matrix, in the replica limit N→1. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases—nontrivially entangled and disentangled, respectively—in the physically relevant replica limit N→1. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size L scales as (ln L)^{2}, in contrast to findings in previously studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model’s phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems. |
| first_indexed | 2024-03-09T01:56:24Z |
| format | Article |
| id | doaj.art-27e83e747e3349c8a9713f413fd1b5e9 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-03-09T01:56:24Z |
| publishDate | 2023-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-27e83e747e3349c8a9713f413fd1b5e92023-12-08T15:03:52ZengAmerican Physical SocietyPhysical Review X2160-33082023-12-0113404104510.1103/PhysRevX.13.041045Nonlinear Sigma Models for Monitored Dynamics of Free FermionsMichele FavaLorenzo PiroliTobias SwannDenis BernardAdam NahumWe derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal N×N matrix, in the replica limit N→1. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases—nontrivially entangled and disentangled, respectively—in the physically relevant replica limit N→1. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size L scales as (ln L)^{2}, in contrast to findings in previously studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model’s phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems.http://doi.org/10.1103/PhysRevX.13.041045 |
| spellingShingle | Michele Fava Lorenzo Piroli Tobias Swann Denis Bernard Adam Nahum Nonlinear Sigma Models for Monitored Dynamics of Free Fermions Physical Review X |
| title | Nonlinear Sigma Models for Monitored Dynamics of Free Fermions |
| title_full | Nonlinear Sigma Models for Monitored Dynamics of Free Fermions |
| title_fullStr | Nonlinear Sigma Models for Monitored Dynamics of Free Fermions |
| title_full_unstemmed | Nonlinear Sigma Models for Monitored Dynamics of Free Fermions |
| title_short | Nonlinear Sigma Models for Monitored Dynamics of Free Fermions |
| title_sort | nonlinear sigma models for monitored dynamics of free fermions |
| url | http://doi.org/10.1103/PhysRevX.13.041045 |
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