Buchhold, M., Minoguchi, Y., Altland, A. and Diehl, S. (2021). Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions. Phys. Rev. X, 11 (4). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2160-3308
Full text not available from this repository.Abstract
A wave function subject to unitary time evolution and exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement-induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantumphase transitions. To access this competition despite the randomness of single quantum trajectories, we construct an n-replica Keldysh field theory for the ensemble average of the nth moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, while n - 1 others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in (1 + 1) dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the nonHermitian Hamiltonian corresponds to a quantum sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a measurement-induced pinning of the trajectory wave function into eigenstates of the measurement operators, which succeeds upon increasing the monitoring rate across a critical threshold.
| Item Type: | Journal Article | ||||||||||||||||||||
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| URN: | urn:nbn:de:hbz:38-570614 | ||||||||||||||||||||
| DOI: | 10.1103/PhysRevX.11.041004 | ||||||||||||||||||||
| Journal or Publication Title: | Phys. Rev. X | ||||||||||||||||||||
| Volume: | 11 | ||||||||||||||||||||
| Number: | 4 | ||||||||||||||||||||
| Date: | 2021 | ||||||||||||||||||||
| Publisher: | AMER PHYSICAL SOC | ||||||||||||||||||||
| Place of Publication: | COLLEGE PK | ||||||||||||||||||||
| ISSN: | 2160-3308 | ||||||||||||||||||||
| Language: | English | ||||||||||||||||||||
| Faculty: | Unspecified | ||||||||||||||||||||
| Divisions: | Unspecified | ||||||||||||||||||||
| Subjects: | no entry | ||||||||||||||||||||
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/57061 |
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