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

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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
Creators:
CreatorsEmailORCIDORCID Put Code
Buchhold, M.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Minoguchi, Y.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Altland, A.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Diehl, S.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
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
Uncontrolled Keywords:
KeywordsLanguage
SINE-GORDON; QUANTUM; RENORMALIZATION; MODELMultiple languages
Physics, MultidisciplinaryMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/57061

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