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Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics

by Y. Minoguchi, P. Rabl, M. Buchhold

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Submission summary

Authors (as registered SciPost users): Michael Buchhold · Yuri Minoguchi · Peter Rabl
Submission information
Preprint Link:  (pdf)
Date accepted: 2021-11-08
Date submitted: 2021-10-29 07:18
Submitted by: Minoguchi, Yuri
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance. Defying the complications imposed by the non-linear and stochastic nature of the measurement process, we introduce a scenario of measurement-induced many body evolution, which possesses an exact analytical solution: bosonic Gaussian measurements. The evolution features a competition between the continuous observation of linear boson operators and a free Hamiltonian, and it is characterized by a unique and exactly solvable covariance matrix. Within this framework, we then consider an elementary model for quantum criticality, the free boson conformal field theory, and investigate in which way criticality is modified under measurements. Depending on the measurement protocol, we distinguish three fundamental scenarios (a) enriched quantum criticality, characterized by a logarithmic entanglement growth with a floating prefactor, or the loss of criticality, indicated by an entanglement growth with either (b) an area-law or (c) a volume-law. For each scenario, we discuss the impact of imperfect measurements, which reduce the purity of the wavefunction and are equivalent to Markovian decoherence, and present a set of observables, e.g., real-space correlations, the relaxation time, and the entanglement structure, to classify the measurement-induced dynamics for both pure and mixed states. Finally, we present an experimental tomography scheme, which grants access to the density operator of the system by using the continuous measurement record only.

List of changes

1. title changed
2. improved introduction
3. revised abstract

Published as SciPost Phys. 12, 009 (2022)

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