Theory of free fermions dynamics under partial post-selected monitoring
- URL: http://arxiv.org/abs/2312.14022v1
- Date: Thu, 21 Dec 2023 16:53:42 GMT
- Title: Theory of free fermions dynamics under partial post-selected monitoring
- Authors: Chun Y. Leung, Dganit Meidan and Alessandro Romito
- Abstract summary: We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement.
We show that the passage to the monitored universality occurs abruptly at finite partial post-selection.
Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
- Score: 49.1574468325115
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Monitored quantum systems undergo Measurement-induced Phase Transitions
(MiPTs) stemming from the interplay between measurements and unitary dynamics.
When the detector readout is post-selected to match a given value, the dynamics
is generated by a Non-Hermitian Hamiltonian with MiPTs characterized by
different universal features. Here, we derive a partial post-selected
stochastic Schr\"odinger equation based on a microscopic description of
continuous weak measurement. This formalism connects the monitored and
post-selected dynamics to a broader family of stochastic evolution. We apply
the formalism to a chain of free fermions subject to partial post-selected
monitoring of local fermion parities. Within a 2-replica approach, we obtained
an effective bosonized Hamiltonian in the strong post-selected limit. Using a
renormalization group analysis, we find that the universality of the
non-Hermitian MiPT is stable against a finite (weak) amount of stochasticity.
We further show that the passage to the monitored universality occurs abruptly
at finite partial post-selection, which we confirm from the numerical finite
size scaling of the MiPT. Our approach establishes a way to study MiPTs for
arbitrary subsets of quantum trajectories and provides a potential route to
tackle the experimental post-selected problem.
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