Quantum criticality under decoherence or weak measurement
- URL: http://arxiv.org/abs/2301.05238v2
- Date: Thu, 27 Jul 2023 00:27:35 GMT
- Title: Quantum criticality under decoherence or weak measurement
- Authors: Jong Yeon Lee, Chao-Ming Jian, and Cenke Xu
- Abstract summary: We focus on decoherence caused by weak measurements with and without post-selection.
An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix.
We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Decoherence inevitably happens when a quantum state is exposed to its
environment, which can affect quantum critical points (QCP) in a nontrivial
way. As was pointed out in recent literature on $(1+1)d$ conformal field theory
(CFT), the effect of weak measurement can be mathematically mapped to the
problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose
boundary and defect effects have attracted enormous theoretical and numerical
interests very recently. We focus on decoherence caused by weak measurements
with and without post-selecting the measurement outcomes. Our main results are:
(1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection,
an observer would in general observe two different types of boundary/defect
criticality with very different behaviors from the well-known Wilson-Fisher
fixed points; in particular, it is possible to observe the recently proposed
exotic "extraordinary-log" correlation. (2) An extra quantum phase transition
can be driven by decoherence, if we consider quantities nonlinear with the
decohered density matrix, such as the Renyi entropy. We demonstrate the
connection between this transition to the information-theoretic transition
driven by an error in the toric code model. (3) When there is no
post-selection, though correlation functions between local operators remain the
same as the undecohered pure state, nonlocal operators such as the "disorder
operator" would have qualitatively distinct behaviors; and we also show that
the decoherence can lead to confinement.
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