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  • Open Access

Quantum Criticality Under Decoherence or Weak Measurement

Jong Yeon Lee1, Chao-Ming Jian2, and Cenke Xu3

  • 1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 2Department of Physics, Cornell University, Ithaca, New York 14853, USA
  • 3Department of Physics, University of California, Santa Barbara, California 93106, USA

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PRX Quantum 4, 030317 – Published 4 August, 2023

DOI: https://doi.org/10.1103/PRXQuantum.4.030317

Abstract

Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCPs) in a nontrivial way. As was pointed out in the recent literature on (1+1)d conformal field theory (CFT) [Garratt et al. Measurements conspire nonlocally to restructure critical quantum states, arXiv:2207.09476 (2022)], 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 postselecting the measurement outcomes. Our main results are as follows: (1) for an O(N) Wilson-Fisher QCP under weak measurement with postselection, an observer would, in general, observe two different types of boundary and 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 postselection, 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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Popular Summary

Quantum decoherence serves as the link between the microscopic quantum realm and the macroscopic classical realm. This process involves the gradual loss of quantum information in a quantum system as it becomes entangled with environmental degrees of freedom. Decoherence can also be understood as the system being effectively ”measured” by the environment in a certain way. Understanding the behavior of quantum systems, particularly quantum many-body systems, under the influence of decoherence is of significant importance and interest. Quantum critical states represent one big class of archetypal quantum many-body systems, and in this work, we investigate the effect of decoherence and measurement on systems at quantum critical points.

By employing the powerful techniques of field theory and the renormalization group, we demonstrate that decoherence and measurements can steer a conventional quantum critical state to display unusual and unexpected scaling behaviors. In some cases, they can even induce novel phase transitions. Remarkably, an unconventional quantum critical point featuring fractionalization may experience “confinement” as a consequence of decoherence. Furthermore, our investigation reveals that decoherence can drive topological phase transitions for specific types of topological order. This implies that the quantum information encoded within the topological order becomes irretrievably lost once a critical level of entanglement with the environment is surpassed.

Article Text

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PRX Quantum 4, 030317– Published 4 August, 2023
  • Received 11 February 2023
  • Accepted 14 June 2023
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