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arXiv:2207.09476 · Physical Review X

Measurements Conspire Nonlocally to Restructure Critical Quantum States

Samuel J. Garratt, Zack Weinstein, Ehud Altman

Published May 18, 2023• 75 citations
arXivHTMLPDF

Abstract

When quantum critical states are measured in many locations, new collective phenomena can emerge. There are transitions between two regimes: one where the effects of measurements on correlations are negligible, and one where they are dramatic.
DOI
10.1103/physrevx.13.021026

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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.
Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce nonlocalnonlocalnonlocal quantumquantumquantum fluctuationsfluctuationsfluctuations as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.