Probing Conformal Invariant of Non-unitary Two-Dimensional Systems by Central Spin Decoherence

Abstract

Universality classes of non-unitary critical theories in two-dimensions are characterized by a dimensional number, termed central charge or conformal anomaly. Conformal invariance predicts that the leading finite-size correction to the free energy of a two-dimensional system at a conformal invariant critical point is linearly related to the central charge of the corresponding conformal field theory. However, experimental determination of the central charge of a non-unitary conformal invariant critical theory has not been done before because of the intrinsic difficulty that complex parameters occurs in non-unitary theory, which is not physical. Here we propose to extract the central charge of the non-unitary conformal invariant critical point of a two-dimensional lattice models from the quantum coherence measurement of a probe spin which is coupled to the two-dimensional lattice models. A recent discovery shows that quantum decoherence of a probe spin which is coupled to a bath is proportional to the partition function of the bath with a complex parameter. Thus the central charge of a non-unitary conformal field theory could be extracted from quantum decoherence measurement of a probe spin which is coupled to a bath. We have applied the method to a typical non-unitary conformal invariant critical theory, namely the Yang-Lee edge singularity of the two-dimensional Ising model and extracted the central charge of the Yang-Lee edge singularity in two-dimensional Ising model with good precision and tested other predictions of non-unitary conformal field theory. This work paves the way for the first experimental observation of the central charge of non-unitary conformal field theory.

17 pages, 3 Figures. arXiv admin note: substantial text overlap with arXiv:1706.04294

References in corpus (4)

• Observation of Lee-Yang zeros
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Entanglement in non-unitary quantum critical spin chains
• Probing Yang-Lee Edge Singularity by Central Spin Decoherence

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• Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays
• Experimental observation of the Yang-Lee quantum criticality in open systems
• Quantum Algorithms for Open Lattice Field Theory
• Relations between Heat Exchange and Rényi Divergences
• Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
• Dissipation in the Generalized Gibbs Ensemble
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble