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

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.