Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: Jong Yeon Lee, Wenjie Ji, Zhen Bi, Matthew P. A. Fisher,
| Summary:
Measurements allow efficient preparation of interesting quantum many-body
states exhibiting long-range, topological, or fractonic orders. Here, we prove
that the so-called conformal quantum critical points (CQCP) can be obtained by
performing general single-site measurements in appropriate basis on the cluster
states in $dgeq2$. The equal-time correlators of the said states are described
by correlation functions of a certain $d$-dimensional classical model at the
critical temperature, featuring spatial conformal invariance. This establishes
an exact correspondence between the measurement-prepared critical states and
conformal field theories of a range of critical spin models, including familiar
Ising model and gauge theories among others. Furthermore, by mapping the
correlations of the measured quantum state into the statistical mechanics
problem, we establish the stability of long-range or topological orders with
respect to measurements deviating from the ideal setting, without any
post-selection. Therefore, our findings suggest a novel mechanism in which a
quantum critical wavefunction emerges, providing new practical ways to study
quantum phases and conformal quantum critical points.
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