Highly complex novel critical behavior from the intrinsic randomness of quantum mechanical measurements on critical ground states -- a controlled renormalization group analysis

We show that weak measurements performed without postselection on the quantum critical ground state of 1D Hamiltonians can give rise to highly complex novel scaling behavior due to their intrinsically indeterministic ('random') nature, governed by a measurement-dominated RG fixed point. We illustrate this for the (a) tricritical and (b) critical quantum Ising model by studying this RG fixed point within an epsilon expansion, measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. In the tricritical Ising case (a) we find (i): multifractal scaling of energy and spin correlations in the measured ground state, corresponding to an infinite hierarchy of independent critical exponents; (ii): logarithmic factors multiplying powerlaws in correlation functions, a hallmark of a logarithmic-CFT; (iii): universal 'effective central charges' c(eff)n for the nth Rényi entropies, independent for different n, and (iv): a universal (Affleck-Ludwig) 'effective boundary entropy' [PRL 67, 161 (1991)] which we identify with the system-size independent part of the Shannon entropy of the measurement record. – A subset of these results have also been obtained within the epsilon expansion for the measurement-dominated critical point in the critical Ising case (b).