2024/09/03 by Rushikesh A. Patil, Patil, Rushikesh A., Andreas W. W. Ludwig +1 · 5 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2409.02107
openalex publication_date 2024/09/03 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28
We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an ε expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges' c^(\rm eff)n for the prefactors of the logarithm of subsystem size of the nth Rényi entropies, which are independent of each other for different n, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy' S_\rmeff which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the ε expansion for the measurement-dominated critical point in the critical Ising case (b).