Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

1 aZabalo, Aidan1 aGullans, Michael1 aWilson, Justin, H.1 aVasseur, Romain1 aLudwig, Andreas, W. W.1 aGopalakrishnan, Sarang1 aHuse, David, A.1 aPixley, J., H. uhttps://arxiv.org/abs/2107.0339301315nas a2200145 4500008004100000245007600041210006900117260001400186520084500200100002201045700002701067700002001094700001801114856003701132 2021 eng d00aSubdiffusive hydrodynamics of nearly-integrable anisotropic spin chains0 aSubdiffusive hydrodynamics of nearlyintegrable anisotropic spin c9/27/20213 aWe address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent z=4 up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is not generically a continuous function of the integrability-breaking parameter.

1 aDe Nardis, Jacopo1 aGopalakrishnan, Sarang1 aVasseur, Romain1 aWare, Brayden uhttps://arxiv.org/abs/2109.13251