On logarithmic extensions of local scale-invariance

Malte Henkel

Jeffrey Kelling, Géza Ódor, Sibylle Gemming

Abstract Local scale-invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2 + 1 dimensional Kardar–Parisi–Zhang surfaces. Very precise measurements of the universal autoresponse function enabled us to perform nonlinear fitting with the scaling forms, suggested by local scale-invariance (LSI). While the simple LSI ansatz does not seem to work, forms based on logarithmic extension of LSI provide satisfactory description of the full (measured) time evolution of the autoresponse function.

S. B. Rutkevich, Hans Werner Diehl, Mykola A. Shpot

Johnnie Gray, Abolfazl Bayat, Arijeet Pal +1 more

The exact nature of the many-body localization transition remains an open question. An aspect which has been posited in various studies is the emergence of scale invariance around this point, however the direct observation of this phenomenon is still absent. Here we achieve this by studying the logarithmic negativity and mutual information between disjoint blocks of varying size across the many-body localization transition. The two length scales, block sizes and the distance between them, provide a clear quantitative probe of scale invariance across different length scales. We find that at the transition point, the logarithmic negativity obeys a scale invariant exponential decay with respect to the ratio of block separation to size, whereas the mutual information obeys a polynomial decay. The observed scale invariance of the quantum correlations in a microscopic model opens the direction to probe the fractal structure in critical eigenstates using tensor network techniques and provide constraints on the theory of the many-body localization transition.

M. P. Nightingale, A.H. 'T Hooft

Malte Henkel, Michel Pleimling