Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem

Samuel M. Soares; Lucas Squillante; Henrique S. Lima; Constantino Tsallis; Mariano de Souza

Paper

Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem

Abstract

We investigate the influence of the spin magnitude

on the quantum Grüneisen parameter

right at critical points (CPs) for the 1D Ising model under a transverse magnetic field. Our findings are fourfold:

for higher

is increased, but remains finite, reflecting the enhancement of the Hilbert space dimensionality;

the Schmidt decomposition theorem recovers the extensivity of the nonadditive

-entropy

only for a

value of the entropic index

;

the universality class in the frame of

depends only on the symmetry of the system;

we propose an experimental setup to explore finite size effects in connection with the Hilbert space occupation at CPs. Our findings unveil both universal and non-universal aspects of quantum criticality in terms of

and