Physics (Internal)

Shannon-Renyi entropies and participation spectra in quantum many body systems

This event is part of the Condensed Matter Theory Seminar Series.

Abstract: We study universal features in the scalings of Shannon-Renyi entropies of many-body groundstates for interacting spin-$\frac{1}{2}$ systems. In particular, their behavior across quantum phase transitions, such as in the transverse field Ising model and across (2+1) dimensional $O(3)$ critical points is extracted using QMC. We show that for both full systems and line shaped subsystems, the breaking of continuous symmetries is characterized by the presence of a logarithmic term in the scaling of Shannon-Renyi entropies, which is absent in gapped phases. A constant subleading term is found for the breaking of discrete symmetries. Such a difference in the scalings allows to capture the quantum critical points using Shannon-Renyi entropies for line shaped subsystems of length L embedded in L x L tori, as the smaller subsystem entropies are numerically accessible to much higher precision than for the full system. We argue that the value of the subleading terms is universal all over the corresponding phases and find that the constant scaling term at the critical point seems to be determined by the universality class of the transition. For the example of the dimerization/plaquettization transition in the Heisenberg model, we also discuss several features of the participation spectrum, consisting of the diagonal elements of the reduced density matrix of the line subsystem. In particular the Neel ordering transition can be simply understood in the Sz basis by a confinement mechanism of ferromagnetic domain walls.

More details in

D. J. Luitz, F. Alet and N. Laflorencie, Phys. Rev. Lett. 112, 057203 D. J. Luitz, F. Alet and N. Laflorencie, arXiv:1402.???? (Feb 21)