Extensive nonadditive entropy in quantum spin chains

Details Extensive nonadditive entropy in quantum spin chains Extensive nonadditive entropy in quantum spin chains

2007-11-16

arxiv.org/abs/0711.2641v1

AIP conference Proceedings 965 (2007) p. 51

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 figures, Invited Paper presented at the international conference CTNEXT07, satellite of STATPHYS23, 1-5 July 2007,

Scientific paper

10.1063/1.2828759

We present details on a physical realization, in a many-body Hamiltonian system, of the abstract probabilistic structure recently exhibited by Gell-Mann, Sato and one of us (C.T.), that the nonadditive entropy $S_q=k [1- Tr \hat{\rho}^q]/[q-1]$ ($\hat{\rho}\equiv$ density matrix; $S_1=-k Tr \hat{\rho} \ln \hat{\rho}$) can conform, for an anomalous value of q (i.e., q not equal to 1), to the classical thermodynamical requirement for the entropy to be extensive. Moreover, we find that the entropic index q provides a tool to characterize both universal and nonuniversal aspects in quantum phase transitions (e.g., for a L-sized block of the Ising ferromagnetic chain at its T=0 critical transverse field, we obtain $\lim_{L\to\infty}S_{\sqrt{37}-6}(L)/L=3.56 \pm 0.03$). The present results suggest a new and powerful approach to measure entanglement in quantum many-body systems. At the light of these results, and similar ones for a d=2 Bosonic system discussed by us elsewhere, we conjecture that, for blocks of linear size L of a large class of Fermionic and Bosonic d-dimensional many-body Hamiltonians with short-range interaction at T=0, we have that the additive entropy $S_1(L) \propto [L^{d-1}-1]/(d-1)$ (i.e., $ \ln L$ for $d=1$, and $ L^{d-1}$ for d>1), hence it is not extensive, whereas, for anomalous values of the index q, we have that the nonadditive entropy $S_q(L)\propto L^d$ ($\forall d$), i.e., it is extensive. The present discussion neatly illustrates that entropic additivity and entropic extensivity are quite different properties, even if they essentially coincide in the presence of short-range correlations.

Affiliated with

Also associated with

No associations

Rating

Extensive nonadditive entropy in quantum spin chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Extensive nonadditive entropy in quantum spin chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extensive nonadditive entropy in quantum spin chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-4017