2016/07/31 by Cecile Monthus
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1088/1751-8121/aa583f
published as 2017 J. Phys. A: Math. Theor. 50 095002 · v2= revised version with many improvements , 11 pages
arxiv created 2016/09/15 · arxiv updated 2017/02/01
For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle ϕ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the energy levels En(ϕ) is measured by the level curvature Kn=En"(0), or more precisely by the Thouless dimensionless curvature kn=Kn/Δn, where Δn is the level spacing that decays exponentially with the size L of the system. For instance Δn ∝ 2-L in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight Dn=L Kn studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen [arxiv:1606.07291v1] involves a different rescaling. The sensitivity of the eigenstates \vert ψn(ϕ) > is characterized by the susceptibility χn=-Fn"(0) of the fidelity Fn =\vert < ψn(0) \vert ψn(ϕ) >\vert . Both observables are distributed with probability distributions displaying power-law tails Pβ(k) ≃ Aβ \vert k \vert-(2+β) and Q(χ) ≃ Bβ χ-(3+β)/(2) , where β is the level repulsion index taking the values βGOE=1 in the ergodic phase and βloc=0 in the localized phase. The amplitudes Aβ and Bβ of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].