2016/06/30 by Michele Filippone, Piet W. Brouwer, Jens Eisert +1 · 2 citations
Mathematics · Physics and Astronomy · #Cauchy distribution #Condensed matter physics #Delocalized electron #Distribution (mathematics) #Mathematical analysis #Mathematics #Mesoscopic physics #Phase (matter) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quasicrystal #Random matrix #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.94.201112
published as Phys. Rev. B 94, 201112 (2016) · 5 pages, 3 figures + 1 page Supplemental Material, 2 figures
arxiv created 2016/11/18 · openalex publication_date 2016/11/18 · arxiv updated 2016/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We numerically investigate the distribution of Drude weights D of many-body states in disordered one-dimensional interacting electron systems across the transition to a many-body localized phase. Drude weights are proportional to the spectral curvatures induced by magnetic fluxes in mesoscopic rings. They offer a method to relate the transition to the many-body localized phase to transport properties. In the delocalized regime, we find that the Drude weight distribution at a fixed disorder configuration agrees well with the random-matrix-theory prediction P(D)\ensuremath∝(\ensuremathγ2+D2)^\ensuremath-3/2, although the distribution width \ensuremathγ strongly fluctuates between disorder realizations. A crossover is observed towards a distribution with different large-D asymptotics deep in the many-body localized phase, which however differs from the commonly expected Cauchy distribution. We show that the average distribution width \ensuremath⟨\ensuremathγ\ensuremath⟩, rescaled by L\mathrm\ensuremathΔ,\phantom\rule0.28em0ex\mathrm\ensuremathΔ being the average level spacing in the middle of the spectrum and L the systems size, is an efficient probe of the many-body localization transition, as it increases (vanishes) exponentially in the delocalized (localized) phase.