Decay of Complex-Time Determinantal and Pfaffian Correlation Functionals in Lattices

We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903–931, 2016 ) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hada...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2018-06, Vol.360 (2), p.715-726
Main Authors: Aza, N. J. B., Bru, J.-B., de Siqueira Pedra, W.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Correlation analysis
Fermions
Functionals
Lattices
Localization
Many body interactions
Mathematical and Computational Physics
Mathematical Physics
Particle decay
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903–931, 2016 ) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hadamard three-line theorem. We show that the dynamical localization for the one-particle system yields the dynamical localization for the many-point fermionic correlation functions, with respect to the Hausdorff distance in the determinantal case. In Sims and Warzel ( 2016 ), a stronger notion of decay for many-particle configurations was used but only at dimension one and for real times. Considering determinantal and Pfaffian correlation functionals for complex times is important in the study of weakly interacting fermions.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3121-0