Berlin 2005 – scientific programme
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TT: Tiefe Temperaturen
TT 6: Correlated Electrons - (General) Theory I
TT 6.9: Talk
Friday, March 4, 2005, 16:00–16:15, TU H2053
A Quantum Central Limit Theorem for Interacting Many Particle Systems and its Applications — •Michael Hartmann1,2, Günter Mahler2, and Ortwin Hess3 — 1DLR Stuttagrt, Pfaffenwaldring 38-40, 70569 Stuttgart — 2Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart — 3Advanced Techology Institute, University of Surrey, Guildford GU2 7XH, UK
We present a central limit theorem for the distribution of
the total energy in a product state of a quantum many body
system with nearest neighbor or next nearest
neighbor interactions [1].
Using this result, one can draw estimates on quantities
which are functions of the total energy without diagonalizing
the Hamiltonian. Interesting examples are the density of
states and the partition function [2].
On the other hand, information about the local (subsystem-)
states can be obtained, too [3].
An advantage of our approach is its applicability to strongly
interacting and frustrated systems.
[1] Hartmann, Mahler and Hess: Lett. Math. Phys. 68 (2004) 103
[2] Hartmann, Mahler and Hess: cond-mat/0406100
[3] Hartmann, Mahler and Hess: Phys. Rev. Lett. 93 (2004) 080402