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Optimized implementation of the Lanczos method for magnetic systems

Numerically exact investigations of interacting spin systems provide a major tool for an understanding of their magnetic properties. For medium size systems the approximate Lanczos diagonalization is the most common method. In this article we suggest two i

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Optimized implementation of the Lanczos method for magnetic systems J¨u rgen Schnack a ,∗a Universit¨a t Bielefeld,Fakult¨a t f¨u r Physik,Postfach 100131,D-33501Bielefeld,Germany Peter Hage and Heinz-J¨u rgen Schmidt b b Universit¨a t Osnabr¨u ck,Fachbereich Physik,D-49069Osnabr¨u ck,Germany 1Introduction Many magnetic materials can accurately be described by the Heisenberg or

related effective spin models.Due to the vastly increasing size of the under-lying Hilbert space,which grows as (2s +1)N for N spins of spin quantum number s ,only small spin systems can be modeled exactly,i.e.their complete eigenspectrum can be determined.For larger systems approximate methods such as the Lanczos [1]or related methods like the Arnoldi,the projection,or the Density Matrix Renormalization Group (DMRG)method [2,3,4]are used.They usually aim at properties of ground states in orthogonal subspaces,which are provided by symmetry,see e.g.[5,6,7].But also thermal properties can be

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