Numerical study on ESR of V15 IIS, U. Tokyo, Manabu Machida RIKEN, Toshiaki Iitaka Dept. of Phys., Seiji Miyashita June 27- July 1, 2005 Trieste, Italy

Nanoscale molecular magnet V15 ( Vanadiums provide fifteen 1/2 spins. [A. Mueller and J. Doering (1988)]

Hamiltonian and Intensity

[H. De Raedt, et al., PRB 70 (2004) ] [M. Machida, et al., JPSJ (2005) suppl.] The parameter set

Difficulty – Its computation time is of (e.g. S. Miyashita et al. (1999)) – Direct diagonalization requires memory of difficult!

Two numerical methods The double Chebyshev expansion method (DCEM) - speed and memory of O(N) - all states and all temperatures The subspace iteration method (SIM) - ESR at low temperatures.

DCEM

ESR absorption curves Typical calculation time for one absorption curve is about half a day. DCEM

Background of DCEM The DCEM = a slight modification of the Boltzmann-weighted time-dependent method (BWTDM). Making use of the random vector technique and the Chebyshev polynomial expansion [T. Iitaka and T. Ebisuzaki, PRL (2003)]

DCEM (1) Random phase vector

DCEM (2) Chebyshev expansions of the thermal and time-evolution operators. >> small 

Temperature dependence of intensity [Y.Ajiro et al. (2003)] Our calculation Experiment

SIM

ESR at low temperatures by SIM We consider the lowest eight levels. Intensity ratio

Temperature dependence of R(T) With DMWithout DM

Triangle model analysis

Energy levels with weak DM

Intensity ratio of triangle model At zero temperature

Summary O(N) algorithms for the Kubo formula DCEM ESR of V15 ■ High to low temperatures by DCEM ■ Ultra-cold temperature by SIM ■ Triangle model analysis ■ Random vector and Chebyshev polynomials M. Machida, T. Iitaka, and S. Miyashita, JPSJ (2005) suppl. (cond-mat/ )