Giant eigenproblems from lattice gauge theory on CRAY T3E systems

The determination of physical properties of flavor singlet objects like the η′ meson by computer simulation requires the computation of functionals of the inverse fermionic matrix M−1. So far, only stochastic methods could cope with the enormous size of M. In this paper, we introduce an alternative approach which is based on the computation of a subset of low-lying eigenmodes of the fermionic matrix. The high quality of this ‘truncated eigenmode approximation’ (TEA) is demonstrated by comparison with the pion correlator, a flavor octet quantity, which is readily computable through a linear system of equations. We show that TEA can successfully approximate the flavor singlet η′ correlator. We find that the systematic error of the method is tolerable. As the determination of the chosen subset of 300 eigenmodes requires about 3.5 Tflops-hours CPU-time per canonical ensemble and at least 15 GBytes of memory, the power of high-end supercomputers like the CRAY T3E is indispensable.