We have developed an improved version of the quantum transfer matrix algorithm. The extreme eigenvalues and eigenvectors of the transfer matrix are calculated by the recently developed lookahead Lanczos algorithm for non-Hermitian matrices with higher e ciency and accuracy than by the power method. We have applied this method to the Heisenberg ladder. The temperature dependence of the susceptibility, speci c heat, correlation length and nuclear spin relaxation rate 1=T1 are calculated. Our results support the existence of a spin gap of about 0:5J.

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We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.

The one-dimensional Kondo-lattice model is investigated using quantum Monte Carlo and transfermatrix techniques. In the strong-coupling region ferromagnetic ordering is found even at large band billings. In the weak-coupling region the system shows a Ruderman-Kittel-Kasuya-Yosida-like behavior.