Quantum Monte Carlo Studies of Strongly Correlated Electron Systems

Electronic correlations are at the heart of modern solid state physics. The interest lies in emergent collective phenomena which appears at low energy scales and which often originates from competing interactions. In this article, we summarize three research subjects where the effects of correlations dominate and can be elucidated with the combined use of supercomputers and state-of-the-art stochastic algorithms. (i) Cluster methods for models of high-T c cuprates are very promising but need to be generalized to efficiently compute two-particle properties. This aspect is essential for comparison with experiment but also for very understanding of the physics. (ii) Quantum phase transition between broken symmetry states are generically of first order, but need not be. In particular mechanisms in which novel elementary excitations occur at the critical point can generate continuous transitions, between ordered states. In the past years there has been an intensive search for models showing such behavior, in the ultimate aim of understanding if and under what circumstances such exotic phenomena can occur. (iii) Integer one-dimensional spin systems are known to be gap-full and characterized by a hidden order parameter. Such systems can be realized by ferromagnetically coupling spin-1/2 antiferromagnetic chains to form a ladder system. It is known the spin gap grows linearly with the ferromagnetic coupling. We report on aspects of simulations which show that twisting the ladder introduces a novel emergent energy scale which radically alters this behavior.