Strongly correlated electrons
Lattice stochastic methods are used to investigate the electronic properties of strongly correlated electrons in low dimensional geometries.
Scientists within IAS-4/IKP-3 utilize lattice stochastic methods originally developed within the lattice gauge theory community to investigate phenomena due to strongly correlated electrons in low dimensional systems. Such systems include graphene sheets, graphene nano-tubes (GNTs), graphene nano-ribbons (GNRs), and fullerenes (see accompanying figure). The low dimensionality of these systems enhances strong interaction dynamics and therefore lattice stochastic methods provide the ideal choice for simulating these systems. The advances in methods motivated by lattice QCD requirements translates to more precise calculations on ever larger system sizes in these low-D systems. For example, simulations performed by IAS-4/IKP-3 of the quantum phase transition of the 2-D Hubbard model on a honeycomb lattice were obtained on the largest lattices to date, providing the most precise determination of the critical coupling. Conversely, these low-D systems offer an ideal testbed for novel algorithmic developments that could one day be applied to lattice gauge theories. Examples here include the use of machine learning techniques to alleviate the sign problem of chemically doped system, a problem that is pervasive in lattice stochastic simulations in all physics fields.