TECHNICAL EXPLANATION: This award supports computational and theoretical research that aims to elucidate the nature of complex ground states and quantum phase transitions in strongly correlated electron systems. Research involves large-scale simulation studies of quantum spin models. These will use advanced quantum Monte Carlo methods, primarily those based on the stochastic series expansion (SSE) formulation of quantum statistical mechanics developed by the PI. The PI will continue to develop simulation algorithms. The specific models to be studied include a two-dimensional hard-core boson model with a ring-exchange term. An aim of this work is to accurately characterize the superfluid to valence-bond-solid transition, which has been proposed to be a "deconfined" quantum-critical point. A Heisenberg model will be studied with the aim of achieving an O(3)-symmetric antiferromagnetic to spin-liquid transition. Heisenberg models with strong disorder in the form of dilution will be investigated with the aim of characterizing the quantum phase transitions that are possible within this framework. New SSE algorithms that will result from this work may impact research in other fields, for example lattice gauge theory and quantum information theory. Beyond training students in physics and advanced scientific computing, this award supports the construction of a web-site in which the SSE method is presented in a pedagogical manner and along with example programs for a various models.
NON-TECHNICAL EXPLANATION: This award supports computational and theoretical research that engages issues at the heart of modern theoretical condensed matter physics that are inspired by the discovery of materials in which the electrons organize themselves to form unusual states of matter. High temperature superconductors and related compounds are among these materials. The PI will use advanced computational methods and streamlined models designed to strip away unnecessary detail and focus on the essential physics needed to understand these complex materials. The use of computational techniques aimed at ascertaining the exact solution to these models complements analytical theory efforts and provides insight that is not accessible to traditional experiments. The PI will further investigate a transformation among electronic phases that occurs at the absolute zero of temperature, and lies outside the standard theory of phase transitions. This new kind of phase transition advances our understanding of phase transitions and may be a key piece in the challenging puzzle of understanding high temperature superconductors and other strongly correlated materials. The understanding of this and other quantum phase transitions may have impact across physics and other fields. The proposal also supports an outreach activity to make the PI's computational methods more broadly accessible to the research community.
