The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta 1 , who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher multipole moments, e.g., quadrupole and octupole. We define n-th order multipole operators whose expectation values can be used to calculate the n-th multipole moment when all of the lower moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of n − 1-st multipole currents, and encode the adiabatic evolution of the system in the presence of an n − 1-st gradient of the electric field. Finally, we test our operators on a set of tightbinding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole moment from other mechanisms that generate corner charges.

We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

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In her current position at UC Davis, she is integrating computational modules into the undergraduate and graduate materials curriculum. She is specifically interested in students' computational literacy and life-long learning of computational materials science tools.

Oxide materials tend to have anisotropic crystal structures, which results in material properties being dependant on direction. Typically, oxide materials have positive thermal expansion coefficients. However, it has been observed that some directions can have negative thermal expansion coefficients over certain temperature ranges. These oxide materials, which exhibit directions of positive and negative thermal expansion, will also have a particular direction in which the thermal expansion is zero. By using the Quadrupole Lamp Furnace (QLF) developed in the Kriven group, high temperature in-situ x-ray diffraction has been performed at the National Synchrotron Light Source II (NSLSII) X-ray powder diffraction beamline (XPD -28-ID) to track these directions of zero thermal expansion in orthorhombic HfTiO 4 and ZrTiO 4 . These measurements are important for identifying materials which will be dimensionally accurate at elevated temperatures.