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Electronic properties in the vicinity of a Mott insulator

Final Report Summary - MOTTPROXIMITY (Electronic properties in the vicinity of a Mott insulator)

The project’s scientific goals are to understand the properties of physical systems that are near a Mott insulating phase. The primary questions addressed by the project are the possible existence of three-dimensional spin liquid insulators and the dynamical properties of superconductors and superfluids close to the superfluid to Mott insulating transition.
Since the beginning of the project, we have developed a number of numerical and analytical techniques to address these questions. From the numerical standpoint, we have developed algorithms to perform projective wave function Monte Carlo calculations and exact diagonalization to study quantum spin liquids, as well as state-of-the-art Quantum Monte Carlo algorithms to study superconducting fluctuations near the Mott insulator transition. On the analytical side, we have done projective symmetry group and field theoretic analyses to study these same questions. These techniques were first developed in the first two years of the project, and they have been further improved and applied to a number of physical systems in years 3 and 4 of the project.
The research has lead to a number of novel results regarding the dynamics of systems near the Mott insulator transition. These include the realization that Higgs excitations, associated with fluctuations of the superfluid order parameter, can be observed in two dimensional systems provided they are probed using measurements of scalar symmetry. Furthermore, we have established a number of universal properties of the Higgs excitations near the quantum phase transition into the Mott phase, such as the evolution of the Higgs energy and of its line width.

In addition, as part of the project, we have succeeded in suggesting methods to measure vortex properties in the Mott insulator phase. According to duality, a Mott insulator can be through of as a superfluid of vortices. While such a description is often used at a qualitative level, at a quantitative level very little is known about such vortex superfluid. We have shown that measurements of the square capacitance in the Mott phase can give a direct measure of the vortex superfluid density, and have also proposed similar measurements that can be applied to cold atomic gases. We have provided quantitative predictions for the superfluid vortex duality, including its dependence on detuning from the quantum critical point.

The results on the Higgs mode have had an impact on the condensed matter and cold atomic gas communities. Some of our results have been experimentally confirmed by experiments performed on cold Rubidium gas in an optical lattice by the research team of Immanuel Bloch, who succeeded in observing the Higgs mode for the first time in a two dimensional system. They did this by performing a scalar measurement, in which they shook periodically the optical lattice and measured the energy absorbed as a result.

The CIG grant was seminal in my reintegration into Israeli academia. During the period of the grant I was promoted to Associate Professor and granted tenure at the Technion. I was also awarded prestigious Israeli grants: the Wolf Foundation’s 2014 Krill Prize for Outstanding Scientific Achievement, and the Israel Physical Society’s 2014 Young Theorist award.

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