ABSTRACT

NONTECHNICAL SUMMARY

This award supports theoretical research and education in the physics of disorder and its effect on how electrons organize in real materials. Theoretical study and understanding of fundamental properties of solids that exhibit unexpected and often technologically useful properties at low temperatures commonly rely on the assumption that atoms form perfectly periodic lattices. However, disorder (crystal defects or impurities) that exists in real materials cannot always be ignored when studying electronic properties. Together with all the other important players in the system (crystal lattice geometry, interaction between electrons, etc.), their presence can drive the system as a whole to phases that do not appear if one considers disorder alone, or only electronic interactions. The accurate description of such an inclusive system using current numerical techniques can be a daunting task.

In this project, the PI will implement a novel idea for efficiently taking random disorder into account in certain numerical simulations of interacting electrons. The PI will use the method to study the collective rearrangements of electrons and the different transformations they can undergo. The results will help interpret experimental observations, and will ultimately help understand the mechanism behind the creation of exotic phases, such as insulating and superconducting phases, with possible applications in the technology and energy sectors.

The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the field of computational condensed matter physics, and with opportunities to improve their scientific communication skills through writing papers and presenting their findings at national scientific meetings. The award also supports the PI in his efforts to integrate research and undergraduate education through the incorporation of computational methods into physics courses.

TECHNICAL SUMMARY

This award supports theoretical research and education in the physics of disorder and its effect on electronic phase transitions. The interplay of disorder, caused by impurities or crystal defects in real materials, and electronic correlations in condensed matter physics is only poorly understood. Important questions about the effect of disorder on the appearance and nature of phase transitions, as well as on the fate of the Anderson localization upon introduction of electronic interactions in different dimensions, remain largely unsettled. This is especially true for fermionic systems and the corresponding quantum lattice models that emulate disorder effects through random-site or bond energies. Recent experiments with ultracold Fermi gasses on optical lattices have begun to shed light on some of these questions. However, much like in experimental simulations with clean lattices, these experiments rely on approximation-free and highly precise numerical simulations for thermometry and characterization.

In this project the PI will implement a new idea for the treatment of continuous random disorder in the numerical linked-cluster expansion, an emerging and powerful method that yields exact finite-temperature results for strongly correlated electronic systems in the thermodynamic limit. Using this method, the PI will study the thermodynamic properties, including various magnetic and/or superconducting correlations of Heisenberg and Hubbard models in two and three dimensions. The results will improve our understanding of the exotic phenomena that can arise in the presence of both disorder and electronic correlations, and will help interpret results of future experiments with disordered optical lattices. The data obtained, especially in the strong-coupling regimes, can also be used to benchmark other numerical methods for disordered fermionic systems.

The activities will provide several undergraduate students from the diverse population of San Jose State University with hands-on research experience in the field of computational condensed matter physics, and with opportunities to improve their scientific communication skills through writing papers and presenting their findings at national scientific meetings. The award also supports the PI in his efforts to integrate research and undergraduate education through the incorporation of computational methods into physics courses.

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