Variational studies of strongly-correlated systems

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My research program is focused on developing accurate, yet computationally efficient, variational approximations for answering the key questions that arise in the study of strongly correlated systems, i.e. how to predict: (i) the characteristics of the quasiparticle that forms when a charge carrier becomes "dressed'' by a cloud of excitations such as phonons, magnons, plasmons, etc. In certain cases, this quasiparticle is called a polaron; (ii) the characteristics of the effective interactions arising between quasiparticles through exchange of excitations between their clouds; and (iii)  their combined influence on the properties of the host material. There is currently no general theoretical framework for dealing with such problems, hindering progress in identifying optimal materials for technological uses. Our long-term objective is to develop such a framework. Our work is based on our unique approach of identifying the most important real-space configurations that contribute to the structure of the dressing clouds, and keeping their contributions to all orders.  We demonstrated that this leads to very accurate predictions for single polarons and bipolarons even for strong couplings, difficult to study by other means. In the next 5 years we will further expand the capabilities of our method, and use it to study: Project 1: the effects of strong carrier-boson coupling in systems with low carrier concentrations; Project 2: the effects of strong carrier-boson coupling in systems at and near half-filling; Project 3: properties of polarons at finite temperatures; Project 4: properties of polarons in driven systems; Project 5: extensions of our variational approach to strongly correlated electronic Hamiltonians. The steady progress of my research program from the study of single polarons and bipolarons, to the study of systems with finite carrier concentrations, shows that this program has reached a mature stage where it will have a ground-breaking impact: We are currently the only group in the world able to accurately and efficiently solve the problems included in Project 1: the Migdal theorem is not valid here and numerical simulations are difficult at very low densities as they require considering very large systems. We are also the only group currently able to answer the questions of Project 3. Here, state-of-the-art numerical studies are limited to chains with up to 10 sites, whereas we can study any infinite lattices. These are low-risk, high reward projects. In contrast, the high-risk, high reward Projects 2, 4 and 5 focus on expanding our expertise to an even wider class of relevant problems.  All these project offer excellent training to undergraduate and graduate students and postdoctoral fellows, because they combine honing one's physical intuition (in finding the configurations important to the clouds), analytical abilities (deriving the resulting equations), programming abilities (coding the solution) and presentation skills.