2003 — 2010 
Lee, Patrick [⬀] Lee, Patrick [⬀] Todadri, Senthil 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Frustrated Quantum Magnetism in Insulators and Metals @ Massachusetts Institute of Technology
This award supports theoretical research and education on the quantum theory of localized magnetic moments in diverse electronic environments in solids. Specific areas of research include the physics of geometric frustration of quantum magnetism in insulating materials and the interplay between possibly frustrated intermoment exchange and coupling between local moments and conduction electrons in metallic materials. Emphasis will be on understanding low temperature phenomena where quantum mechanical effects dominate. The PI aims to clarify the nature of the ground states and low energy excitations suggested by experiments or numerical calculations on several lowdimensional insulating frustrated quantum magnets. Field theoretical methods will be developed with an aim to obtaining physical insight. The PI will explore whether frustrated quantum magnets display excitations with fractional quantum numbers. The PI seeks to bridge the gap between theory and experiments in this active area of condensed matter physics. The PI will also study Kondo lattice models for metallic systems with localized magnetic moments, for example LiVO. Various phenomena discovered in these systems originate in the competition between possibly frustrated magnetic exchange between the local moments and the interaction between the local moments and the conduction electrons. This award also supports education at the graduate level in advanced theoretical condensed matter physics. The PI plans to involve undergraduate students in the research. %%% This award supports fundamental theoretical condensed matter physics research on phenomena that arise from geometrical frustration of quantum magnetic materials and the interaction between magnetic moments localized on particular atomic sites with itinerant conduction electrons. Geometrical frustration occurs when the interactions between magnetic moments cannot be simply satisfied because of the geometrical arrangement of the moments on the crystal lattice. This is fundamental research in an active and challenging area that involves strongly correlated electron materials including heavy fermion materials and quantum magnets like Cs2CuCl4. Research in this area has revealed subtle and beautiful phenomena in condensed matter physics and provides the intellectual foundation for future materials and device technologies. This award also supports education at the graduate level in advanced theoretical condensed matter physics. The PI plans to involve undergraduate students in the research. ***

1 
2010 — 2014 
Todadri, Senthil 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Physics Near the Mott Transition @ Massachusetts Institute of Technology
TECHNICAL SUMMARY
This award supports theoretical research and education on novel phenomena that occur in the vicinity of the Mott metalinsulator transition in interacting electron systems. Specific areas of interest are the physics of continuous Mott transitions, and of quantum spin liquid Mott phases that are proximate to such transitions. The emphasis will be on developing theoretical concepts in the context of either experiments on specific materials or numerical work on specific microscopic models.
Specific foci of the research include:
(i) new theoretical approaches to the electronic Mott transition based on insights from the better understood Mott transition of bosons,
(ii) the theory of gapless quantum spin liquid phases with a focus on identifying unique experimental signatures
(iii) the interplay between electronic nematic order and spin liquid physics in Mott insulators.
Project (i) is an exploration of new theoretical methods to address fundamental questions concerning the fate of the electronic Fermi surface as a metal evolves into a Mott insulator. This is a key challenge in many problems in modern quantum manybody theory. Projects (ii) and (iii) are directly motivated by experiments on weak Mott insulators that find evidence for the occurrence of quantum spin liquid phases. It is expected that the work proposed will provide key insights that will be useful in interpreting the results from experiments on weakly Mott insulating materials, and would help suggest new ones. All of the projects tie in nicely with some long term research interests of the PI on developing an understanding of nonfermi liquid physics near heavy electron critical points, and in the cuprate materials.
This award also supports the training of graduate students in advanced theoretical concepts and methods. The PI will involve undergraduates in the research, when possible, through the Undergraduate Research Opportunities Program at MIT. The PI will continue his efforts, begun recently, to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials.
NONTECHNICAL SUMMARY
This award supports theoretical research and education that seeks to predict new phenomena occurring in materials that are near a special insulating state called a Mott state. Standard theoretical methods would predict that these Mott insulators are actually metallic. These methods inadequately account for the strong interactions between electrons in Mott insulators. When this is done, the metallic state gives way to an insulating state. The parent compounds of the high temperature superconductors with the highest transition temperatures are Mott insulators. Adding charges to these materials moves them from the Mott state to the high temperature superconducting state. The PI will use advanced theoretical tools to understand proposed new states of matter that occur near Mott states. The vicinity of a Mott state is thought to be a conspicuously fertile area for the discovery of new electronic states of matter and to lead to unusual electronic properties of materials that lie outside the standard textbooks. The PI also seeks to predict new phenomena near a Mott state.
This is fundamental research with high risk elements. The research will advance our fundamental conceptual understanding of the electronic properties and phenomena of this class of materials. The research may also contribute to the intellectual foundations of new device technologies, particularly with increased ability to control the processing of these materials.
This award also supports the training of graduate students in advanced theoretical concepts and methods. The PI will involve undergraduates in the research, when possible, through the Undergraduate Research Opportunities Program at MIT. The PI will continue his efforts, begun recently, to design lectures to expose graduate students to experimental methods and the phenomenology of modern correlated materials.

1 
2013 — 2016 
Todadri, Senthil 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Novel Phases of Electronic Mott Insulators @ Massachusetts Institute of Technology
Technical summary
This award supports theoretical research and education to study novel Mott insulating states of electronic matter. Specific phases of interest are quantum spin liquids, and phases of quantum magnetism that are the spin analogs of interacting topological insulators. The emphasis will be on the development of theoretical concepts and methods which will be placed in the context of experiments and/or numerical work. The PI will pursue three topics:
(i) the theory and phenomenology of quantum spin liquids in the organic salts and other materials;
(ii) a theoretical description of a new class of gapless quantum spin liquid states that are likely beyond the existing paradigm;
(iii) the theory and realization of spin analogs of topological insulators.
Projects (i) and (ii) are motivated by experiments on many Mott insulators that provide evidence for various kinds of quantum spin liquid phases, typically with gapless excitations. Project (iii) is on a new and rapidly evolving area which can deepen our understanding both of quantum magnetism and topological insulators.
The award supports the training of graduate students in modern concepts and methods in condensed matter physics. Undergraduates will be involved in the research. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and their experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.
Nontechnical summary
This award supports theoretical research and education on interesting new kinds of insulating states of matter. It has long been known that in certain materials insulating behavior develops as a result of the Coulomb interaction between the electrons rather than due to the filling of quantum mechanical energy bands. Modern developments show that some of these Mott insulators can be in very novel states of matter where the microscopic degrees of freedom are quantum mechanically entangled over macroscopic distances.
Several unusual counter intuitive phenomena arise as a result of the long range quantum mechanical entanglement. The PI will develop new concepts and methods to deal with insulators with long range quantum entanglement, and their experimental signatures. He will also develop a deeper understanding of the interplay between symmetry and quantum effects in such interaction driven insulators.
This fundamental research has potential to generate concepts that will underlie future quantum technologies. The study of long range entangled phases is a relatively new chapter in condensed matter physics which holds promise to have similar impact on technology as the previous chapter of the study of long range ordered phases. This award also supports the training of graduate students in modern concepts and methods in condensed matter physics. Undergraduates will be involved in the research. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and their experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.

1 
2017 — 2022 
Todadri, Senthil 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Novel Phases of Electronic Insulators and Quantum Hall Systems @ Massachusetts Institute of Technology
NONTECHNICAL SUMMARY
This award supports theoretical research and education on the physics of new kinds of quantum phenomena in materials. The electronic properties of most solids are understood within a quantum mechanical description of a large number of interacting electrons that are moving in the background of charged atom cores that form the bulk of the solid. An important modern realization is that due to quantum mechanics, the properties of spatially distant electrons in the solid can be inextricably tied together, a phenomenon called entanglement. Quantum mechanical entanglement plays a role in determining macroscopic properties of the solid. A striking and paradigmatic example occurs when the motion of electrons is restricted to two dimensions and is subjected to a strong perpendicular magnetic field.
The PI will develop new concepts and methods to deal with such electronic states and their identification in experiments. He will also develop a deeper understanding of the interplay between symmetry and entanglement, which are two of the central pillars of modern quantum physics.
Historically, such fundamental research on electronic materials has generated many of the concepts that underlie modern electronic technology. The proposed research will contribute to the continuum of scientific and technological knowledge enabling future technology that harvests quantum entanglement in fundamental ways.
In addition to research, the award supports the training of graduate students in modern concepts and methods in condensedmatter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.
TECHNICAL SUMMARY
This award supports theoretical research and education on the physics of novel quantum states of electronic insulators and quantum Hall systems. Specific phases of interest are liquids of composite fermions in quantum Hall systems, quantum spin liquids in insulating magnets, and strongly correlated relatives of topological insulators. There has been a remarkable convergence of these three seemingly different topics in the last two years. The project will develop these connections further and exploit them to further our understanding of each topic.
Specific questions that will be pursued are: i) a microscopic lowestLandaulevel theory of the metallic particleholesymmetric halffilled Landau level, ii) a theoretical description of current experiments on quantum spin liquid states, iii) theory and realization of strong correlation effects in topological insulators.
Project (i) is fundamental to the theory of the quantum Hall effect and seeks to provide a microscopic foundation to recent developments on a longwavelength effective theory for the metallic state in the halffilled Landau level. Project (ii) will seek to develop the theory of quantum spin liquids in contact with many ongoing experiments on Mott insulators that find evidence for various kinds of quantum spinliquid phases. Project (iii) will study the interplay of strong correlation effects and topological insulator phenomena, two cornerstones of modern work on quantum materials.
In addition to research, the award supports the training of graduate students in modern concepts and methods in condensedmatter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.

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