Density Matrix Renormalization Group Studies of Strongly Correlated Systems

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This grant supports theoretical research on the properties of strongly interacting electron systems in low dimensions. In particular, the research will further develop algorithms associated with the density matrix renormalization group method so that this computational method can be applied to a wider variety of condensed matter systems and phenomena.One of the most exciting areas in condensed matter physics is the study of strong correlationeffects in low dimensional systems. These systems exhibit a wide range of behavior, such as hightemperature superconductivity, antiferromagnetism, striped, and spin liquid phases. They also show great promise, as fabrication techniques develop control on the nanoscale, for use in a new generation of electronic and spintronic devices. Numerical simulation techniques have become increasingly necessary to understand these systems, as the systems have strong coupling terms and competition between different types of order. The principal investigator (PI) is the creator of the density matrix renormalization group (DMRG), which is one of the most effective numerical techniques for studying strongly correlated systems. The PI and his group will apply DMRG to a variety of these systems, including spin chains, ladders, Y-junctions, both for pure spin systems and with hole doping.Understanding dynamical properties of these systems is essential for comparisons with experi-ments and for describing transport. Recently, there have been dramatic breakthroughs in the ability to simulate dynamics within DMRG. These new techniques allow for simulations in real time, with high accuracy and efficiency, even for systems far from equilibrium.With these new capabilities, the PI will study the spectral functions of a variety of chains andladder systems. In most cases, accurate, high-resolution dynamical properties for these systems have not been available previously. In addition, the PI plans to study a variety of junctions built out of chains and ladders, for which neither ground state nor dynamical simulation results have been performed. Novel techniques for simulating steady-state current flow conditions will be developed and applied to junctions. These studies are meant to pave the way for new generations of nano-scale electronic and spintronic devices built out of chains and ladders.There has also been recent major progress in the ability to simulate doped and frustrated systems in two dimensions, although the algorithms are not yet well characterized or tested. In order to develop and improve these techniques in a simpler context, they will be adapted to ladders and junctions. Subsequently, experience in improving the techniques will be applied to two dimensions. Successful application to two dimensions would have a major impact on the understanding of the cuprate superconductors and related materials.In terms of the Broader Impacts of this work, there will be significant impact in a number ofdifferent areas. One of the most important areas is the spreading of numerical and algorithm ad-vances from one area of science to another. The PI has worked and will continue to work to spread the use of the DMRG method to other fields. Most notably, the PI has initiated the use of DMRG in quantum chemistry, and several chemistry groups have now begun utilizing it. The PI is also working to improve the level of training both graduate and undergraduate students receive in computational methods. The PI has developed several new courses, both graduate and undergraduate, to introduce modern computational methods to physics students. Several of these courses have been made permanent additions to the UCI curriculum, and the PI continues to teach them. The PI is also working to encourage better scientific programming techniques in physics research, including maintaining a free downloadable highly efficient C++ matrix library.Non-Technical Abstract: This grant supports primarily computational research on the properties of strongly interacting systems of electrons in one-and two-dimensions as might be found in nano-scale devices. The behavior of electrons when they are confined in these small spaces and when they are very close to each other can lead to novel effects. This grant supports work that will develop computational techniques to describe these types of electrons. In addition to discovering and understanding these novel properties, which may lead to new devices, the computational techniques developed will find wide application in other fields of study. This is the power of developing computational methods in one field that can be applied to many other applications. Students involved in this research will receive excellent training in condensed matter physics and computational physics.