This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This grant supports theoretical research on the properties of strongly interacting electron systems in low dimensions. In particular, the research focuses on the application of the density-matrix renormalization group (DMRG) method, developed by the PI in 1992, to several relevant problems of strongly correlated electrons. This method is one of the most reliable and now widely used techniques to treat strong correlations and quantum systems, and has been extended to several other areas in materials theory. The study of strong correlation effects in low dimensional systems is one of the most exciting areas in condensed matter physics. These systems exhibit a wide range of behavior, such as high temperature superconductivity, antiferromagnetism, striped, and spin liquid phases. 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.
This research will develop improved methods for describing transport and consequently being able to compare theory with experiment. For example, recent breakthroughs in real-time DMRG will allow the study of spectral functions for a variety of chain, ladder, and small 2D cluster systems. The PI anticipates being able to calculate temperature-dependent dynamical properties of 2D copper-oxygen plane models which can be compared directly with scanning tunneling microscopy (STM) experiments. The development of methods for simulating 2D doped and frustrated systems will also be pursued, using both traditional 2D DMRG "wide ladders" and novel algorithms based on tensor networks. Two-dimensional models for cuprate superconductors and recently discovered Fe-superconductors will be studied using large 2D clusters.
Another important component of this research will be the development of a general purpose software library for matrix computations used within DMRG simulations, which will be made freely available to other researchers.
NONTECHNICAL SUMMARY This grant supports primarily computational research on the properties of strongly interacting systems of electrons in one- and two-dimensions, with particular application to nanodevices and superconducting materials. 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 effects. In addition to discovering and understanding 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.
