DMRG Studies of Doped Antiferromagnets

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One of the most exciting areas in condensed matter physics is the study of strong correlation effects in low dimensional systems. Of particular interest are the high temperature superconducting cuprates. These systems exhibit a wide range of behavior in addition to superconductivity, including antiferromagnetism and striped phases. Numerical simulations of models of these systems play a crucial role, since the systems have strong coupling terms and competition between different types of order. The principal investigator is the creator of the density matrix renormalization group (DMRG), which is one of the most effective techniques for studying strongly correlated systems. This project will apply DMRG to models of the cuprates in a variety of circumstances.In one set of studies, the properties of a superconducting vortex core in a two-dimensional antiferromagnet will be studied. Recent scanning tunneling microscopy studies have revealed intriguing checkerboard patterns in the local density of states surrounding vortex cores which are not yet understood. The DMRG method id particularly well adapted to study this phenomenon. If these patterns are reproduced in the simulations, a clear understanding will be obtained about their origins. In another set of studies, the nature of the correlations around doped impurities in the copper oxygen layers common to cuprates will be studied. These impurities provide a window into the normal state underlying these superconductors.A novel technique for determining the superfluid stiffness and superfluid density will be developed for ladder systems. This will provide much more direct information about superconductivity than the usual pairing correlation measurements. In another set of studies, a new type of diagonally oriented ladder system will be studied in order to understand nodal quasiparticles in the 2D copper oxygen layers.Using another numerical method, numerical canonical transformations, we will work to derive models for the cuprates from ab initio calculations and from more basic models. Curently, the construction of models is an art rather than a standard technique, and a better method may reveal important inadequacies in current models. Algorithms developed in the course of this research have wide applicability and are accessible via the internet.%%%One of the most exciting areas in condensed matter physics is the study of strong correlation effects in low dimensional systems. Of particular interest are the high temperature superconducting cuprates. These systems exhibit a wide range of behavior in addition to superconductivity, including antiferromagnetism and striped phases. Numerical simulations of models of these systems play a crucial role, since the systems have strong coupling terms and competition between different types of order. The principal investigator is the creator of the density matrix renormalization group (DMRG), which is one of the most effective techniques for studying strongly correlated systems. This project will apply DMRG to models of the cuprates in a variety of circumstances.***