Cluster Dynamical MeanField Theory: Applications to HighTc Cuprates and to Quantum Chemistry
 Title:

Cluster Dynamical MeanField Theory: Applications to HighTc Cuprates and to Quantum Chemistry
 Author(s):

Lin, Nan
 Thesis Advisor(s):

Millis, Andrew J.
Reichman, David R.
 Date:

2012
 Type:

Dissertations
 Department(s):

Physics
Chemistry
 Persistent URL:

http://hdl.handle.net/10022/AC:P:13443
 Notes:

Ph.D., Columbia University.
 Abstract:

In this thesis we use the recently developed dynamical meanfield approximation to study problems in strongly correlated electron systems, including highTc cuprate superconductors as well as a few quantum chemical reference systems. We start with an introduction to the background of the interacting electron systems, followed by a brief description on the current understanding of the physics of highTc cuprate superconductors. The approximate models that enter the theoretical framework will be discussed afterwards. Some quantum chemical methods for manybody quantum systems are included for review. Next we present the numerical methods employed in our study. The formalism of the dynamical meanfield approximation will be introduced including the singlesite and cluster versions, followed by the Exact Diagonalization impurity solver for the solution of the quantum impurity model. Maximum Entropy analytic continuation method is also discussed, which is useful to obtain the physically relevant response functions. Then we apply dynamical meanfield approximation to highTc cuprate superconductors. The twoparticle response functions, such as Raman scattering intensity and optical conductivity, are computed for the two dimensional Hubbard model. The calculations include the vertex corrections which are essential to obtain physically reasonable results in interacting electron systems. We also study the physics of the pseudogap in cuprates. The suppression of density of states near Fermi surface is present in our calculations, which is in qualitative agreement with the experimental data. Finally we discuss the application of dynamical meanfield theory to quantum chemistry. We extend the formalism of dynamical meanfield approximation to finite systems, and compare its performance in hydrogen clusters with different spatial configurations to other leading quantum chemical approaches. Dynamical meanfield theory involves mapping onto a quantum impurity model. We further examine the quantum impurity model representation of the transition metal dioxide molecules. The conceptual and technical difficulties will be discussed.
 Subject(s):

Condensed matter physics
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 Suggested Citation:
 Nan Lin, 2012, Cluster Dynamical MeanField Theory: Applications to HighTc Cuprates and to Quantum Chemistry, Columbia University Academic Commons, http://hdl.handle.net/10022/AC:P:13443.