Quantum Cluster Theories Short Course

By N. S. Vidhyadhiraja

JNCASR, India

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Courses

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Abstract

Quantum cluster theories for strongly correlated Systems: Model Hamiltonians and real materials.

Strongly correlated electron systems encompass transition metal oxides, rare earth intermetallics, manganites, ruthenates, vanadates, ultra-cold bosonic, fermionic and mixed systems. This set of lectures is a brief and general introduction to recently developed techniques for investigating models and real correlated materials. These methods are based on quantum many body theory. They are widely applicable and have been extremely successful in providing insight into complex issues and phenomena such as the Mott transition, high temperature superconductivity, colossal magnetoresistance, heavy fermion behaviour and Kondo volume collapse. The first lecture will introduce the material systems, models and techniques at a general level and highlight the successes and failures of these methods. In the second lecture, a slightly in- depth introduction to dynamical mean field theory (DMFT) will be followed by its extensions to disordered, layered, nano-systems and integration with density functional theory based approaches to describe real materials. DMFT neglects non-local dynamical fluctuations, which can be incorporated through cluster extensions, such as dynamical cluster approximation (DCA) and cluster-DMFT. In the third lecture, an introduction to these cluster extensions will be given, with a special focus on DCA. Even with cluster extensions, it turns out that coherent back-scattering effects are ignored, and hence phenomena such as Anderson localization are not captured within DCA. In the last lecture, I will describe some recent developments to describe the phenomenon of Anderson localization in metals, interacting systems, superconductors and real materials.

Bio

N. S. Vidhyadhiraja is Associate Professor in the Theoretical Sciences Unit at the Jawaharlal Nehru Centre for Advanced Scientific Research in Bangalore, India. Prof. Vidhyadhiraja completed the integrated M.Sc in physics from IIT Kanpur in 1995, and the PhD in theoretical condensed matter physics from the Indian Institute of Science in Bangalore, India in 2001, where he studied under Prof. H. R. Krishnamurthy. He is an expert in theoretical and computational methods in condensed matter physics, specializing in strongly correlated electronic systems including Kondo physics, heavy fermion materials, and the Mott metal-insulator transition.

Sponsored by

This lecture series was made possible through an APS-IUSSTF Professorship/Lectureship Award from the American Physical Society.

Department of Physics

Cite this work

Researchers should cite this work as follows:

  • N. S. Vidhyadhiraja (2015), "Quantum Cluster Theories Short Course," https://nanohub.org/resources/22378.

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Location

242 Physics, Purdue University, West Lafayette, IN

Tags

Lecture Number/Topic Online Lecture Video Lecture Notes Supplemental Material Suggested Exercises
Quantum Cluster Theories Lecture 1: Quantum Cluster Approaches for Investigating Strongly Correlated Electronic Systems View HTML
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In this lecture we introduce the material systems, models and techniques at a general level and highlight the successes and failures of these methods.



Quantum Cluster Theories Lecture 2: Dynamical Mean Field Theories for Bulk, Layered, Disordered and Nano-systems View HTML
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In this lecture, a slightly in-depth introduction to dynamical mean field theory (DMFT) will be followed by its extensions to disordered, layered, nano-systems and integration with density...

Quantum Clusters Theories Lecture 3: Nonlocal Dynamical Fluctuations Beyond DMFT and the Dynamical Cluster Approximation View HTML
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In this lecture, an introduction to these cluster extensions is given, with a special focus on dynamical cluster approximation (DCA). Even with cluster extensions, it turns out that coherent...

Quantum Clusters Theories Lecture 4: Ongoing Work - A Quantum Cluster Theory for Anderson Localization in Correlated Systems View HTML
View Notes (pdf)