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Quantum Many-Body Physics of Ultracold Molecules in Optical Lattices

Models and Simulation Methods

  • Book
  • © 2015

Overview

Authors:
  1. Michael L. Wall

    1. Colorado School of Mines, Golden, CO, USA and JILA, NIST, and University of Colorado, Boulder, USA

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  • Nominated by the Colorado School of Mines, USA, as an outstanding Ph.D. thesis
  • Presents a newly invented Molecular Hubbard Hamiltonian (MHH) describing the quantum many-body physics of ultracold molecules in optical lattices
  • Develops new algorithms dealing with dynamics and excited states in systems with long-range interactions
  • Covers open-source implementations of matrix products state algorithms and educational materials to help understand such methods

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxx
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. General Introduction

      • Michael L. Wall
      Pages 3-36

    3. Models for Strongly Correlated Lattice Physics

      • Michael L. Wall
      Pages 37-51

  3. The Molecular Hubbard Hamiltonian

    1. Front Matter

      Pages 53-53
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    2. Emergent Timescales in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices

      • Michael L. Wall
      Pages 55-91

    3. Hyperfine Molecular Hubbard Hamiltonian

      • Michael L. Wall
      Pages 93-119

  5. Matrix Product States

    1. Front Matter

      Pages 139-139
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    2. Matrix Product States: Foundations

      • Michael L. Wall
      Pages 141-176

    3. Out-of-Equilibrium Dynamics with Matrix Product States

      • Michael L. Wall
      Pages 177-222

    4. The Infinite Size Variational Matrix Product State Algorithm

      • Michael L. Wall
      Pages 223-240

    5. Finite Temperature Matrix Product State Algorithms and Applications

      • Michael L. Wall
      Pages 241-251

  6. Open Source Code and Educational Materials

    1. Front Matter

      Pages 253-253
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    2. Open Source Code Development

      • Michael L. Wall
      Pages 255-271

    3. Educational Materials

      • Michael L. Wall
      Pages 273-281

  7. Conclusions and Appendices

    1. Front Matter

      Pages 283-283
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    2. Conclusions and Suggestions for Future Research

      • Michael L. Wall
      Pages 285-290

  8. Back Matter

    Pages 291-374
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Keywords

About this book

This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source implementations of matrix product state algorithms, as well as educational material designed to aid in the use of understanding such methods.

Authors and Affiliations

  • Colorado School of Mines, Golden, CO, USA and JILA, NIST, and University of Colorado, Boulder, USA

    Michael L. Wall

About the author

Michael Wall performed research for his thesis at the Colorado School of Mines, USA. He has since received the Nicholas Metropolis award for outstanding doctoral thesis work in computational physics and is currently a postdoctoral fellow at NIST NRC.

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