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Simulation of strongly correlated quantum many-body systems

Citation

Bilgin, Ersen (2011) Simulation of strongly correlated quantum many-body systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:04082011-161930834

Abstract

In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum Algorithms; Quantum Many-Body Systems; Simulation; anyons; thermalization;
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Kitaev, Alexei
  • Refael, Gil
  • Yeh, Nai-Chang
Defense Date:6 April 2011
Funders:
Funding AgencyGrant Number
U.S. Dept. of EnergyDE- FG03-92-ER40701
NSFPHY- 0803371
Record Number:CaltechTHESIS:04082011-161930834
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:04082011-161930834
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6282
Collection:CaltechTHESIS
Deposited By: Ersen Bilgin
Deposited On:17 May 2011 22:52
Last Modified:16 Apr 2013 22:41

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