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Reducing Computational Costs for Many-Body Physics Problems


Ye, Erika (2021) Reducing Computational Costs for Many-Body Physics Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xpvv-ar02.


Three different computational physics problems are discussed. The first project is solving the semi-classical Boltzmann transport equation (BTE) to compute the thermal conductivity of 1-D superlattices. We consider various spectral scattering models at each interface. This computation requires the inversion of a matrix whose size scales with the number of points used in the discretization of the Brillouin zone. We use spatial symmetries to reduce the size of data points and make the computation manageable. The other two projects involve quantum systems. Simulating quantum systems can potentially require exponential resources because of the exponential scaling of Hilbert space with system size. However, it has been observed that many physical systems, which typically exhibit locality in space or time, require much fewer resources to accurately simulate within some small error tolerance. The second project in the thesis is a two-step factorization of the electronic structure Hamiltonian that allows for efficient implementation on a quantum computer and also systematic truncation of small contributions. By using truncations that only incur errors below chemical accuracy, one is able to reduce the number of terms in the Hamiltonian from O(N⁴) to O(N³), where N is the number of molecular orbitals in the system. The third project is a tensor network algorithm based on the concept of influence functionals (IFs) to compute long-time dynamics of single-site observables. IFs are high-dimensional objects that describe the influence of the bath on the dynamics of the subsystem of interest over all times, and we are interested in their low-rank approximations. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap, and find that the IFs can be efficiently computed and represented using tensor network methods. Consistent with physical intuition, the correlations in the IFs appear to decrease with increased bath sizes, suggesting that the low-rank nature of the IF is due to nontrivial cancellations in the bath.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Computational physics, quantum physics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Chan, Garnet K. (co-advisor)
  • Minnich, Austin J. (co-advisor)
Thesis Committee:
  • Motrunich, Olexei I. (chair)
  • Refael, Gil
  • Chan, Garnet K.
  • Minnich, Austin J.
Defense Date:22 March 2021
Record Number:CaltechTHESIS:05112021-235754667
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 2 adapted for Chapter 3 adapted for Chapter 4
Ye, Erika0000-0001-9694-568X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14144
Deposited By: Erika Ye
Deposited On:27 May 2021 15:40
Last Modified:03 Jun 2021 15:53

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