Benchmark studies using quantum Monte Carlo: pressure estimators, energy, and entanglement

McMinis, Jeremy

Permalink

https://hdl.handle.net/2142/44344 Copy

Description

Title

Benchmark studies using quantum Monte Carlo: pressure estimators, energy, and entanglement

Author(s)

McMinis, Jeremy

Issue Date

2013-05-24T22:08:26Z

Director of Research (if dissertation) or Advisor (if thesis)

Ceperley, David M.

Doctoral Committee Chair(s)

Trinkle, Dallas R.

Committee Member(s)

• Ceperley, David M.
• Makri, Nancy
• Abbamonte, Peter M.

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Quantum Monte Carlo
• Electronic Structure
• Condensed Matter Physics
• Fermi Liquids
• Entanglement
• Low Density Hydrogen
• Metal insulator transition
• Momentum Distribution
• Strongly Correlated Systems

Abstract

Trial wave function based quantum Monte Carlo is a promising family of methods for the solution of quantum mechanical Hamiltonians. These fundamentally non-perturbative methods can be used to treat bosons or fermions in weakly or strong interacting systems and in any phase. Properties computed for particles with bosonic statistics can be converged to their exact value at relatively moderate computational cost using diffusion quantum Monte Carlo. For fermions the problem is slightly more complicated. Exact methods, such as released-node diffusion quantum Monte Carlo, exist for computing unbiased fermion properties, however their computational expense increases rapidly with the Bose-Fermi energy gap and system size. It is possible to use a fixed-node version of diffusion quantum Monte Carlo, but it introduces a bias due to the nodes of the trial wave function. In this thesis we work towards reducing trial wave function bias in fixed-node calculations and then perform several benchmark studies. We begin with a pedagogical overview of the three methods used throughout the thesis, variational, diffusion, and reptation quantum Monte Carlo. Then we discuss the problem, trial wave function bias in the energy and other observables. Next we outline the Hamiltonians we are typically interested in for electronic systems and trial wave function forms used to solve them. The algorithm used to optimize the trial wave functions is presented along with special considerations for some particular cases. Next we present three studies of the pressure of the electron gas using improved estimators in variational, diffusion, and reptation quantum Monte Carlo. Benchmark results for a set of molecules are then presented for the massive multi-determinant expansion and optimization algorithm tailored to suit it. We conclude with two studies of the interacting Fermi liquid, one on the momentum properties of the electron gas in three dimensions and another on the entanglement properties of interacting Fermi liquids in two dimensions.

Graduation Semester

2013-05

Permalink

http://hdl.handle.net/2142/44344

Copyright and License Information

Copyright 2013 Jeremy McMinis

Owning Collections