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Numerical Methods for Two-Particle Fluctuations and Real-Time Dynamics of Strongly Correlated Electron Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical Methods for Two-Particle Fluctuations and Real-Time Dynamics of Strongly Correlated Electron Systems./
Author:	Dong, Xinyang.
Description:	1 online resource (257 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
Subject:	Physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29705081click for full text (PQDT)
ISBN:	9798845449443

Numerical Methods for Two-Particle Fluctuations and Real-Time Dynamics of Strongly Correlated Electron Systems.
Dong, Xinyang.

Numerical Methods for Two-Particle Fluctuations and Real-Time Dynamics of Strongly Correlated Electron Systems. - 1 online resource (257 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--University of Michigan, 2022.

Includes bibliographical references

This thesis contains a series of numerical studies of strongly correlated electron systems. In these systems, interesting emergent properties are brought about by strong electron correlations, leading to unusual fluctuations and phase transitions.We start with a review of basic concepts in many-body physics from a field theory point of view, including second quantization and path integral formalisms. We then introduce extensions of the single-particle and two-particle Green's function formalisms in the singlet superconducting state, which enable us to extract physical information of the systems in the symmetry-broken phase.Next, we proceed to the models and numerical methods we use to study the strongly correlated systems. We introduce a low energy effective model -- the Hubbard model, which contains a subset of the electron degrees of freedom and can be solved numerically using advanced many-body methods. With the dynamical cluster approximation and continuous-time quantum Monte Carlo impurity solver, we are able to study the competing fluctuations in the paramagnetic state and analyze the fluctuations behind superconductivity in the singlet superconducting state.We introduce self-consistent diagrammatic methods used in realistic material calculations in the last part of this thesis, with an outline of group theory concepts that can be used to optimize the simulations. Numerical representations and methods for effectively solving equations in realistic material calculations are discussed afterwards. We briefly review some of the developments in this field, and then introduce spectral methods that are based on mathematical properties of Legendre polynomials for solving both the imaginary- and real-time Dyson equations.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798845449443Subjects--Topical Terms:

516296
Physics.
Subjects--Index Terms:

Strongly correlated electron systemsIndex Terms--Genre/Form:

542853
Electronic books.

Numerical Methods for Two-Particle Fluctuations and Real-Time Dynamics of Strongly Correlated Electron Systems.
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502 $a Thesis (Ph.D.)--University of Michigan, 2022.
504 $a Includes bibliographical references
520 $a This thesis contains a series of numerical studies of strongly correlated electron systems. In these systems, interesting emergent properties are brought about by strong electron correlations, leading to unusual fluctuations and phase transitions.We start with a review of basic concepts in many-body physics from a field theory point of view, including second quantization and path integral formalisms. We then introduce extensions of the single-particle and two-particle Green's function formalisms in the singlet superconducting state, which enable us to extract physical information of the systems in the symmetry-broken phase.Next, we proceed to the models and numerical methods we use to study the strongly correlated systems. We introduce a low energy effective model -- the Hubbard model, which contains a subset of the electron degrees of freedom and can be solved numerically using advanced many-body methods. With the dynamical cluster approximation and continuous-time quantum Monte Carlo impurity solver, we are able to study the competing fluctuations in the paramagnetic state and analyze the fluctuations behind superconductivity in the singlet superconducting state.We introduce self-consistent diagrammatic methods used in realistic material calculations in the last part of this thesis, with an outline of group theory concepts that can be used to optimize the simulations. Numerical representations and methods for effectively solving equations in realistic material calculations are discussed afterwards. We briefly review some of the developments in this field, and then introduce spectral methods that are based on mathematical properties of Legendre polynomials for solving both the imaginary- and real-time Dyson equations.
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538 $a Mode of access: World Wide Web
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653 $a Numerical methods
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