Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function

Welden, Alicia Rae; Rusakov, Alexander A.; Zgid, Dominika

doi:10.1063/1.4967449

Title: Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function

Abstract

Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature methods, since these methods require an explicit evaluation of multiple excited states in order to account for any finite-temperature effects. Using a Matsubara Green’s function formalism remains a viable alternative, since in this formalism it is easier to include thermal effects and to connect the dynamic quantities such as the self-energy with static thermodynamic quantities such as the Helmholtz energy, entropy, and internal energy. However, despite the promising properties of this formalism, little is known about the multiple solutions of the non-linear equations present in the self-consistent Matsubara formalism and only a few cases involving a full Coulomb Hamiltonian were investigated in the past. Here, to shed some light onto the iterative nature of the Green’s function solutions, we self-consistently evaluate the thermodynamic quantities for a one-dimensional (1D) hydrogen solid at various interatomic separations and temperatures using the self-energy approximated to second-order (GF2). At many points in the phase diagram of this system, multiple phases such as a metal and an insulator exist, and we are able to determine the mostmore »« less

Authors:

Welden, Alicia Rae ^[1];

^[1]; Zgid, Dominika ^[1]

Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Chemistry

Publication Date:: Mon Nov 28 00:00:00 EST 2016

Research Org.:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1535288

Alternate Identifier(s):: OSTI ID: 1333351; OSTI ID: 1843756

Grant/Contract Number:: SC0010381; ER16391

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 145; Journal Issue: 20; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; chemistry; physics

Citation Formats


                    Welden, Alicia Rae, Rusakov, Alexander A., and Zgid, Dominika. Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4967449.

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                    Welden, Alicia Rae, Rusakov, Alexander A., & Zgid, Dominika. Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function.  United States.  https://doi.org/10.1063/1.4967449

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                    Welden, Alicia Rae, Rusakov, Alexander A., and Zgid, Dominika. Mon .  
"Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function".  United States.  https://doi.org/10.1063/1.4967449.  https://www.osti.gov/servlets/purl/1535288.

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@article{osti_1535288,

  title        = {Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function},

  author       = {Welden, Alicia Rae and Rusakov, Alexander A. and Zgid, Dominika},

  abstractNote = {Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature methods, since these methods require an explicit evaluation of multiple excited states in order to account for any finite-temperature effects. Using a Matsubara Green’s function formalism remains a viable alternative, since in this formalism it is easier to include thermal effects and to connect the dynamic quantities such as the self-energy with static thermodynamic quantities such as the Helmholtz energy, entropy, and internal energy. However, despite the promising properties of this formalism, little is known about the multiple solutions of the non-linear equations present in the self-consistent Matsubara formalism and only a few cases involving a full Coulomb Hamiltonian were investigated in the past. Here, to shed some light onto the iterative nature of the Green’s function solutions, we self-consistently evaluate the thermodynamic quantities for a one-dimensional (1D) hydrogen solid at various interatomic separations and temperatures using the self-energy approximated to second-order (GF2). At many points in the phase diagram of this system, multiple phases such as a metal and an insulator exist, and we are able to determine the most stable phase from the analysis of Helmholtz energies. Additionally, we show the evolution of the spectrum of 1D boron nitride to demonstrate that GF2 is capable of qualitatively describing the temperature effects influencing the size of the band gap.},

  doi          = {10.1063/1.4967449},

  journal      = {Journal of Chemical Physics},

  number       = 20,

  volume       = 145,

  place        = {United States},

  year         = {Mon Nov 28 00:00:00 EST 2016},

  month        = {Mon Nov 28 00:00:00 EST 2016}

}

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Title: Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function

Abstract

Citation Formats

Total energies from variational functionals of the Green function and the renormalized four-point vertex journal, November 2006

Fractional charge and spin errors in self-consistent Green’s function theory journal, May 2015

Excitation spectra of aromatic molecules within a real-space G W -BSE formalism: Role of self-consistency and vertex corrections journal, August 2016

Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods? journal, December 2010

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Self-consistent second-order Green’s function perturbation theory for periodic systems journal, February 2016

A Finite-Temperature Generalisation of the Coupled Cluster Method: a Non-Perturbative Access to Grand Partition Functions journal, November 2003

Accessing thermodynamics from dynamical cluster-embedding approaches journal, November 2009

A Temperature Dependent Coupled Cluster Method book, January 1987

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Conservation Laws and Correlation Functions journal, October 1961

Resorcinol Crystallization from the Melt: A New Ambient Phase and New “Riddles” journal, March 2016

Temperature-Accelerated Method for Exploring Polymorphism in Molecular Crystals Based on Free Energy journal, June 2011

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Communication: Towards ab initio self-energy embedding theory in quantum chemistry journal, December 2015

On the Kohn–Luttinger conundrum journal, May 2013

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Thermal Properties of the Inhomogeneous Electron Gas journal, March 1965

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition journal, December 2003

All-Electron Self-Consistent G W Approximation: Application to Si, MnO, and NiO journal, September 2004

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling journal, October 1999

Finite-temperature full configuration interaction journal, April 2014

Self-consistent G W : All-electron implementation with localized basis functions journal, August 2013

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms journal, January 2016

Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic G W Approach journal, August 2014

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions journal, April 2016

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Variational Cluster Approach to Correlated Electron Systems in Low Dimensions journal, November 2003

Ground-State Energy of a Many-Fermion System. II journal, June 1960

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First-principles treatment of Mott insulators: linearized QSGW+DMFT approach journal, July 2016

Many-Body Theory Exposed!: Propagator Description of Quantum Mechanics in Many-Body Systems book, May 2008

Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy journal, September 2016

Stability of the thermal Hartree-Fock approximation journal, January 1963

Nonequilibrium Many-Body Theory of Quantum Systems book, March 2013

A Finite-Temperature Generalisation of the Coupled Cluster Method: a Non-Perturbative Access to Grand Partition Functions conference, November 2011

Accessing thermodynamics from dynamical cluster-embedding approaches text, January 2009

Fully selfconsistent GW calculations for molecules text, January 2010

The ALPS project release 2.0: Open source software for strongly correlated systems text, January 2011

Self-consistent GW: All-electron implementation with localized basis functions text, January 2013

Systematically improvable multi-scale solver for correlated electron systems text, January 2014

First-principles treatment of Mott insulators: linearized QSGW+DMFT approach text, January 2015

Current issues in finite-$T$ density-functional theory and Warm-Correlated Matter preprint, January 2016

Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy text, January 2016

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition text, January 2003

All-electron self-consistent GW approximation: Application to Si, MnO, and NiO text, January 2003

Quasiparticle Self-Consistent GW Theory text, January 2005

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling text, January 1999

Ground state properties of 3d metals from self-consistent GW approach journal, October 2017

Finite temperature quantum embedding theories for correlated systems journal, February 2017

Effect of propagator renormalization on the band gap of insulating solids journal, August 2019

Sparse sampling approach to efficient ab initio calculations at finite temperature journal, January 2020

Testing self-energy embedding theory in combination with GW journal, October 2017

To the Theory of Inhomogeneous Electron Gas journal, August 2018

Finite temperature quantum embedding theories for correlated systems text, January 2016

Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods text, January 2017

Ground state properties of 3d metals from self-consistent GW approach text, January 2017

Spectral properties from Matsubara Green's function approach - application to molecules text, January 2017

Effect of propagator renormalization on the band gap of insulating solids text, January 2018

Legendre-spectral Dyson equation solver with super-exponential convergence text, January 2020

Total energies from variational functionals of the Green function and the renormalized four-point vertex
journal, November 2006

Fractional charge and spin errors in self-consistent Green’s function theory
journal, May 2015

Excitation spectra of aromatic molecules within a real-space $G W$ -BSE formalism: Role of self-consistency and vertex corrections
journal, August 2016

Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?
journal, December 2010

Finite-temperature coupled-cluster, many-body perturbation, and restricted and unrestricted Hartree–Fock study on one-dimensional solids: Luttinger liquids, Peierls transitions, and spin- and charge-density waves
journal, September 2015

The ALPS project release 2.0: open source software for strongly correlated systems
journal, May 2011

Self-consistent second-order Green’s function perturbation theory for periodic systems
journal, February 2016

A Finite-Temperature Generalisation of the Coupled Cluster Method: a Non-Perturbative Access to Grand Partition Functions
journal, November 2003

Accessing thermodynamics from dynamical cluster-embedding approaches
journal, November 2009

A Temperature Dependent Coupled Cluster Method
book, January 1987

Local Hamiltonians for quantitative Green's function embedding methods
journal, November 2014

Conservation Laws and Correlation Functions
journal, October 1961

Resorcinol Crystallization from the Melt: A New Ambient Phase and New “Riddles”
journal, March 2016

Temperature-Accelerated Method for Exploring Polymorphism in Molecular Crystals Based on Free Energy
journal, June 2011

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory
journal, June 2014

Communication: Towards ab initio self-energy embedding theory in quantum chemistry
journal, December 2015

On the Kohn–Luttinger conundrum
journal, May 2013

Systematically improvable multiscale solver for correlated electron systems
journal, March 2015

Self-energy-functional approach to systems of correlated electrons
journal, April 2003

Thermal Properties of the Inhomogeneous Electron Gas
journal, March 1965

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
journal, December 2003

All-Electron Self-Consistent $G W$ Approximation: Application to Si, MnO, and NiO
journal, September 2004

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
journal, October 1999

Finite-temperature full configuration interaction
journal, April 2014

Self-consistent $G W$ : All-electron implementation with localized basis functions
journal, August 2013

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms
journal, January 2016

Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic $G W$ Approach
journal, August 2014

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions
journal, April 2016

Two-particle renormalizations in many-fermion perturbation theory: the importance of the Ward identity
journal, May 2003

Variational Cluster Approach to Correlated Electron Systems in Low Dimensions
journal, November 2003

Ground-State Energy of a Many-Fermion System. II
journal, June 1960

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations
journal, February 2014

Variational Total Energies from Φ- and Ψ- Derivable Theories
journal, March 1999

Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †
journal, March 2016

Large Scale GW Calculations
journal, May 2015

First-principles treatment of Mott insulators: linearized QSGW+DMFT approach
journal, July 2016

Many-Body Theory Exposed!: Propagator Description of Quantum Mechanics in Many-Body Systems
book, May 2008

Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy
journal, September 2016

Stability of the thermal Hartree-Fock approximation
journal, January 1963

Nonequilibrium Many-Body Theory of Quantum Systems
book, March 2013

A Finite-Temperature Generalisation of the Coupled Cluster Method: a Non-Perturbative Access to Grand Partition Functions
conference, November 2011

Accessing thermodynamics from dynamical cluster-embedding approaches
text, January 2009

Fully selfconsistent GW calculations for molecules
text, January 2010

The ALPS project release 2.0: Open source software for strongly correlated systems
text, January 2011

Self-consistent GW: All-electron implementation with localized basis functions
text, January 2013

Systematically improvable multi-scale solver for correlated electron systems
text, January 2014

First-principles treatment of Mott insulators: linearized QSGW+DMFT approach
text, January 2015

Current issues in finite-$T$ density-functional theory and Warm-Correlated Matter
preprint, January 2016

Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy
text, January 2016

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
text, January 2003

All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
text, January 2003

Quasiparticle Self-Consistent GW Theory
text, January 2005

Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
text, January 1999

Ground state properties of 3d metals from self-consistent GW approach
journal, October 2017

Finite temperature quantum embedding theories for correlated systems
journal, February 2017

Effect of propagator renormalization on the band gap of insulating solids
journal, August 2019

Sparse sampling approach to efficient ab initio calculations at finite temperature
journal, January 2020

Testing self-energy embedding theory in combination with GW
journal, October 2017

To the Theory of Inhomogeneous Electron Gas
journal, August 2018

Finite temperature quantum embedding theories for correlated systems
text, January 2016

Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
text, January 2017

Ground state properties of 3d metals from self-consistent GW approach
text, January 2017

Spectral properties from Matsubara Green's function approach - application to molecules
text, January 2017

Effect of propagator renormalization on the band gap of insulating solids
text, January 2018

Legendre-spectral Dyson equation solver with super-exponential convergence
text, January 2020