The JAGP variational wavefunction

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Table of contents

1 Introduction 
2 Quantum Monte Carlo methods for finite systems 
2.1 Introduction
2.1.1 Organization of the Chapter
2.2 Density functional theory on a localized basis set
2.2.1 The Kohn Sham equations
2.2.2 Kohn-Sham problem on non-orthogonal basis set
2.3 The JAGP variational wavefunction
2.3.1 Multi-configurational AGP ansatz
2.3.2 The missing ingredient: Jastrow factor
2.3.3 Functional forms of the ansatz
2.4 Evaluating physical observables within QMC
2.4.1 Variational Monte Carlo
2.4.2 Diffusion Monte Carlo
2.4.3 Pseudopotentials and lattice regularized DMC
2.5 Efficient wavefunction optimization
2.5.1 Stochastic reconfiguration method
2.5.2 Stochastic reconfiguration with ionic forces
2.5.3 An alternative route to derivatives: adjoint algorithmic differentiation
2.6 Conclusions
3 Applications to aqueous systems: proton transfer reactions 
3.1 Introduction
3.1.1 Organization of the Chapter
3.2 Geminal embedded orbitals
3.2.1 Embedding scheme
3.2.2 Detailed procedure
3.2.3 Comparison with standard natural orbitals
3.2.4 Application to the water monomer
3.3 Proton transfer reactions made simple: the Zundel model
3.3.1 Properties of the symmetric global minimum
3.3.2 Stretching the OO distance
3.3.3 Implications for more realistic PT models
3.3.4 Properties of the symmetry-broken configurations
3.3.5 Perspectives on realistic simulations
3.4 Conclusions
4 QMC simulations of extended systems 
4.1 Introduction
4.1.1 Organization of the Chapter
4.2 Localized basis DFT calculations for periodic systems
4.2.1 Primitive cell calculations
4.2.2 The Bloch theorem
4.2.3 Gaussian basis set for periodic systems
4.2.4 Generic boundary conditions
4.2.5 Numerical Brillouin zone integration
4.3 Periodic systems with QMC
4.3.1 Many-body Hamiltonian in supercell calculations
4.3.2 Twisted boundary conditions
4.3.3 Complex JAGP ansatz
4.4 Single-point QMC calculations with complex wavefunctions
4.4.1 Variational Monte Carlo
4.4.2 Fixed-phase diffusion Monte Carlo
4.5 Wavefunction optimization with periodic systems
4.5.1 Stochastic reconfiguration with complex wavefunction
4.5.2 Twist independent parameterization of the pairing function
4.6 Conclusions
5 Alternative approaches to reduce finite size effects in QMC solid state calculations 
5.1 Introduction
5.1.1 Organization of the Chapter
5.2 Kinetic energy shell fluctuations
5.3 Twist averaging techniques
5.4 Special twist methods
5.4.1 Theoretical foundations
5.4.2 The Baldereschi method
5.5 Exact special twist procedure
5.5.1 Detailed procedure
5.5.2 Benchmark calculations on 3D homogeneous electron gas
5.6 Realistic systems with the EST method
5.6.1 Many-body errors correction
5.6.2 Total energy
5.6.3 Comparison of errors in the EST method
5.6.4 Energy derivatives
5.7 Flavor twist method
5.8 Conclusions
6 Applications to iron-based superconductors: the case of iron selenide 
6.1 High-temperature superconductivity from first principles
6.1.1 Introduction
6.1.2 QMC: an appropriate first-principle framework
6.1.3 The case of FeSe: simplicity does not exclude complexity
6.1.4 Organization of the Chapter
6.2 Technical details of the QMC calculations
6.2.1 Two complementary QMC flavors
6.2.2 Simulation setup: supercells and magnetic phases
6.2.3 Wavefunction and basis set
6.2.4 Finite-size effects and lattice extrapolation
6.3 Structural properties
6.4 Magnetic properties
6.4.1 FeSe energetics under pressure
6.4.2 Comments on the paramagnetic phase
6.5 Interaction between structure and magnetism
6.5.1 Relevance of stripe-like magnetic orderings
6.5.2 Connection with Hund’s rule coupling
6.6 Conclusions
7 Conclusions and outlook 
Bibliography