(Downloads - 0)
For more info about our services contact : help@bestpfe.com
Table of contents
Introduction
Overview
I Large-order behavior and resummation for the unitary Fermi gas
1 Introduction
1.1 The unitary Fermi gas
1.2 The unitary Fermi gas as the continuum limit of lattice models
1.3 Diagrammatic dressing: bare, ladder, and bold expansions
2 Summary of main results
3 Large-order behavior for the pressure in the ladder scheme
3.1 Shifted action for the ladder scheme
3.2 Obtaining the large-order behavior for the pressure from the partition function
3.3 Integration over fermions
3.4 Saddle point for the large-order behavior of the determinant
3.5 Functional integration in the large-n limit
4 Analytic reconstruction by conformal-Borel transform
4.1 Unicity of Taylor coefficients
4.2 Borel summability and conformal mapping
5 Generalizations
5.1 Borel summability of the self-energies in the ladder expansion
5.2 Alternative view: discontinuities near the origin
5.3 Discussion of the bold scheme
6 Numerical results
7 Conclusions and outlook
Appendices of Part I
A Shifted action for the ladder scheme
B Interchanging thermodynamic and large-order limit
C Renormalized Fredholm determinants
D Large-field behavior of the determinant
E No imaginary-time dependence of the instanton
F Sobolev bound
G Variational principle
H High and low temperature limits of the action functional
I Symmetric decreasing rearrangement
J Gaussian zero modes
K Gaussian integration
L Bound on derivatives
M Unicity of analytic continuation
N Ramis’s theorem
O Consistency condition for the maximal analytic extension
P Construction of the conformal map
Q Some properties of Gevrey asymptotic series
R Dispersion relation
S Pair propagator in terms of the fields
T Generalized Pauli formulas
U Numerical computation of the minimum of the action
V Legendre-Bateman expansion
W Discontinuities of the bold self-energies
II Connected determinant diagrammatic Monte Carlo: polynomial complexity despite fermionic sign
Article 1: Determinant Diagrammatic Monte Carlo in the thermodynamic limit
Article 2: Polynomial complexity despite the fermionic sign
Complements
1 The recursive formula for many-variable formal power series
2 Example: two-body interactions with a linear quadratic shift .
2.1 Calculation of aE(V )
2.2 Monte Carlo integration and computational cost of the non-deterministic part
2.3 Generalizations
2.4 Computation of physical correlation functions
3 Polynomial-time scaling
Conclusion and outlook
Appendices of Part II
A Computational cost of the recursive formula
B Computational cost of the determinants
C Hybrid sampling
D Binary representation
III Multivaluedness of the Luttinger-Ward functional and applicability of dressed diagrammatic schemes
1 Introduction and overview
2 The dangers of dressing
2.1 The formal definition of the bold series
2.2 The Kozik-Ferrero-Georges branch of the Luttinger-Ward functional
2.3 Misleading convergence of the bold scheme
3 An insightful model
3.1 Feynman diagrams definition
3.2 Grassmann integral representation
3.3 The KFG branch of the toy model
3.4 Misleading convergence of the bold scheme within the toy model
4 Semi-bold scheme: partial dressing with no misleading convergence
4.1 Shifted-action expansion
4.2 Semi-bold scheme
5 Applicability of the bold scheme
6 Conclusions and outlook
Article 3: Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
Article 4: Shifted-action expansion and applicability of dressed diagrammatic schemes
Bibliography
