Final Report Summary - MOTTMETALS (Quantitative approaches for strongly correlated quantum systems in equilibrium and far from equilibrium.)
The main achievements of this project are the introduction and development of a
new generation of quantum embedded method beyond Dynamical Mean Field Theory
(DMFT), i.e. the TRILEX method (Triply Irreducible Local Expansion), some new
results for out of equilibrium systems including a new real time Quantum Monte Carlo,
and the development of the TRIQS project and its applications.
TRILEX is based on a local approximation of the effective interaction vertex
between electrons and any bosonic fluctuation, using self-consistently
determined quantum impurity models. Although similar to DMFT (Dynamical Mean
Field Theory) methods, it departs radically from it in that the
self-consistency is made on the vertex function, not the self-energy. It can
however reuse the algorithmic developments made in the last decades
to solve DMFT problems.
TRILEX is a minimal and controllable formalism capable of describing
simultaneously the local strong correlation effects à la DMFT together with
long range bosonic fluctuations. In the context of high temperature
superconductors, it therefore unifies two of the most studied family of
theoretical approaches: cluster DMFT methods, where the pseudogap is due to
short range antiferromagnetic fluctuations close to the Mott insulator and
"spin fluctuations" approaches, which emphasizes the role of long range
antiferromagnetic fluctuations.
We have introduced the formalism, generalized it to "cluster TRILEX" methods to
make it controlled, benchmarked it against cluster DMFT methods, using the
recent converged benchmarks on the Hubbard model at high temperature
established by the Simons Many-Electrons Collaboration. We have shown that a
single site TRILEX applied to the Hubbard model yields a normal phase with a
momentum differentiation between nodes and antinodes (Fermi Arcs), and a dome
shaped d-wave superconducting phase. TRILEX also brings a much better
resolution in momentum space for the self-energy than cluster DMFT methods,
which is a major limitation of these methods at low temperature.
For non-equilibrium problems, the main achievement of the project is our new
diagrammatic Quantum Monte Carlo (QMC) for interacting quantum systems far from
equilibrium. It is the first diagrammatic QMC using a explicit sum of the
Feynman diagrams in terms of an exponential number (2^n at order n) of
determinants to eliminate the disconnected vaccuum diagrams. It computes the
expansion in power of the interaction, at any time, even in the infinite time
steady-state limit. This class of algorithm does not exhibit a standard "dynamical sign problem"
at long time.
Finally, we developed and published the TRIQS open source code project (Toolbox
for Interacting Quantum Systems), including the core TRIQS library, the CT-HYB
(QMC based on the hybridization expansion) quantum impurity solver and
DFT-tools, a package to interface TRIQS with several electronic structure
codes. We have obtained several results with this package,
e.g. on spin-orbit coupling and electronic correlations in
Sr2RuO4, superconductivity in A3C60 fullerides, energetics of vacancies in
alpha-Fe, spectral properties of the cobalt pnictide BaCo2As2, equation of
state and transport in ε-Fe, rare-earth nickelate LuNiO3.
new generation of quantum embedded method beyond Dynamical Mean Field Theory
(DMFT), i.e. the TRILEX method (Triply Irreducible Local Expansion), some new
results for out of equilibrium systems including a new real time Quantum Monte Carlo,
and the development of the TRIQS project and its applications.
TRILEX is based on a local approximation of the effective interaction vertex
between electrons and any bosonic fluctuation, using self-consistently
determined quantum impurity models. Although similar to DMFT (Dynamical Mean
Field Theory) methods, it departs radically from it in that the
self-consistency is made on the vertex function, not the self-energy. It can
however reuse the algorithmic developments made in the last decades
to solve DMFT problems.
TRILEX is a minimal and controllable formalism capable of describing
simultaneously the local strong correlation effects à la DMFT together with
long range bosonic fluctuations. In the context of high temperature
superconductors, it therefore unifies two of the most studied family of
theoretical approaches: cluster DMFT methods, where the pseudogap is due to
short range antiferromagnetic fluctuations close to the Mott insulator and
"spin fluctuations" approaches, which emphasizes the role of long range
antiferromagnetic fluctuations.
We have introduced the formalism, generalized it to "cluster TRILEX" methods to
make it controlled, benchmarked it against cluster DMFT methods, using the
recent converged benchmarks on the Hubbard model at high temperature
established by the Simons Many-Electrons Collaboration. We have shown that a
single site TRILEX applied to the Hubbard model yields a normal phase with a
momentum differentiation between nodes and antinodes (Fermi Arcs), and a dome
shaped d-wave superconducting phase. TRILEX also brings a much better
resolution in momentum space for the self-energy than cluster DMFT methods,
which is a major limitation of these methods at low temperature.
For non-equilibrium problems, the main achievement of the project is our new
diagrammatic Quantum Monte Carlo (QMC) for interacting quantum systems far from
equilibrium. It is the first diagrammatic QMC using a explicit sum of the
Feynman diagrams in terms of an exponential number (2^n at order n) of
determinants to eliminate the disconnected vaccuum diagrams. It computes the
expansion in power of the interaction, at any time, even in the infinite time
steady-state limit. This class of algorithm does not exhibit a standard "dynamical sign problem"
at long time.
Finally, we developed and published the TRIQS open source code project (Toolbox
for Interacting Quantum Systems), including the core TRIQS library, the CT-HYB
(QMC based on the hybridization expansion) quantum impurity solver and
DFT-tools, a package to interface TRIQS with several electronic structure
codes. We have obtained several results with this package,
e.g. on spin-orbit coupling and electronic correlations in
Sr2RuO4, superconductivity in A3C60 fullerides, energetics of vacancies in
alpha-Fe, spectral properties of the cobalt pnictide BaCo2As2, equation of
state and transport in ε-Fe, rare-earth nickelate LuNiO3.