88 research outputs found
Mott physics and spin fluctuations: a unified framework
We present a formalism for strongly correlated electrons systems which
consists in a local approximation of the dynamical three-leg interaction
vertex. This vertex is self-consistently computed with a quantum impurity model
with dynamical interactions in the charge and spin channels, similar to
dynamical mean field theory (DMFT) approaches. The electronic self-energy and
the polarization are both frequency and momentum dependent. The method
interpolates between the spin-fluctuation or GW approximations at weak coupling
and the atomic limit at strong coupling. We apply the formalism to the Hubbard
model on a two-dimensional square lattice and show that as interactions are
increased towards the Mott insulating state, the local vertex acquires a strong
frequency dependence, driving the system to a Mott transition, while at low
enough temperatures the momentum-dependence of the self-energy is enhanced due
to large spin fluctuations. Upon doping, we find a Fermi arc in the
one-particle spectral function, which is one signature of the pseudo-gap state.Comment: 7 pages, 6 figure
Mott physics and spin fluctuations: a functional viewpoint
We present a formalism for strongly correlated systems with fermions coupled
to bosonic modes. We construct the three-particle irreducible functional
by successive Legendre transformations of the free energy of the
system. We derive a closed set of equations for the fermionic and bosonic
self-energies for a given . We then introduce a local
approximation for , which extends the idea of dynamical mean field
theory (DMFT) approaches from two- to three-particle irreducibility. This
approximation entails the locality of the three-leg electron-boson vertex
, which is self-consistently computed using a quantum
impurity model with dynamical charge and spin interactions. This local vertex
is used to construct frequency- and momentum-dependent electronic self-energies
and polarizations. By construction, the method interpolates between the
spin-fluctuation or GW approximations at weak coupling and the atomic limit at
strong coupling. We apply it to the Hubbard model on two-dimensional square and
triangular lattices. We complement the results of Phys.Rev. B 92, 115109 by (i)
showing that, at half-filling, as DMFT, the method describes the Fermi-liquid
metallic state and the Mott insulator, separated by a first-order
interacting-driven Mott transition at low temperatures, (ii) investigating the
influence of frustration and (iii) discussing the influence of the bosonic
decoupling channel.Comment: 29 pages, 14 figure
Enhancement of Local Pairing Correlations in Periodically Driven Mott Insulators
We investigate a model for a Mott insulator in presence of a time-periodic
modulated interaction and a coupling to a thermal reservoir. The combination of
drive and dissipation leads to non-equilibrium steady states with a large
number of doublon excitations, well above the maximum thermal-equilibrium
value. We interpret this effect as an enhancement of local pairing
correlations, providing analytical arguments based on a Floquet Hamiltonian.
Remarkably, this Hamiltonian shows a tendency to develop long-range staggered
superconducting correlations. This suggests the possibility of realizing the
elusive eta-pairing phase in driven-dissipative Mott Insulators.Comment: 6+5 page
Continuous-time auxiliary field Monte Carlo for quantum impurity models
We present a continuous-time Monte Carlo method for quantum impurity models,
which combines a weak-coupling expansion with an auxiliary-field decomposition.
The method is considerably more efficient than Hirsch-Fye and free of time
discretization errors, and is particularly useful as impurity solver in large
cluster dynamical mean field theory (DMFT) calculations.Comment: 6 pages, 5 figure
Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
14 pages, 6 figuresWe discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (DA), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with DA and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions
Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions
We propose a systematic approach to the non-equilibrium dynamics of strongly
interacting many-body quantum systems, building upon the standard perturbative
expansion in the Coulomb interaction. High order series are derived from the
Keldysh version of determinantal diagrammatic Quantum Monte Carlo, and the
reconstruction beyond the weak coupling regime of physical quantities is
obtained by considering them as analytic functions of a complex-valued
interaction . Our advances rely on two crucial ingredients: i) a conformal
change of variable, based on the approximate location of the singularities of
these functions in the complex -plane; ii) a Bayesian inference technique,
that takes into account additional known non-perturbative relations, in order
to control the amplification of noise occurring at large . This general
methodology is applied to the strongly correlated Anderson quantum impurity
model, and is thoroughly tested both in- and out-of-equilibrium. In the
situation of a finite voltage bias, our method is able to extend previous
studies, by bridging with the regime of unitary conductance, and by dealing
with energy offsets from particle-hole symmetry. We also confirm the existence
of a voltage splitting of the impurity density of states, and find that it is
tied to a non-trivial behavior of the non-equilibrium distribution function.
Beyond impurity problems, our approach could be directly applied to
Hubbard-like models, as well as other types of expansions.Comment: 16 pages, 18 figures, added comparison with Bethe Ansatz, appendix B
and some discussio
TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
We present TRIQS/CTHYB, a state-of-the art open-source implementation of the
continuous-time hybridisation expansion quantum impurity solver of the TRIQS
package. This code is mainly designed to be used with the TRIQS library in
order to solve the self-consistent quantum impurity problem in a multi-orbital
dynamical mean field theory approach to strongly-correlated electrons, in
particular in the context of realistic calculations. It is implemented in C++
for efficiency and is provided with a high-level Python interface. The code is
ships with a new partitioning algorithm that divides the local Hilbert space
without any user knowledge of the symmetries and quantum numbers of the
Hamiltonian. Furthermore, we implement higher-order configuration moves and
show that such moves are necessary to ensure ergodicity of the Monte Carlo in
common Hamiltonians even without symmetry-breaking.Comment: 19 pages, this is a companion article to that describing the TRIQS
librar
Discrete Lehmann representation of imaginary time Green's functions
We present an efficient basis for imaginary time Green's functions based on a
low rank decomposition of the spectral Lehmann representation. The basis
functions are simply a set of well-chosen exponentials, so the corresponding
expansion may be thought of as a discrete form of the Lehmann representation
using an effective spectral density which is a sum of functions. The
basis is determined only by an upper bound on the product , with the inverse temperature and an
energy cutoff, and a user-defined error tolerance . The number of
basis functions scales as . The discrete Lehmann representation of a particular
imaginary time Green's function can be recovered by interpolation at a set of
imaginary time nodes. Both the basis functions and the interpolation nodes
can be obtained rapidly using standard numerical linear algebra routines. Due
to the simple form of the basis, the discrete Lehmann representation of a
Green's function can be explicitly transformed to the Matsubara frequency
domain, or obtained directly by interpolation on a Matsubara frequency grid. We
benchmark the efficiency of the representation on simple cases, and with a high
precision solution of the Sachdev-Ye-Kitaev equation at low temperature. We
compare our approach with the related intermediate representation method, and
introduce an improved algorithm to build the intermediate representation basis
and a corresponding sampling grid
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