69 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
Uncertainty principle for experimental measurements: Fast versus slow probes
The result of a physical measurement depends on the timescale of the
experimental probe. In solid-state systems, this simple quantum mechanical
principle has far-reaching consequences: the interplay of several degrees of
freedom close to charge, spin or orbital instabilities combined with the
disparity of the time scales associated to their fluctuations can lead to
seemingly contradictory experimental findings. A particularly striking example
is provided by systems of adatoms adsorbed on semiconductor surfaces where
different experiments -- angle-resolved photoemission, scanning tunneling
microscopy and core-level spectroscopy -- suggest different ordering phenomena.
Using most recent first principles many-body techniques, we resolve this puzzle
by invoking the time scales of fluctuations when approaching the different
instabilities. These findings suggest a re-interpretation of ordering phenomena
and their fluctuations in a wide class of solid-state systems ranging from
organic materials to high-temperature superconducting cuprates.Comment: 12 pages, 4 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
Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory
We present a fully self-consistent combined GW and dynamical mean field
(GW+DMFT) study of the spectral properties of the extended two-dimensional
Hubbard model. The inclusion of the local dynamical vertex stemming from the
DMFT self-energy and polarization is shown to cure the problems of
self-consistent GW in the description of spectral properties. We calculate the
momentum-resolved spectral functions, the two-particle polarization and
electron loss spectra, and show that the inclusion of GW in extended DMFT leads
to a narrowing of the quasi-particle width and more pronounced Hubbard bands in
the metallic regime as one approaches the charge-ordering transition. Finally,
the momentum-dependence introduced by GW into the extended DMFT description of
collective modes is found to affect their shape, giving rise to dispersive
plasmon-like long-wavelength and stripe modes.Comment: 5 pages, 4 figure
Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations
Noisy, intermediate-scale quantum computers come with intrinsic limitations
in terms of the number of qubits (circuit "width") and decoherence time
(circuit "depth") they can have. Here, for the first time, we demonstrate a
recently introduced method that breaks a circuit into smaller subcircuits or
fragments, and thus makes it possible to run circuits that are either too wide
or too deep for a given quantum processor. We investigate the behavior of the
method on one of IBM's 20-qubit superconducting quantum processors with various
numbers of qubits and fragments. We build noise models that capture
decoherence, readout error, and gate imperfections for this particular
processor. We then carry out noisy simulations of the method in order to
account for the observed experimental results. We find an agreement within 20%
between the experimental and the simulated success probabilities, and we
observe that recombining noisy fragments yields overall results that can
outperform the results without fragmentation.Comment: Accepted in ISVLSI 202
Benchmarking quantum co-processors in an application-centric, hardware-agnostic and scalable way
Existing protocols for benchmarking current quantum co-processors fail to
meet the usual standards for assessing the performance of
High-Performance-Computing platforms. After a synthetic review of these
protocols -- whether at the gate, circuit or application level -- we introduce
a new benchmark, dubbed Atos Q-score (TM), that is application-centric,
hardware-agnostic and scalable to quantum advantage processor sizes and beyond.
The Q-score measures the maximum number of qubits that can be used effectively
to solve the MaxCut combinatorial optimization problem with the Quantum
Approximate Optimization Algorithm. We give a robust definition of the notion
of effective performance by introducing an improved approximation ratio based
on the scaling of random and optimal algorithms. We illustrate the behavior of
Q-score using perfect and noisy simulations of quantum processors. Finally, we
provide an open-source implementation of Q-score that makes it easy to compute
the Q-score of any quantum hardware
TRIQS: A Toolbox for Research on Interacting Quantum Systems
We present the TRIQS library, a Toolbox for Research on Interacting Quantum
Systems. It is an open-source, computational physics library providing a
framework for the quick development of applications in the field of many-body
quantum physics, and in particular, strongly-correlated electronic systems. It
supplies components to develop codes in a modern, concise and efficient way:
e.g. Green's function containers, a generic Monte Carlo class, and simple
interfaces to HDF5. TRIQS is a C++/Python library that can be used from either
language. It is distributed under the GNU General Public License (GPLv3).
State-of-the-art applications based on the library, such as modern quantum
many-body solvers and interfaces between density-functional-theory codes and
dynamical mean-field theory (DMFT) codes are distributed along with it.Comment: 27 page
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