57 research outputs found
Valence-skipping and negative-U in the d-band from repulsive local Coulomb interaction
We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate d-band, resulting in effective negative-U. This effect is shown to originate from anisotropic orbital-multipole scattering, and it occurs only for d1,d4,d6, and d9 fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived, and the paramagnetic phase diagram for d4 and d6 is calculated. We also establish that the valence-skipping metal is very different, in terms of its local valence distribution, compared to the atomiclike Hund's metal. These findings explain why transition-metal compounds with the aforementioned d-band fillings are more prone to valence-skipping charge order and anomalous superconductivity
Nonequilibrium dynamical mean-field theory for bosonic lattice models
We develop the nonequilibrium extension of bosonic dynamical mean field
theory (BDMFT) and a Nambu real-time strong-coupling perturbative impurity
solver. In contrast to Gutzwiller mean-field theory and strong coupling
perturbative approaches, nonequilibrium BDMFT captures not only dynamical
transitions, but also damping and thermalization effects at finite temperature.
We apply the formalism to quenches in the Bose-Hubbard model, starting both
from the normal and Bose-condensed phases. Depending on the parameter regime,
one observes qualitatively different dynamical properties, such as rapid
thermalization, trapping in metastable superfluid or normal states, as well as
long-lived or strongly damped amplitude oscillations. We summarize our results
in non-equilibrium "phase diagrams" which map out the different dynamical
regimes.Comment: 18 pages, 8 figure
A fast time domain solver for the equilibrium Dyson equation
We consider the numerical solution of the real time equilibrium Dyson
equation, which is used in calculations of the dynamical properties of quantum
many-body systems. We show that this equation can be written as a system of
coupled, nonlinear, convolutional Volterra integro-differential equations, for
which the kernel depends self-consistently on the solution. As is typical in
the numerical solution of Volterra-type equations, the computational bottleneck
is the quadratic-scaling cost of history integration. However, the structure of
the nonlinear Volterra integral operator precludes the use of standard fast
algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects
the structure of the nonlinear integral operator. The resulting method can
reach large propagation times, and is thus well-suited to explore quantum
many-body phenomena at low energy scales. We demonstrate the solver with two
standard model systems: the Bethe graph, and the Sachdev-Ye-Kitaev model
Magnetic response of SrRuO: quasi-local spin fluctuations due to Hund's coupling
We study the magnetic susceptibility in the normal state of SrRuO
using dynamical mean-field theory including dynamical vertex corrections.
Besides the well known incommensurate response, our calculations yield
quasi-local spin fluctuations which are broad in momentum and centered around
the point, in agreement with recent inelastic neutron scattering
experiments [P. Steffens, et al., Phys. Rev. Lett. 122, 047004 (2019)]. We show
that these quasi-local fluctuations are controlled by the Hund's coupling and
account for the dominant contribution to the momentum-integrated response.
While all orbitals contribute equally to the incommensurate response, the
enhanced point response originates from the planar xy orbital.Comment: 6 pages, 5 figure
Excitations and spectra from equilibrium real-time Green's functions
The real-time contour formalism for Green's functions provides time-dependent
information of quantum many-body systems. In practice, the long-time simulation
of systems with a wide range of energy scales is challenging due to both the
storage requirements of the discretized Green's function and the computational
cost of solving the Dyson equation. In this manuscript, we apply a real-time
discretization based on a piece-wise high-order orthogonal-polynomial expansion
to address these issues. We present a superconvergent algorithm for solving the
real-time equilibrium Dyson equation using the Legendre spectral method and the
recursive algorithm for Legendre convolution. We show that the compact high
order discretization in combination with our Dyson solver enables long-time
simulations using far fewer discretization points than needed in conventional
multistep methods. As a proof of concept, we compute the molecular spectral
functions of H, LiH, He and CHO using self-consistent
second-order perturbation theory and compare the results with standard quantum
chemistry methods as well as the auxiliary second-order Green's function
perturbation theory method
Inchworm quasi Monte Carlo for quantum impurities
The inchworm expansion is a promising approach to solving strongly correlated
quantum impurity models due to its reduction of the sign problem in real and
imaginary time. However, inchworm Monte Carlo is computationally expensive,
converging as where is the number of samples. We show that the
imaginary time integration is amenable to quasi Monte Carlo, with enhanced
convergence, by mapping the Sobol low-discrepancy sequence from the
hypercube to the simplex with the so-called Root transform. This extends the
applicability of the inchworm method to, e.g., multi-orbital Anderson impurity
models with off-diagonal hybridization, relevant for materials simulation,
where continuous time hybridization expansion Monte Carlo has a severe sign
problem
Bosonic self-energy functional theory
We derive the self-energy functional theory for bosonic lattice systems with broken U(1) symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean-field theory when constraining to local fields, whereas when neglecting kinetic contributions of noncondensed bosons, it reduces to the static mean-field approximation. To benchmark the theory, we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest-neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase boundaries and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings, we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g., in the presence of nontrivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters but nevertheless remain computable by modest means
Principle of maximum entanglement entropy and local physics of strongly correlated materials
We argue that, because of quantum entanglement, the local physics of strongly correlated materials at zero temperature is described in a very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number of local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits and present numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller approximation that strongly support our theory in general
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