2,357 research outputs found
Rigorous wave function embedding with dynamical fluctuations
The dynamical fluctuations in approaches such as dynamical mean-field theory
(DMFT) allow for the self-consistent optimization of a local fragment,
hybridized with a true correlated environment. We show that these correlated
environmental fluctuations can instead be efficiently captured in a wave
function perspective in a computationally cheap, frequency-independent,
zero-temperature approach. This allows for a systematically improvable,
short-time wave function analogue to DMFT, which entails a number of
computational and numerical benefits. We demonstrate this approach to solve the
correlated dynamics of the paradigmatic Bethe lattice Hubbard model, as well as
detailing cluster extensions in the one-dimensional Hubbard chain where we
clearly show the benefits of this rapidly convergent description of correlated
environmental fluctuations
Spectral functions of strongly correlated extended systems via an exact quantum embedding
Density matrix embedding theory (DMET) [Phys. Rev. Lett., 109, 186404
(2012)], introduced a new approach to quantum cluster embedding methods,
whereby the mapping of strongly correlated bulk problems to an impurity with
finite set of bath states was rigorously formulated to exactly reproduce the
entanglement of the ground state. The formalism provided similar physics to
dynamical mean-field theory at a tiny fraction of the cost, but was inherently
limited by the construction of a bath designed to reproduce ground state,
static properties. Here, we generalize the concept of quantum embedding to
dynamic properties and demonstrate accurate bulk spectral functions at
similarly small computational cost. The proposed spectral DMET utilizes the
Schmidt decomposition of a response vector, mapping the bulk dynamic
correlation functions to that of a quantum impurity cluster coupled to a set of
frequency dependent bath states. The resultant spectral functions are obtained
on the real-frequency axis, without bath discretization error, and allows for
the construction of arbitrary dynamic correlation functions. We demonstrate the
method on the 1D and 2D Hubbard model, where we obtain zero temperature,
thermodynamic limit spectral functions, and show the trivial extension to
two-particle Green functions. This advance therefore extends the scope and
applicability of DMET in condensed matter problems as a computationally
tractable route to correlated spectral functions of extended systems, and
provides a competitive alternative to dynamical mean-field theory for dynamic
quantities.Comment: 6 pages, 6 figure
Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods
In this article we study examples of systematic biases that can occur in
quantum Monte Carlo methods due to the accumulation of non-linear expectation
values, and approaches by which these errors can be corrected. We begin with a
study of the Krylov-projected FCIQMC (KP-FCIQMC) approach, which was recently
introduced to allow efficient, stochastic calculation of dynamical properties.
This requires the solution of a sampled effective Hamiltonian, resulting in a
non-linear operation on these stochastic variables. We investigate the
probability distribution of this eigenvalue problem to study both stochastic
errors and systematic biases in the approach, and demonstrate that such errors
can be significantly corrected by moving to a more appropriate basis. This is
lastly expanded to include consideration of the correlation function QMC
approach of Ceperley and Bernu, showing how such an approach can be taken in
the FCIQMC framework.Comment: 12 pages, 7 figure
Systematic improvability in quantum embedding for real materials
Quantum embedding methods have become a powerful tool to overcome
deficiencies of traditional quantum modelling in materials science. However,
while these are systematically improvable in principle, in practice it is
rarely possible to achieve rigorous convergence and often necessary to employ
empirical parameters. Here, we formulate a quantum embedding theory, building
on the methods of density-matrix embedding theory combined with local
correlation approaches from quantum chemistry, to ensure the ability to
systematically converge properties of real materials with accurate correlated
wave~function methods, controlled by a single, rapidly convergent parameter. By
expanding supercell size, basis set, and the resolution of the fluctuation
space of an embedded fragment, we show that the systematic improvability of the
approach yields accurate structural and electronic properties of realistic
solids without empirical parameters, even across changes in geometry. Results
are presented in insulating, semi-metallic, and more strongly correlated
regimes, finding state of the art agreement to experimental data
A framework for efficient ab initio electronic structure with Gaussian Process States
We present a general framework for the efficient simulation of realistic
fermionic systems with modern machine learning inspired representations of
quantum many-body states, towards a universal tool for ab initio electronic
structure. These machine learning inspired ansatzes have recently come to the
fore in both a (first quantized) continuum and discrete Fock space
representations, where however the inherent scaling of the latter approach for
realistic interactions has so far limited practical applications. With
application to the 'Gaussian Process State', a recently introduced ansatz
inspired by systematically improvable kernel models in machine learning, we
discuss different choices to define the representation of the computational
Fock space. We show how local representations are particularly suited for
stochastic sampling of expectation values, while also indicating a route to
overcome the discrepancy in the scaling compared to continuum formulated
models. We are able to show competitive accuracy for systems with up to 64
electrons, including a simplified (yet fully ab initio) model of the Mott
transition in three-dimensional hydrogen, indicating a significant improvement
over similar approaches, even for moderate numbers of configurational samples.Comment: 15 pages, 5 figure
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
We present an investigation into the use of an explicitly correlated plane
wave basis for periodic wavefunction expansions at the level of second-order
M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic
correlation energy with respect to the one-electron basis set is investigated
and compared to conventional MP2 theory in a finite homogeneous electron gas
model. In addition to the widely used Slater-type geminal correlation factor,
we also derive and investigate a novel correlation factor that we term
Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic
results for two electrons in a box and allows for a further improved
convergence of the correlation energies with respect to the employed basis set.
We find the combination of the infinitely delocalized plane waves and local
short-ranged geminals provides a complementary, and rapidly convergent basis
for the description of periodic wavefunctions. We hope that this approach will
expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure
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