3,332 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
Impact of conditional modelling for a universal autoregressive quantum state
We present a generalized framework toadapt universal quantum state approxima-tors, enabling them to satisfy rigorous nor-malization and autoregressive properties.We also introduce filters as analogues toconvolutional layers in neural networks toincorporate translationally symmetrizedcorrelations in arbitrary quantum states.By applying this framework to the Gaus-sian process state, we enforce autoregres-sive and/or filter properties, analyzingthe impact of the resulting inductive bi-ases on variational flexibility, symmetries,and conserved quantities. In doing sowe bring together different autoregressivestates under a unified framework for ma-chine learning-inspired ans ̈atze. Our re-sults provide insights into how the autore-gressive construction influences the abilityof a variational model to describe corre-lations in spin and fermionic lattice mod-els, as well as ab initio electronic structureproblems where the choice of representa-tion affects accuracy. We conclude that,while enabling efficient and direct sam-pling, thus avoiding autocorrelation andloss of ergodicity issues in Metropolis sam-pling, the autoregressive construction ma-terially constrains the expressivity of themodel in many systems
Fast and accurate nonadiabatic molecular dynamics enabled through variational interpolation of correlated electron wavefunctions
We build on the concept of eigenvector continuation to develop an efficient multi-state method for the rigorous and smooth interpolation of a small training set of many-body wavefunctions through chemical space at mean-field cost. The inferred states are represented as variationally optimal linear combinations of the training states transferred between the many-body basis of different nuclear geometries. We show that analytic multi-state forces and nonadiabatic couplings from the model enable application to nonadiabatic molecular dynamics, developing an active learning scheme to ensure a compact and systematically improvable training set. This culminates in application to the nonadiabatic molecular dynamics of a photoexcited 28-atom hydrogen chain, with surprising complexity in the resulting nuclear motion. With just 22 DMRG calculations of training states from the low-energy correlated electronic structure at different geometries, we infer the multi-state energies, forces and nonadiabatic coupling vectors at 12,000 geometries with provable convergence to high accuracy along an ensemble of molecular trajectories, which would not be feasible with a brute force approach. This opens up a route to bridge the timescales between accurate single-point correlated electronic structure methods and timescales of relevance for photo-induced molecular dynamics
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
A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
Highly accurate results for the homogeneous electron gas (HEG) have only been
achieved to date within a diffusion Monte Carlo (DMC) framework. Here, we
introduce a newly developed stochastic technique, Full Configuration
Interaction Quantum Monte Carlo (FCIQMC), which samples the exact wavefunction
expanded in plane wave Slater determinants. Despite the introduction of a basis
set incompleteness error, we obtain a finite-basis energy which is
significantly, and variationally lower than any previously published work for
the 54-electron HEG at = 0.5 a.u., in a Hilbert space of
Slater determinants. At this value of , as well as of 1.0 a.u., we remove
the remaining basis set incompleteness error by extrapolation, yielding results
comparable or better than state-of-the-art DMC backflow energies. In doing so,
we demonstrate that it is possible to yield highly accurate results with the
FCIQMC method in sizable periodic systems.Comment: 4-page lette
The reflections of the Hellenistic influence in the Fourth Gospel
Thesis (M.A.)--Boston University This item was digitized by the Internet Archive
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