3,609 research outputs found
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo
We review recent advances in the capabilities of the open source ab initio
Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for
greater efficiency and reproducibility. The auxiliary field QMC (AFQMC)
implementation has been greatly expanded to include k-point symmetries,
tensor-hypercontraction, and accelerated graphical processing unit (GPU)
support. These scaling and memory reductions greatly increase the number of
orbitals that can practically be included in AFQMC calculations, increasing
accuracy. Advances in real space methods include techniques for accurate
computation of band gaps and for systematically improving the nodal surface of
ground state wavefunctions. Results of these calculations can be used to
validate application of more approximate electronic structure methods including
GW and density functional based techniques. To provide an improved foundation
for these calculations we utilize a new set of correlation-consistent effective
core potentials (pseudopotentials) that are more accurate than previous sets;
these can also be applied in quantum-chemical and other many-body applications,
not only QMC. These advances increase the efficiency, accuracy, and range of
properties that can be studied in both molecules and materials with QMC and
QMCPACK
Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
In numerical simulations, spontaneously broken symmetry is often detected by
computing two-point correlation functions of the appropriate local order
parameter. This approach, however, computes the square of the local order
parameter, and so when it is {\it small}, very large system sizes at high
precisions are required to obtain reliable results. Alternatively, one can pin
the order by introducing a local symmetry breaking field, and then measure the
induced local order parameter infinitely far from the pinning center. The
method is tested here at length for the Hubbard model on honeycomb lattice,
within the realm of the projective auxiliary field quantum Monte Carlo
algorithm. With our enhanced resolution we find a direct and continuous quantum
phase transition between the semi-metallic and the insulating antiferromagnetic
states with increase of the interaction. The single particle gap in units of
the Hubbard tracks the staggered magnetization. An excellent data collapse
is obtained by finite size scaling, with the values of the critical exponents
in accord with the Gross-Neveu universality class of the transition.Comment: 7 pages, 6 figures, Published versio
Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
A comprehensive study of the two-dimensional (2D) compass model on the square
lattice is performed for classical and quantum spin degrees of freedom using
Monte Carlo and quantum Monte Carlo methods. We employ state-of-the-art
implementations using Metropolis, stochastic series expansion and parallel
tempering techniques to obtain the critical ordering temperatures and critical
exponents. In a pre-investigation we reconsider the classical compass model
where we study and contrast the finite-size scaling behavior of ordinary
periodic boundary conditions against annealed boundary conditions. It is shown
that periodic boundary conditions suffer from extreme finite-size effects which
might be caused by closed loop excitations on the torus. These excitations also
appear to have severe effects on the Binder parameter. On this footing we
report on a systematic Monte Carlo study of the quantum compass model. Our
numerical results are at odds with recent literature on the subject which we
trace back to neglecting the strong finite-size effects on periodic lattices.
The critical temperatures are obtained as and
for the classical and quantum version, respectively,
and our data support a transition in the 2D Ising universality class for both
cases.Comment: 8 pages, 7 figures, differs slightly from published versio
Stochastic linear scaling for metals and non metals
Total energy electronic structure calculations, based on density functional
theory or on the more empirical tight binding approach, are generally believed
to scale as the cube of the number of electrons. By using the localisaton
property of the high temperature density matrix we present exact deterministic
algorithms that scale linearly in one dimension and quadratically in all
others. We also introduce a stochastic algorithm that scales linearly with
system size. These results hold for metallic and non metallic systems and are
substantiated by numerical calculations on model systems.Comment: 9 pages, 2 figure
Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
We study one-dimensional Su-Schrieffer-Heeger (SSH) models with quantum
phonons using a continuous-time quantum Monte Carlo method. Within statistical
errors, we obtain identical results for the SSH model with acoustic phonons,
and a related model with a coupling to an optical bond phonon mode. Based on
this agreement, we first study the Peierls metal-insulator transition of the
spinless SSH model, and relate it to the Kosterlitz-Thouless transition of a
spinless Luttinger liquid. In the Peierls phase, the spectral functions reveal
the single-particle and charge gap, and a central peak related to long-range
order. For the spinful SSH model, which has a dimerized ground state for any
nonzero coupling, we reveal a symmetry-related degeneracy of spin and charge
excitations, and the expected spin and charge gaps as well as a central peak.
Finally, we study the SSH- model with electron-phonon and electron-electron
interaction. We observe a Mott phase with critical spin and bond correlations
at weak electron-phonon coupling, and a Peierls phase with gapped spin
excitations at strong coupling. We relate our findings to the extended Hubbard
model, and discuss the physical origin of the agreement between optical and
acoustic phonons.Comment: 12 pages, 13 figure
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