Extracting infinite system properties from finite size clusters: “phase randomization/boundary condition averaging”

Gammel, J. Tinka; Campbell, David; Loh, Eugene

doi:10.1016/0379-6779(93)90763-m

Cited by 15 publications

(7 citation statements)

References 9 publications

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“…The total energy as well as expectation values of other periodic operators are calculated as an average over all twisted boundary conditions [110,111]. In practice, the integral in (3.8) is approximated by a discrete sum.…”

Section: Twist-averaged Boundary Conditionsmentioning

confidence: 99%

Applications of quantum Monte Carlo methods in condensed systems

2011

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The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

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Section: Twist-averaged Boundary Conditionsmentioning

confidence: 99%

Applications of quantum Monte Carlo methods in condensed systems

2011

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“…Periodic boundary conditions (PBC) correspond to tpij = 0,Vi,j, and antiperiodic ones correspond to <^y = 7T,Vi,j. Different sets of pairs < p = (<px,cpy) yield different allowed k points, and finite-size effects are minimized by considering an ensemble of random sets <p^e\ l = 1 ,...,M; for each (p(i\ we calculate the quantities of interest (see below) and average over the M realizations [12][13][14][15][16]. In so doing, the number of allowed k points increases, mimicking the dense (Ns -> oo) Brillouin zone (BZ).…”

Section: Model and Methodologymentioning

confidence: 99%

Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

2015

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We investigate the harmonic-trap control of the size and shape of Mott regions in the Fermi-Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduces finite-size effects in some ground-state properties; calculations in the grand-canonical ensemble together with a local-density approximation allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state to a Mott core and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A "phase diagram" in terms of an effective density and of the on-site repulsion is proposed as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative), display detectable signatures of the core-ring transition. Some spin-correlation functions are also calculated and predict the existence Neel-like ordering within Mott cores and rings.

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“…The integration of the results over the twist is called twist-averaged boundary condition (TABC), and it has been proven that it will produce exact results in the Hubbard model in a grand canonical ensemble, as well as for non-interacting systems [79], and that it will make certain lattice models converge faster to the TL [80]. In the context of nuclear matter, TABC has been used for the reduction of FSEs in QMC calculations regarding the EoS of nucleonic matter [81] and in Skyrme-Hartree-Fock calculations of the energy in various nuclear pasta phases [82].…”

Section: Finite-size Effects and Twisted Boundary Conditionsmentioning

confidence: 99%

Superfluid Neutron Matter with a Twist

Palkanoglou

Gezerlis

2021

Universe

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Superfluid neutron matter is a key ingredient in the composition of neutron stars. The physics of the inner crust are largely dependent on those of its S-wave neutron superfluid, which has made its presence known through pulsar glitches and modifications in neutron star cooling. Moreover, with recent gravitational-wave observations of neutron star mergers, the need for an equation of state for the matter of these compact stars is further accentuated and a model-independent treatment of neutron superfluidity is important. Ab initio techniques developed for finite systems can be guided to perform extrapolations to the thermodynamic limit and attain this model-independent extraction of various quantities of infinite superfluid neutron matter. To inform such an extrapolation scheme, we performed calculations of the neutron 1S0 pairing gap using model-independent odd–even staggering in the context of the particle-conserving, projected Bardeen–Cooper–Schrieffer (BCS) theory under twisted boundary conditions. While the practice of twisted boundary conditions is standard in solid-state physics and has been used repeatedly in the past to reduce finite-size effects, this is the first time that it has been employed in the context of pairing. We find that a twist-averaging approach results in a substantial reduction of the finite-size effects, bringing systems with N⪆50 within a 2% error margin from the infinite system. This can significantly reduce extrapolation-related errors in the extraction of superfluid neutron matter quantities.

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Extracting infinite system properties from finite size clusters: “phase randomization/boundary condition averaging”

Cited by 15 publications

References 9 publications

Applications of quantum Monte Carlo methods in condensed systems

Applications of quantum Monte Carlo methods in condensed systems

Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

Superfluid Neutron Matter with a Twist

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