Exact special twist method for quantum Monte Carlo simulations

Dagrada, Mario; Karakuzu, Seher; Vildosola, V.; Casula, Michele; Sorella, Sandro

doi:10.1103/physrevb.94.245108

Cited by 27 publications

(30 citation statements)

References 74 publications

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“…In most calculations we consider 24 carbon atoms in an orthorombic supercell with rectangular basis, whereas for the size scaling of Fig.3b (main text) we use also 12, 36, 48, and 96 carbon supercells. In order to minimize finite-size effects, we adopt the twist-averaged-boundary conditions [44][45][46] in the x and y directions with averaging over a 6 × 8 Monkhorst-Pack grid [39], whereas in the z direction, we adopt simple periodic-boundary conditions with a very large distance (300 Bohrs) between the graphene images. In order to minimize the number of variational parameters and achieve a faster and smoother convergence in…”

Section: Quantum Monte Carlo Calculationmentioning

confidence: 99%

Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene

et al. 2018

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The phase diagram of isotropically expanded graphene cannot be correctly predicted by ignoring either electron correlations, or mobile carbons, or the effect of applied stress, as was done so far. We calculate the ground state enthalpy (not just energy) of strained graphene by an accurate off-lattice quantum Monte Carlo correlated ansatz of great variational flexibility. Following undistorted semimetallic graphene at low strain, multideterminant Heitler-London correlations stabilize between ≃8.5% and ≃15% strain an insulating Kekulé-like dimerized (DIM) state. Closer to a crystallized resonating-valence bond than to a Peierls state, the DIM state prevails over the competing antiferromagnetic insulating state favored by density-functional calculations which we conduct in parallel. The DIM stressed graphene insulator, whose gap is predicted to grow in excess of 1 eV before failure near 15% strain, is topological in nature, implying under certain conditions 1D metallic interface states lying in the bulk energy gap.

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Section: Quantum Monte Carlo Calculationmentioning

confidence: 99%

Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene

et al. 2018

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“…In the case of weakly correlated systems, size effects are most pronounced and calculations of observables with a single boundary condition such as PBC or anti-periodicboundary condition (APBC) may have serious difficulties in determining the correct thermodynamic limit. In order to mimic the Brillouin zone of the thermodynamic limit, TABCs have been proposed and indeed it has been shown that TABCs eliminate one-body error very successfully [25,26,28].…”

Section: Twist-averaged Boundary Conditionsmentioning

confidence: 99%

“…In order to control the finite size effects discussed above, twist-averaged boundary conditions (TABCs) have been introduced for Monte Carlo simulations on lattice model [22][23][24][25][26][27] and in continuum systems [28,29]. Within TABCs, physical quantities are estimated by averaging them over several twisted-boundary conditions [30], rather than limiting the calculation to a single twist, such as PBC.…”

Section: Introductionmentioning

confidence: 99%

“…Within TABCs, physical quantities are estimated by averaging them over several twisted-boundary conditions [30], rather than limiting the calculation to a single twist, such as PBC. In this way, TABCs can substantially reduce finite-size effects [24][25][26][27][28], at the expense of performing several independent calculations with several twists. In QMC this overhead is not even relevant because, at given computational resources, the statistical errors of the twisted-averaged quantities do not grow with the number N TABC of twists.…”

Section: Introductionmentioning

confidence: 99%

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Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

2018

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By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the s-wave superconducting order parameter and the pairing correlations for the negative-U Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs is much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of |U |/t and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behaviour of the superconducting phase, by means of a suitably chosen Jastrow factor including long-range density-density correlations.arXiv:1806.06736v1 [cond-mat.str-el]

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“…At variance of Refs. [16,38] we take care of finite size-effects using a recently developed [39] k− point sampling of the Brillouin zone [40,41] (BZ). In most simulations we use a cubic supercell containing 64 atoms and a 4×4×4 Monkhorst and Pack k-point mesh, which looks clearly consistent with larger systems calculations (see Fig.…”

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confidence: 99%

Acceleratingab initioMolecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen

Mazzola

Sorella

2017

Phys. Rev. Lett.

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We propose an ab-initio molecular dynamics method, capable to reduce dramatically the autocorrelation time required for the simulation of classical and quantum particles at finite temperature. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix S. Here we apply this technique, within a Quantum Monte Carlo (QMC) based wavefunction approach and within the Born-Oppheneimer approximation, for determining the phase diagram of high-pressure Hydrogen with simulations much longer than the autocorrelation time. With the proposed method, we are able to equilibrate in few hundreds steps even close to the liquid-liquid phase transition (LLT). Within our approach we find that the LLT transition is consistent with recent density functionals predicting a much larger transition pressures when the long range dispersive forces are taken into account.One of the most important problems in ab-initio molecular dynamics (MD) is the coexistence of much different time scales underlying physical processes, even when computing equilibrium finite temperature properties. This has been a challenge for most ab-initio simulations in systems of biophysical interest, the most striking one being protein folding [1,2], where the microscopic time scale of molecular vibration is of the order of f s, while the macroscopic time scale of the folding exceeds the µs. Also in water system simulations, the weak Van der Waals (vdW) interactions and the related hydrogen bond imply very difficult equilibration properties at ambient conditions, so that the most accurate simulations are based on force field fitting forces. We will show here that, a computationally expensive ab-initio method for dense liquid hydrogen can be combined with a sampling technique capable to reduce drastically the autocorrelation times. This method has the potential, due to its simplicity, to be applied with success also to much more complex systems and other ab-initio techniques.At variance of all previous attempts[3-10], we propose that an optimal way to get rid of different time scales is based on the use of first order Langevin dynamics:where T is the temperature, f Ri = −∂ Ri V ( R) and V R is an energy potential of the classical coordinates R, e.g. atomic positions. For S ij = δ ij this is the conventional first order Langevin dynamics (CFOLD). Preconditioned Langevin equations, formally similar to Eq. 40, have been already introduced in several fields different from molecular dynamics, such as gauge field theories[11], statistics [12] and machine learning [13], with different definitions of the preconditioning matrix S. Instead, the main idea of this work is based on the simple solution of CFOLD for the harmonic potential V (R) = −K R, where K is the elastic matrix term. In this case one is able to show that the i) the autocorrelation time is independent of temperature τ −1 corr = K min , where K min (K max ) is the lowest (largest) non-zero eigenvalue of the elastic matrix...

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Exact special twist method for quantum Monte Carlo simulations

Cited by 27 publications

References 74 publications

Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene

Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

Acceleratingab initioMolecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen

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