arXiv subjects

Sandro Sorella

Publications and source records attributed to Sandro Sorella.

At least 73 records · Page 4Linked to original sources

arXiv2014

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.

cond-mat.quant-gas↗

arXiv2013

Quantum Monte Carlo study of the protonated water dimer

We report an extensive theoretical study of the protonated water dimer (Zundel ion) by means of the highly correlated variational Monte Carlo and lattice regularized Monte Carlo approaches. This system represents the simplest model for proton transfer (PT) and a correct description of its properties is essential in order to understand the PT mechanism in more complex acqueous systems. Our Jastrow correlated AGP wave function ensures an accurate treatment of electron correlations. Exploiting the advantages of contracting the primitive basis set over atomic hybrid orbitals, we are able to limit dramatically the number of variational parameters with a systematic control on the numerical precision, crucial in order to simulate larger systems. We investigate energetics and geometrical properties of the Zundel ion as a function of the oxygen-oxygen distance, taken as reaction coordinate. In both cases, our QMC results are found in excellent agreement with coupled cluster CCSD(T) technique, the quantum chemistry "gold standard". Calculations on proton transfer static barriers and dissociation energies display the same agreement. A comparison with density functional theory (DFT) results in the PBE approximation points out the crucial role of electron correlations for a correct description of the PT in the dimer. Our method is able to resolve the tiny energy differences (~ 0.1 Kcal/mol) and the corresponding structural variations at which the proton transfer takes place; it combines these features with a N^3-N^4 scaling with number of particles (favorable with respect to other post-DFT methods), as proven by a benchmark calculation on a larger protonated water cluster. The QMC approach used here represents a promising candidate to provide the first high-level ab initio description of PT in water.

physics.chem-ph↗

arXiv2013

Improper s-wave symmetry for the electronic pairing in iron-based superconductors by first-principles calculation

By means of space-group symmetry arguments, we argue that the electronic pairing in iron-based high temperature superconductors shows a structure which is a linear combination of planar s-wave and d-wave symmetry channels, both preserving the 3-dimensional A_1g irreducible representation of the corresponding crystal point-group. We demonstrate that the s- and d-wave channels are determined by the parity under reflection of the electronic orbitals through the iron planes, and by improper rotations around the iron sites. We provide evidence of these general properties by performing accurate quantum Monte Carlo ab-initio calculations of the pairing function, for a FeSe lattice with tetragonal experimental geometry at ambient pressure. We find that this picture survives even in the FeSe under pressure and at low temperatures, when the tetragonal point-group symmetry is slightly broken. In order to achieve a higher resolution in momentum space we introduce a BCS model that faithfully describes our QMC variational pairing function on the simulated 4x4 FeSe unit cell. This allows us to provide a k-resolved image of the pairing function, and show that non-isotropic contributions in the BCS gap function are related to the improper s-wave symmetry. Our theory can rationalize and explain a series of contradictory experimental findings, such as the observation of twofold symmetry in the FeSe superconducting phase, the anomalous drop of T_c with Co-impurity in LaFeAsO_(1-x)F_x, the s-to-d-wave gap transition in BaFe_2As_2 under K doping, and the nodes appearing in the LiFeAs superconducting gap upon P isovalent substitution.

cond-mat.supr-con↗

arXiv2013

Molecular properties by Quantum Monte Carlo: an investigation on the role of the wave function ansatz and the basis set in the water molecule

Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely: the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudo potential, and the basis set for QMC calculations. We also introduce a new strategy for the definition of the atomic orbitals involved in the Jastrow - Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.

physics.chem-ph↗

arXiv2013

Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism

By direct calculations of the spin gap in the frustrated Heisenberg model on the square lattice, with nearest- ($J_1$) and next-nearest-neighbor ($J_2$) super-exchange couplings, we provide a solid evidence that the spin-liquid phase in the frustrated regime $0.45 \lesssim J_2/J_1 \lesssim 0.6$ is gapless. Our numerical method is based on a variational wave function that is {\it systematically} improved by the application of few Lanczos steps and allows us to obtain reliable extrapolations in the thermodynamic limit. The peculiar nature of the non-magnetic state is unveiled by the existence of S=1 gapless excitations at $k=(π,0)$ and $(0,π)$. The magnetic transition can be described and interpreted by a variational state that is built from Abrikosov fermions having a $Z_2$ gauge structure and four Dirac points in the spinon spectrum.

cond-mat.str-el↗

arXiv2013

Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet

We study the energy and the static spin structure factor of the ground state of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2 spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site E/J=-0.4365(2), which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.

cond-mat.str-el↗

arXiv2012

Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice

A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.

cond-mat.str-el↗

arXiv2012

Finite temperature electronic simulations beyond the Born-Oppenheimer approximation

We introduce a general technique to compute finite temperature electronic properties by a novel covariant formulation of the electronic partition function. By using a rigorous variational upper bound to the free energy we are led to the evaluation of a partition function that can be computed stochastically by sampling electronic wave functions and atomic positions (assumed classical). In order to achieve this target we show that it is extremely important to consider the non trivial geometry of the space defined by the wave function ansatz. The method can be extended to any technique capable to provide an energy value over a given wave function ansatz depending on several variational parameters and atomic positions. In particular we can take into account electronic correlation, by using the standard variational quantum Monte Carlo method, that has been so far limited to zero temperature ground state properties. We show that our approximation reduces correctly to the standard Born-Oppenheimer (BO) one at zero temperature and to the correct high temperature limit. At large enough temperatures this method allows to improve the BO, providing lower values of the electronic free energy, because within this method it is possible to take into account the electron entropy. We test this new method on the simple hydrogen molecule, where at low temperature we recover the correct BO low temperature limit. Moreover, we show that the dissociation of the molecule is possible at a temperature much smaller than the BO prediction. Several extension of the proposed technique are also discussed, as for instance the calculation of critical (magnetic, superconducting) temperatures, or transition rates in chemical reactions.

cond-mat.str-el↗

arXiv2012

Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz

We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1, when the Marshall sign rule begins to be essentially violated, and a first-order transition around J2=0.6J1 are present. Most importantly, the triplet gap is found to have a non-monotonic behavior, reaching a maximum around J2=0.51J1, when the lowest spinon excitation moves from the Γto the M point, i.e., k=(π,0).

cond-mat.str-el↗

arXiv2012

Absence of static stripes in the two-dimensional $t{-}J$ model by an accurate and systematic quantum Monte Carlo approach

We examine the two-dimensional $t{-}J$ model by using variational approach combined with well established quantum Monte Carlo techniques [S. Sorella {\it et al.}, \prl {\bf 88}, 117002 (2002)] that are used to improve systematically the accuracy of the variational ansatz. Contrary to recent density-matrix renormalization group and projected entangled-pair state calculations [P. Corboz {\it et al.}, \prb {\bf 84}, 041108(R) (2011)], a uniform phase is found for $J/t=0.4$, even when the calculation is biased with an ansatz that explicitly contains stripe order. Moreover, in the small hole doping regime, i.e., $δ\lesssim 0.1$, our results support the coexistence of antiferromagnetism and superconductivity.

cond-mat.str-el↗

arXiv2011

Linearized Auxiliary fields Monte Carlo: efficient sampling of the fermion sign

We introduce a method that combines the power of both the lattice Green function Monte Carlo (LGFMC) with the auxiliary field techniques (AFQMC), and allows us to compute exact ground state properties of the Hubbard model for U<~ 4t on finite clusters. Thanks to LGFMC one obtains unbiased zero temperature results, not affected by the so called Trotter approximation of the imaginary time propagator exp(- H t). On the other hand the AFQMC formalism yields a remarkably fast convergence in t before the fermion sign problem becomes prohibitive. As a first application we report ground state energies in the Hubbard model at U/t=4 with up to one hundred sites.

cond-mat.str-el↗

arXiv2011

Strong electronic correlation in the Hydrogen chain: a variational Monte Carlo study

In this article, we report a fully ab initio variational Monte Carlo study of the linear, and periodic chain of Hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density matrix renormalization group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in details the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

cond-mat.str-el↗

arXiv2011

The fate of the resonating valence bond in graphene

We apply a variational wave function capable of describing qualitatively and quantitatively the so called "resonating valence bond" in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($\simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains only within a small "resonance length" of few atomic units.

cond-mat.str-el↗

arXiv2010

Ab-initio calculations for the beta-tin diamond transition in Silicon: comparing theories with experiments

We investigate the pressure-induced metal-insulator transition from diamond to beta-tin in bulk Silicon, using quantum Monte Carlo (QMC) and density functional theory (DFT) approaches. We show that it is possible to efficiently describe many-body effects, using a variational wave function with an optimized Jastrow factor and a Slater determinant. Variational results are obtained with a small computational cost and are further improved by performing diffusion Monte Carlo calculations and an explicit optimization of molecular orbitals in the determinant. Finite temperature corrections and zero point motion effects are included by calculating phonon dispersions in both phases at the DFT level. Our results indicate that the theoretical QMC (DFT) transition pressure is significantly larger (smaller) than the accepted experimental value. We discuss the limitation of DFT approaches due to the choice of the exchange and correlation functionals and the difficulty to determine consistent pseudopotentials within the QMC framework, a limitation that may significantly affect the accuracy of the technique.

cond-mat.mtrl-sci↗

arXiv2010

Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.

cond-mat.other↗

arXiv2010

Size-consistent variational approaches to non-local pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited

We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat non-local pseudopotential in a variational way. We show that such scheme --when applied to large enough systems-- maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term, and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space.

cond-mat.other↗

arXiv2009

The nature and strength of inter-layer binding in graphite

We computed the inter-layer bonding properties of graphite using an ab-initio many body theory. We carried out variational and diffusion quantum Monte Carlo calculations and found an equilibrium inter-layer binding energy in good agreement with most recent experiments. We also analyzed the behavior of the total energy as a function of interlayer separation at large distances comparing the results with the predictions of the random phase approximation.

cond-mat.mtrl-sci↗

arXiv2009

A consistent description of the iron dimer spectrum with a correlated single-determinant wave function

We study the iron dimer by using an accurate ansatz for quantum chemical calculations based on a simple variational wave function, defined by a single geminal expanded in molecular orbitals and combined with a real space correlation factor. By means of this approach we predict that, contrary to previous expectations, the neutral ground state is $^7 Δ$ while the ground state of the anion is $^8 Σ_g^-$, hence explaining in a simple way a long standing controversy in the interpretation of the experiments. Moreover, we characterize consistently the states seen in the photoemission spectroscopy by Leopold \emph{et al.}. It is shown that the non-dynamical correlations included in the geminal expansion are relevant to correctly reproduce the energy ordering of the low-lying spin states.

cond-mat.other↗