arXiv subjects

S. Sorella

Publications and source records attributed to S. Sorella.

At least 19 recordsLinked to original sources

arXiv2016

Exact special twist method for quantum Monte Carlo simulations

We present a systematic investigation of the special twist method introduced by Rajagopal $\textit{et al.}$ [ Phys. Rev. B 51, 10591 (1995) ] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the 3D electron gas. Afterwards, we test its efficiency within $\textit{ab initio}$ quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost, since it involves the evaluation of just one wavefunction. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations, our method will be particularly relevant when the physical problem under consideration requires large periodic cells.

cond-mat.str-el↗

arXiv2015

Electronic Origin of the Volume Collapse in Cerium

The cerium alpha-gamma phase transition is characterized by means of a many-body Jastrow-correlated wave function, which minimizes the variational energy of the first-principles scalar-relativistic Hamiltonian, and includes correlation effects in a non-perturbative way. Our variational ansatz accurately reproduces the structural properties of the two phases, and proves that even at temperature $T=0$K the system undergoes a first order transition, with ab initio parameters which are seamlessly connected to the ones measured by experiment at finite $T$. We show that the transition is related to a complex rearrangement of the electronic structure, with key role played by the p-f hybridization. The underlying mechanism unveiled by this work can hold in many Ce-bearing compounds, and more generally in other f-electron systems.

cond-mat.str-el↗

arXiv2010

Systematically convergent method for accurate total energy calculations with localized atomic orbitals

We introduce a method for solving a self consistent electronic calculation within localized atomic orbitals, that allows us to converge to the complete basis set (CBS) limit in a stable, controlled, and systematic way. We compare our results with the ones obtained with a standard quantum chemistry package for the simple benzene molecule. We find perfect agreement for small basis set and show that, within our scheme, it is possible to work with a very large basis in an efficient and stable way. Therefore we can avoid to introduce any extrapolation to reach the CBS limit. In our study we have also carried out variational Monte Carlo (VMC) and lattice regularized diffusion Monte Carlo (LRDMC) with a standard many-body wave function (WF) defined by the product of a Slater determinant and a Jastrow factor. Once the Jastrow factor is optimized by keeping fixed the Slater determinant provided by our new scheme, we obtain a very good description of the atomization energy of the benzene molecule only when the basis of atomic orbitals is large enough and close to the CBS limit, yielding the lowest variational energies.

cond-mat.str-el↗

arXiv2009

Resonating valence bond wave function with molecular orbitals: Application to first-row molecules

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant non-dynamical correlations are correctly reproduced once an appropriate number $n$ of molecular orbitals is considered. The value of $n$ is determined by requiring that, in the atomization limit, the atoms are described by Hartree-Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be2, B2, C2, N2, O2, and F2) and heteronuclear (LiF, and CN) dimers for which strong non-dynamical correlations and/or weak van der Waals interactions are present.

cond-mat.mtrl-sci↗

arXiv2006

Alleviation of the Fermion-sign problem by optimization of many-body wave functions

We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wav e function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C$_2$ molecule to the experimental accuracy of 0.02 eV.

cond-mat.other↗

arXiv2005

Do Bose metals exist in Nature?

We revisit the concept of superfluidity in bosonic lattice models in low dimensions. Then, by using numerical and analytical results obtained previously for equivalent spinless fermion models, we show that the gapless phase of 1D interacting bosons may be either superfluid or -remarkably- metallic and not superfluid. The latter phase -the Bose metal- should be, according to the mentioned results, a robust and stable phase in 1D. In higher dimensionalities we speculate on the possibility of a stable Bose metallic phase on the verge of a Mott transition.

cond-mat.str-el↗

arXiv2004

Role of strong correlation in the recent ARPES experiments for cuprate superconductors

Motivated by recent photoemission experiments on cuprates, the low-lying excitations of a strongly correlated superconducting state are studied numerically. It is observed that along the nodal direction these low-lying one-particle excitations show a linear momentum dependence for a wide range of excitation energies and, thus, they do not present a kink-like structure. The nodal Fermi velocity $v_{\rm F}$, as well as other observables, are systematically evaluated directly from the calculated dispersions, and they are found to compare well with experiments. It is argued that the parameter dependence of $v_{\rm F}$ is quantitatively explained by a simple picture of a renormalized Fermi velocity.

cond-mat.str-el↗

arXiv2004

Correlated geminal wave function for molecules: an efficient resonating valence bond approach

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an Antisymmetrized Geminal Power (AGP), based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several Resonating Valence Bonds (RVB) can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similarly to more conventional methods, such as Hartree-Fock (HF) or Density Functional Theory (DFT). Moreover we describe an extension of the Stochastic Reconfiguration (SR) method, that was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, that can be optimized together with the remaining ones. The method is applied to several molecules from Li_2 to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multi configuration schemes.

cond-mat.other↗

arXiv2004

Resonating valence bond wave function for the two dimensional fractional spin liquid

The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on ${\rm Cs_2 Cu Cl_4}$, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems, and remains similarly accurate in the two-dimensional model corresponding to ${\rm Cs_2 Cu Cl_4}$, thus representing a good ansatz for describing spin fractionalization in two dimensions.

cond-mat.str-el↗

arXiv2003

Electron-hole asymmetry in magnetic properties of lightly doped high-$T_{\rm C}$ superconductors: a quantum Monte Carlo study

Using a recently developed variational quantum Monte Carlo method, magnetic properties of high-$T_{\rm C}$ superconductors are studied at zero temperature ($T$), by numerical simulations on the 2D t-J model. Our focus here is to explore the difference in the properties of $p$-type and $n$-type cuprates as a function of the carrier concentrations close to half filling. As observed experimentally, it is found that the antiferromagnetically ordered phase persists even for a small, yet finite amount of carrier doping, and that this phase is more robust in the electron doped case.

cond-mat.str-el↗

arXiv2003

A chiral spin liquid wave function and the Lieb-Schulz-Mattis theorem

We study a chiral spin liquid wave function defined as a Gutwziller projected BCS state with a complex pairing function. After projection, spontaneous dimerization is found for any odd but finite number of chains, thus satisfying the Lieb-Schultz-Mattis theorem, whereas for even number of chains there is no dimerization. The two-dimensional thermodynamic limit is consistently reached for large number of chains since the dimer order parameter vanishes in this limit. This property clearly supports the possibility of a spin liquid ground state in two dimensions with a gap to all {\em physical} excitations and with no broken translation symmetry.

cond-mat.str-el↗

arXiv2003

Increasing d-wave superconductivity by on site repulsion

We study by Variational Monte Carlo an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange $J$ favoring d-wave superconductivity and a repulsion $V$ opposing against it. We find that the on-site repulsion $U$ effectively enhances the strength of $J$ meanwhile suppressing that of $V$, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.

cond-mat.supr-con↗

arXiv2002

First Principle Electronic Model for High-Temperature Superconductivity

Using the structural data of the La2CuO4 compound both in the low temperature tetragonal phase and in the isotropic phase we have derived an effective t-J model with hoppings t and superexchange interactions J extended up to fourth and second neareast neighbors respectively. By numerically studying this hamiltonian we have then reproduced the main experimental features of this HTc compound: d-wave superconductivity is stabilized at small but finite doping delta>6% away from the antiferromagnetic region and some evidence of dynamical stripes is found at commensurate filling 1/8.

cond-mat.supr-con↗

arXiv2001

Superconductivity in the two-dimensional t-J model

Using computational techniques, it is shown that pairing is a robust property of hole doped antiferromagnetic (AF) insulators. In one dimension (1D) and for two-leg ladder systems, a BCS-like variational wave function with long-bond spin-singlets and a Jastrow factor provides an accurate representation of the ground state of the t-J model, even though strong quantum fluctuations destroy the off-diagonal superconducting (SC) long-range order in this case. However, in two dimensions (2D) it is argued -- and numerically confirmed using several techniques, especially quantum Monte Carlo (QMC) -- that quantum fluctuations are not strong enough to suppress superconductivity.

cond-mat.str-el↗

arXiv2000

Spatially homogeneous ground state of the two-dimensional Hubbard model

We investigate the stability with respect to phase separation or charge density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit ($U=4t$) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t$.

cond-mat.str-el↗

arXiv2000

Generalized Lanczos Algorithm for Variational Quantum Monte Carlo

We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign problem instability. With this scheme a few Lanczos steps over a given variational wavefunction are possible even for large size as a particular case of a more general and more accurate technique that allows to obtain lower variational energies. This method has been tested extensively for a strongly correlated model like the t-J model. With the standard Lanczos technique it is possible to compute any kind of correlation functions, with no particular computational effort. By using that the variance $ - ^2$ is zero for an exact eigenstate, we show that the approach to the exact solution with few Lanczos ite rations is indeed possible even for $\sim 100$ electrons for reasonably good initial wavefunctions.The variational stochastic reconfiguration technique presented here allows in general a many-parameter energy optimization of any computable many-body wavefunction, including for inst ance generic long range Jastrow factors and arbitrary site dependent orbital determinants. This scheme improves further the accuracy of the calculation, especially for long distance correlation functions.

cond-mat.str-el↗

arXiv1999

Does the Heisenberg model describe the multimagnon spin dynamics in antiferromagnetic CuO layers ?

We compute the absorption spectrum for multimagnon excitations assisted by phonons in insulating layered cuprates using exact diagonalization in clusters of up to 32 sites. The resulting line shape is very sensitive to the underlying magnetic Hamiltonian describing the spin dynamics. For the usual Heisenberg description of undoped Cu-O planes we find, in accordance with experiment, a two-magnon peak followed by high energy side bands. However the relative weight of the side bands is too small to reproduce the experiment. An extended Heisenberg model including a sizable four-site cyclic exchange term is shown to be consistent with the experimental data.

cond-mat.str-el↗

arXiv1999

Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease

A recent technique, proposed to alleviate the ``sign problem disease'', is discussed in details. As well known the ground state of a given Hamiltonian $H$ can be obtained by applying the imaginary time propagator $e^{-H τ}$ to a given trial state $ψ_T$ for large imaginary time $τ$ and sampling statistically the propagated state $ ψ_τ = e^{-H τ} ψ_T$. However the so called ``sign problem'' may appear in the simulation and such statistical propagation would be practically impossible without employing some approximation such as the well known ``fixed node'' approximation (FN). This method allows to improve the FN dynamic with a systematic correction scheme. This is possible by the simple requirement that, after a short imaginary time propagation via the FN dynamic, a number $p$ of correlation functions can be further constrained to be {\em exact} by small perturbation of the FN propagated state, which is free of the sign problem. By iterating this scheme the Monte Carlo average sign, which is almost zero when there is sign problem, remains stable and finite even for large $τ$. The proposed algorithm is tested against the exact diagonalization results available on finite lattice. It is also shown in few test cases that the dependence of the results upon the few parameters entering the stochastic technique can be very easily controlled, unless for exceptional cases.

cond-mat↗