Searcharxiv⌕ Search

arXiv subjects

Sandro Sorella

Publications and source records attributed to Sandro Sorella.

At least 109 records · Page 6Linked to original sources
arXiv2006

Finite compressibility in the low-doping region of the two-dimensional $t{-}J$ model

We revisit the important issue of charge fluctuations in the two-dimensional $t{-}J$ model by using an improved variational method based on a wave function that contains both the antiferromagnetic and the d-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by J.P. Bouchaud, A. Georges, and C. Lhuillier [J. de Physique {\bf 49}, 553 (1988)] by considering also a {\it long-range} spin-spin Jastrow factor, in order to correctly reproduce the small-$q$ behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J/t \sim 0.4$ and find that, contrary to previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain a clear evidence that the $t{-}J$ model does not phase separate for $J/t \lesssim 0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.

cond-mat.str-el↗
arXiv2006

Two spin liquid phases in the spatially anisotropic triangular Heisenberg model

The quantum spin-1/2 antiferromagnetic Heisenberg model on a two dimensional triangular lattice geometry with spatial anisotropy is relevant to describe materials like ${\rm Cs_2 Cu Cl_4}$ and organic compounds like {$κ$-(ET)$_2$Cu$_2$(CN)$_3$}. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these intriguing phenomena, quantum Monte Carlo methods are used to study this model system as a function of the anisotropic strength, represented by the ratio $J'/J$ between the intra-chain nearest neighbor coupling $J$ and the inter-chain one $J'$. We have found evidence of two spin liquid regions. The first one is stable for small values of the coupling $J'/J \alt 0.65$, and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid with a small spin gap and is energetically favored in the region $0.65\alt J'/J \alt 0.8$. We have also shown that in both spin liquid phases there is no evidence of broken translation symmetry with dimer or spin-Peirls order or any broken spatial reflection symmetry of the lattice. The various phases are in good agreement with the experimental findings, thus supporting the existence of spin liquid phases in two dimensional quantum spin-1/2 systems.

cond-mat.str-el↗
arXiv2005

Theoretical constraints for the magnetic-dimer transition in two-dimensional spin models

From general arguments, that are valid for spin models with sufficiently short-range interactions, we derive strong constraints on the excitation spectrum across a continuous phase transition at zero temperature between a magnetic and a dimerized phase, that breaks the translational symmetry. From the different symmetries of the two phases, it is possible to predict, at the quantum critical point, a branch of gapless excitations, not described by standard semi-classical approaches. By using these arguments, supported by intensive numerical calculations, we obtain a rather convincing evidence in favor of a first-order transition from the ferromagnetic to the dimerized phase in the two-dimensional spin-half model with four-spin ring-exchange interaction, recently introduced by A.W. Sandvik et al. [Phys. Rev. Lett. 89, 247201 (2002)].

cond-mat.str-el↗
arXiv2005

From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach

We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small-$q$ part of the Jastrow factor.

cond-mat.str-el↗
arXiv2005

Wave function optimization in the variational Monte Carlo method

An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring and the 2D t-J model and show that, with the present scheme, very accurate and efficient calculations are possible, even for several variational parameters. Indeed, by using a very efficient statistical evaluation of the first and the second energy derivatives, it is possible to define a very rapidly converging iterative scheme that, within VMC, is much more convenient than the standard Newton method. It is also shown how to optimize simultaneously both the Jastrow and the determinantal part of the wave function.

cond-mat.str-el↗
arXiv2005

Diffusion Monte Carlo with lattice regularization

We introduce an efficient lattice regularization scheme for quantum Monte Carlo calculations of realistic electronic systems. The kinetic term is discretized by a finite difference Laplacian with two mesh sizes, a and a', where a'/a is an irrational number so that the electronic coordinates are not defined on a particular lattice but on the continuous configuration space. The regularized Hamiltonian goes to the continuous limit for a -> 0 and provides several advantages. In particular, it allows the inclusion of non-local potentials in a consistent variational scheme, substantially improving the accuracy upon previous non-variational approaches.

cond-mat.other↗
arXiv2005

The resonating valence bond wave functions in quantum antiferromagnets

Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and gapped spin liquids may be described by the same class of wave functions, which, therefore, represent an extremely flexible variational tool. A close connection between spin liquids and

cond-mat.str-el↗
arXiv2004

Variational description of Mott insulators

The Gutzwiller wave function for a strongly correlated model can, if supplemented with a long-range Jastrow factor, provide a proper variational description of Mott insulators, so far unavailable. We demonstrate this concept in the prototypical one-dimensional $t-t^\prime$ Hubbard model, where at half filling we reproduce all known phases, namely the ordinary Mott undimerized insulator with power-law spin correlations at small $t^\prime/t$, the spin-gapped metal above a critical $t^\prime/t$ and small $U$, and the dimerized Mott insulator at large repulsion.

cond-mat.str-el↗
arXiv2004

Resonating Valence Bond wave function: from lattice models to realistic systems

Although mean field theories have been very successful to predict a wide range of properties for solids, the discovery of high temperature superconductivity in cuprates supported the idea that strongly correlated materials cannot be qualitatively described by a mean field approach. After the original proposal by Anderson, there is now a large amount of numerical evidence that the simple but general resonating valence bond (RVB) wave function contains just those ingredients missing in uncorrelated theories, so that the main features of electron correlation can be captured by the variational RVB approach. Strongly correlated antiferromagnetic (AFM) systems, like Cs2CuCl4, displaying unconventional features of spin fractionalization, are also understood within this variational scheme. From the computational point of view the remarkable feature of this approach is that several resonating valence bonds 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 or Density Functional Theory. Recently several molecules have been studied by using the RVB wave function; we have always obtained total energies, bonding lengths and binding energies comparable with more demanding multi configurational methods, and in some cases much better than single determinantal schemes. Here we present the paradigmatic case of benzene.

cond-mat.str-el↗
arXiv2004

From the triangular to the kagome lattice: Following the footprints of the ordered state

We study the spin-1/2 Heisenberg model in a lattice that interpolates between the triangular and the kagome lattices. The exchange interaction along the bonds of the kagome lattice is J, and the one along the bonds connecting kagome and non-kagome sites is J', so that J'=J corresponds to the triangular limit and J'=0 to the kagome one. We use variational and exact diagonalization techniques. We analyze the behavior of the order parameter for the antiferromagnetic phase of the triangular lattice, the spin gap, and the structure of the spin excitations as functions of J'/J. Our results indicate that the antiferromagnetic order is not affected by the reduction of J' down to J'/J ~ 0.2. Below this value, antiferromagnetic correlations grow weaker, a description of the ground state in terms of a Neel phase renormalized by quantum fluctuations becomes inadequate, and the finite-size spectra develop features that are not compatible with antiferromagnetic ordering. However, this phase does not appear to be connected to the kagome phase as well, as the low-energy spectra do not evolve with continuity for J'-> 0 to the kagome limit. In particular, for any non-zero value of J', the latter interaction sets the energy scale for the low-lying spin excitations, and a gapless triplet spectrum, destabilizing the kagome phase, is expected.

cond-mat.str-el↗
arXiv2004

d-wave pairing in lightly doped Mott insulators

We define a suitable quantity $Z_c$ that measures the pairing strength of two electrons added to the ground state wave function by means of the anomalous part of the one-particle Green's function. $Z_c$ discriminates between systems described by one-electron states, like ordinary metals and band insulators, for which $Z_c=0$, and systems where the single particle picture does not hold, like superconductors and resonating valence bond insulators, for which $Z_c \ne 0$. By using a numerically exact projection technique for the Hubbard model at $U/t=4$, a finite value of $Z_c$, with d-wave symmetrry, is found at half filling and in the lightly doped regime, thus emphasizing a qualitatively new feature coming from electronic correlation.

cond-mat.str-el↗
arXiv2003

Effective hamiltonian approach and the lattice fixed node approximation

We define a numerical scheme that allows to approximate a given Hamiltonian by an effective one, by requiring several constraints determined by exact properties of generic ''short range'' Hamiltonians. In this way the standard lattice fixed node is also improved as far as the variational energy is concerned. The effective Hamiltonian is defined in terms of a guiding function $ψ_G$ and can be solved exactly by Quantum Monte Carlo methods. We argue that, for reasonable $ψ_G$ and away from phase transitions, the long distance, low energy properties are rather independent on the chosen guiding function, thus allowing to remove the well known problem of standard variational Monte Carlo schemes based only on total energy minimizations, and therefore insensitive to long distance low energy properties.

cond-mat.str-el↗
arXiv2003

Geminal wavefunctions with Jastrow correlation: a first application to atoms

We introduce a simple generalization of the well known geminal wavefunction already applied in Quantum Chemistry to atoms and small molecules. The main feature of the proposed wavefunction is the presence of the antisymmetric geminal part together with a Jastrow factor. Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the many-body state: the former permits the correct treatment of the nondynamic correlation effects, the latter allows the wavefunction to fulfill the cusp conditions and makes the geminal expansion rapidly converging to the lowest possible variational energies. This ansatz is expected to provide a substantial part of the correlation energy for general complex atomic and molecular systems. The antisymmetric geminal term can be written as a single determinant even in the polarized cases. In general, therefore, the computational effort to sample this correlated wavefunction is not very demanding. We applied this Jastrow-geminal approach to atoms up to Z=15, always getting good variational energies, by particularly improving those with a strong multiconfigurational nature. Our wavefunction is very useful for Monte Carlo techniques, such as Fixed node. Indeed, the nodal surface obtained within this approach can be substantially improved through the geminal expansion.

cond-mat↗
arXiv2003

Ground State of a Heisenberg Chain with Next-Nearest-Neighbor Bond Alternation

We investigate the ground-state properties of the spin-half $J_1{-}J_2$ Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen, we find that for small frustration ($J_2/J_1$) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.

cond-mat.str-el↗
arXiv2002

Projected BCS Wave Functions for Low Dimensional Frustrated Spin Systems

Twenty-five years after the first proposal, the question whether the ground state of a frustrated spin-half system is well described by a spin-liquid Resonating Valence Bond (RVB) wave function is still controversial. A physically transparent representation of a RVB state can be obtained in fermionic representation with a standard BCS-type pairing wave function, working in the subspace with fixed number of electrons and no double occupancies. In this work, we show that, using this variational wave function with a careful parameterization of the pairing function, it is possible to obtain an extremely accurate {\em ansatz} for the ground state of the Heisenberg antiferromagnet with next-nearest neighbors interactions ($J_{1}{-}J_{2}$ model) in the regime of strong frustration. Indeed, in the spin-half realization of this model, it is known that the combined effect of frustration and zero-point motion interferes with the mechanism of spontaneously broken symmetry, giving rise to a non-magnetic phase of purely quantum-mechanical nature ($J_2/J_1\simeq 0.5$). This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.

cond-mat.str-el↗
arXiv2002

Effective hamiltonian approach for strongly correlated lattice models

We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a given variational wavefunction, that allow to estimate exact energies and correlation functions, whenever the starting variational wavefunction is a qualitatively correct description of the ground state. The stability of the variational wavefunction against possible phases, not described at the variational level can be tested by using the ''effective Hamiltonian'' approach. In fact Monte Carlo methods, such as the ''fixed node approximation'' and the ''generalized Lanczos technique'' (Phys. Rev. B 64,024512, 2001) allow to obtain exact ground state properties of an effective Hamiltonian, chosen to be as close as possible to the exact Hamiltonian, thus yielding the most reasonable estimates of correlation functions. We also describe a simplified one-parameter scheme that improve substantially the efficiency of the generalized Lanczos method. This is tested on the t-J model, with a special effort to obtain accurate pairing correlations, and provide a possible non-phonon mechanism for High temperature superconductivity.

cond-mat.str-el↗
arXiv2001

Stripes and spin-incommensurabilities are favored by lattice anisotropies

Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions ($t_x \ne t_y$ and $J_x \ne J_y$). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are almost unaffected with respect to the isotropic case.

cond-mat.str-el↗