arXiv subjects

Federico Becca

Publications and source records attributed to Federico Becca.

At least 109 records · Page 6Linked to original sources

arXiv2008

Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model

We introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting systems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^\prime/t$.

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arXiv2008

Mott transition in bosonic systems: Insights from the variational approach

We study the Mott transition occurring for bosonic Hubbard models in one, two, and three spatial dimensions, by means of a variational wave function benchmarked by Green's function Monte Carlo calculations. We show that a very accurate variational wave function, constructed by applying a long-range Jastrow factor to the non-interacting boson ground state, can describe the superfluid-insulator transition in any dimensionality. Moreover, by mapping the quantum averages over such a wave function into the the partition function of a classical model, important insights into the insulating phase are uncovered. Finally, the evidence in favor of anomalous scenarios for the Mott transition in two dimensions are reported whenever additional long-range repulsive interactions are added to the Hamiltonian.

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arXiv2007

Magnetism and superconductivity in the $t{-}t^\prime{-}J$ model

We present a systematic study of the phase diagram of the $t{-}t^\prime{-}J$ model by using the Green's function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^\prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $δ_c \sim 0.10$ for $J/t=0.2$ and $δ_c \sim 0.13$ for $J/t=0.4$. The presence of a finite $t^\prime/t<0$ induces a strong suppression of both magnetic (with $δ_c \lesssim 0.03$, for $J/t=0.2$ and $t^\prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $δ\sim 0.25$, where strong size effects are present.

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arXiv2007

Crystallization of the resonating valence bond liquid as vortex condensation

We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons''. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with the earlier prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)].

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arXiv2007

Superfluid to Mott-insulator transition in Bose-Hubbard models

We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition,most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].

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arXiv2007

Exotic gapless spectrum induced by frustration in quantum antiferromagnets

We show strong numerical evidence in favor of an unexpected virtually gapless spectrum, with edge states localized at the boundaries, in frustrated spin-1/2 antiferromagnetic ladders with an odd number of legs. These features can be accurately reproduced by using a projected BCS wave function with a non-trivial pairing, that mixes even and odd reflection symmetries. This approach gives the correct classification of the excitations and provides a simple and very appealing picture of an unconventional spin-liquid phase stabilized by frustration.

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arXiv2007

Magneto-elastic effects and magnetization plateaus in two dimensional systems

We show the importance of both strong frustration and spin-lattice coupling for the stabilization of magnetization plateaus in translationally invariant two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model coupled to adiabatic phonons under an external magnetic field. At zero magnetization, simple structures with two or at most four spins per unit cell are stabilized, forming dimers or $2 \times 2$ plaquettes, respectively. A much richer scenario is found in the case of magnetization $m=1/2$, where larger unit cells are formed with non-trivial spin textures and an analogy with the corresponding classical Ising model is detectable. Specific predictions on lattice distortions and local spin values can be directly measured by X-rays and Nuclear Magnetic Resonance experiments.

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arXiv2006

Jastrow theory of the Mott transition in bosonic Hubbard models

We show that the Mott transition occurring in bosonic Hubbard models can be successfully described by a simple variational wave function that contains all important long-wavelength correlations. Within this approach, a smooth metal-insulator transition is made possible by means of a long-range Jastrow correlation term that binds in real space density fluctuations. We find that the Mott transition has similar properties in two and three dimensions but differs in one dimension. We argue that our description of the Mott transition in terms of a binding-unbinding transition is of general validity and could also be applied to realistic electronic systems.

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arXiv2006

Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms

Starting from the mean-field solution of a spin-orbital model of LiNiO$_2$, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on 4-site plaquettes and 6-site loops. Using numerical exact diagonalizations and Green's function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the 6--site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions.

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arXiv2006

Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell.

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arXiv2006

Unconventional metal-insulator transition in two dimensions

We show, by using a correlated Jastrow wave function and a mapping onto a classical model, that the two-dimensional Mott transition in a simple half-filled one-band model can be unconventional and very similar to the binding-unbinding Kosterlitz-Thouless transition of vortices and anti-vortices, here identified by empty and doubly occupied sites. Within this framework, electrons strongly interact with collective plasmon excitations that induce anomalous critical properties on both sides of the transition. In particular, the insulating phase is characterized by a singular power law behavior in the photoemission spectrum, that can be continuously connected to the fully-projected insulating state, relevant to strongly correlated low-energy models.

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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.

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arXiv2006

Doping quantum dimer models on the square lattice

A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (NY) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at **finite doping** which can be mapped on a **doped** interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped VBS phase exhibiting holon pairing but **no** phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.

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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)].

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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.

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arXiv2005

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.

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arXiv2005

Finite-temperature properties of frustrated classical spins coupled to the lattice

We present extensive Monte Carlo simulations for a classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice coupled to the lattice degrees of freedom. The Ising-like phase transition, that appears for $J_2/J_1>1/2$ in the pure spin model, is strengthened by the spin-lattice coupling, and is accompanied by a lattice deformation from a tetragonal symmetry to an orthorhombic one. Evidences that the universality class of the transition does not change with the inclusion of the spin-lattice coupling are reported. Implications for ${\rm Li_2VOSiO_4}$, the prototype for a layered $J_1{-}J_2$ model in the collinear regime, are also discussed.

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arXiv2005

Zero-Temperature Properties of the Quantum Dimer Model on the Triangular Lattice

Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. {\bf 86}, 1881 (2001)].

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