arXiv subjects

Federico Becca

Publications and source records attributed to Federico Becca.

At least 55 records · Page 3Linked to original sources

arXiv2019

Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model

The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with $M$ legs (with $M$ ranging from $2$ to $10$) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity $λ=8$ in the charge and $2λ=16$ in the spin can be stabilized at doping $δ=1/8$. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with $λ=6$, appears at $δ=1/6$. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at $δ=1/12$ and metallic with strong superconducting correlations at $δ=1/10$, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.

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arXiv2019

Nematic and Antiferromagnetic Quantum Criticality in a Multi-Orbital Hubbard Model for Iron Pnictides

The extent to which quantum criticality drives the physics of iron pnictides is a central question in the field. Earlier theoretical considerations were based on an effective field theory, and the proposed realization in P-doped iron arsenides has received extensive experimental evidence. To connect the quantum critical behavior with the underlying electronic physics, it is important to analyze it within microscopic models. Here, we do so for a multi-orbital model containing both Hubbard and Hund's interactions, by a variational Monte Carlo method based on Jastrow-Slater wave functions that allow for a non-perturbative treatment of electron correlations. We find strong evidence for the existence of a unique quantum critical point, where both nematic and $(π,0)$ antiferromagnetic orders develop together, in the bad-metal regime of the phase diagram. Implications of our results for the iron-based superconductivity are discussed.

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arXiv2019

Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders

Short-range antiferromagnetic correlations are known to open a spin gap in the repulsive Hubbard model on ladders with $M$ legs, when $M$ is even. We show that the spin gap originates from the formation of correlated pairs of electrons with opposite spin, captured by the hidden ordering of a spin-parity operator. Since both spin gap and parity vanish in the two-dimensional limit, we introduce the fractional generalization of spin parity and prove that it remains finite in the thermodynamic limit. Our results are based upon variational wave functions and Monte Carlo calculations: performing a finite size-scaling analysis with growing $M$, we show that the doping region where the parity is finite coincides with the range in which superconductivity is observed in two spatial dimensions. Our observations support the idea that superconductivity emerges out of spin gapped phases on ladders, driven by a spin-pairing mechanism, in which the ordering is conveniently captured by the finiteness of the fractional spin-parity operator.

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arXiv2018

Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a Néel antiferromagnet to a $\mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly-deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results show how free spinons emerge across a quantum critical point, providing evidence for the fractionalization of magnons into deconfined spinons.

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arXiv2018

Metal-insulator transitions, superconductivity, and magnetism in the two-band Hubbard model

We explore the ground-state properties of the two-band Hubbard model with degenerate electronic bands, parametrized by nearest-neighbor hopping $t$, intra- and inter-orbital on-site Coulomb repulsions $U$ and $U^\prime$, and Hund coupling $J$, focusing on the case with $J>0$. Using Jastrow-Slater wave functions, we consider both states with and without magnetic/orbital order. Electron pairing can also be included in the wave function, in order to detect the occurrence of superconductivity for generic electron densities $n$. When no magnetic/orbital order is considered, the Mott transition is continuous for $n=1$ (quarter filling); instead, at $n=2$ (half filling), it is first order for small values of $J/U$, while it turns out to be continuous when the ratio $J/U$ is increased. A significant triplet pairing is present in a broad region around $n=2$. By contrast, singlet superconductivity (with $d$-wave symmetry) is detected only for small values of the Hund coupling and very close to half filling. When including magnetic and orbital order, the Mott insulator acquires antiferromagnetic order for $n=2$; instead, for $n=1$ the insulator has ferromagnetic and antiferro-orbital orders. In the latter case, a metallic phase is present for small values of $U/t$ and the metal-insulator transition becomes first order. In the region with $1<n<2$, we observe that ferromagnetism (with no orbital order) is particularly robust for large values of the Coulomb repulsion and that triplet superconductivity is strongly suppressed by the presence of antiferromagnetism. The case with $J=0$, which has an enlarged SU(4) symmetry due to the interplay between spin and orbital degrees of freedom, is also analyzed.

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arXiv2018

Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach

The dynamical spin structure factor is computed within a variational framework to study the one-dimensional $J_1-J_2$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, also including incommensurate structures for $J_2/J_1>0.5$. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (non-integrable) frustrated spin models.

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arXiv2018

Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{\vartriangle}$ and $J_{\triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $\mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{\triangledown}/J_{\vartriangle}$, the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the "simplex" $\mathbb{Z}_{2}$ resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., $J_{\triangledown} \ll J_{\vartriangle}$.

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arXiv2017

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping $t$, the on-site electron-electron interaction $U$, the phonon energy $ω_0$, and the electron-phonon coupling $g$. At half filling, the ground state is an antiferromagnetic insulator for $U \gtrsim 2g^2/ω_0$, while it is a charge-density-wave (or bi-polaronic) insulator for $U \lesssim 2g^2/ω_0$. In addition to these phases, we find a superconducting phase that intrudes between them. For $ω_0/t=1$, superconductivity emerges when both $U/t$ and $2g^2/tω_0$ are small; then, by increasing the value of the phonon energy $ω_0$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.

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arXiv2017

Charge orders in organic charge-transfer salts

Motivated by recent experimental suggestions of charge-order-driven ferroelectricity in organic charge-transfer salts, such as $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Cl, we investigate magnetic and charge-ordered phases that emerge in an extended two-orbital Hubbard model on the anisotropic triangular lattice at $3/4$ filling. This model takes into account the presence of two organic BEDT-TTF molecules, which form a dimer on each site of the lattice, and includes short-range intramolecular and intermolecular interactions and hoppings. By using variational wave functions and quantum Monte Carlo techniques, we find two polar states with charge disproportionation inside the dimer, hinting to ferroelectricity. These charge-ordered insulating phases are stabilized in the strongly correlated limit and their actual charge pattern is determined by the relative strength of intradimer to interdimer couplings. Our results suggest that ferroelectricity is not driven by magnetism, since these polar phases can be stabilized also without antiferromagnetic order and provide a possible microscopic explanation of the experimental observations. In addition, a conventional dimer-Mott state (with uniform density and antiferromagnetic order) and a nonpolar charge-ordered state (with charge-rich and charge-poor dimers forming a checkerboard pattern) can be stabilized in the strong-coupling regime. Finally, when electron-electron interactions are weak, metallic states appear, with either uniform charge distribution or a peculiar $12$-site periodicity that generates honeycomb-like charge order.

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arXiv2017

Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice

Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence bond state gives an excellent approximation to the exact ground-state energy. For $0.23 \lesssim J_2/J_1 \lesssim 0.4$, a gapless $Z_2$ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the Néel order melts, this ordered state becomes clearly favored only for $J_2/J_1 \gtrsim 0.3$. Finally, for $0.36 \lesssim J_2/J_1 \le 0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the Néel antiferromagnet from the plaquette valence-bond solid.

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arXiv2017

Non local parity order in the two-dimensional Mott insulator

The Mott insulator is characterized by having small deviations around the (integer) average particle density n, with pairs with n-1 and n+1 particles forming bound states. In one dimension, the effect is captured by a non-zero value of a non-local "string" of parities, which instead vanishes in the superfluid phase where density fluctuations are large. Here, we investigate the interaction induced transition from the superfluid to the Mott insulator, in the paradigmatic Bose Hubbard model at n=1. By means of quantum Monte Carlo simulations and finite size scaling analysis on LxM ladders, we explore the behavior of "brane" parity operators for L going to infinity from one dimension (i.e., M=1) to two dimensions (i.e., M going to infinity). We confirm the conjecture that, adopting a standard definition, their average value decays to zero in two dimensions also in the insulating phase, evaluating the scaling factor of the "perimeter law" [S.P. Rath et al., Ann. Phys. (N.Y.) 334, 256 (2013)]. Upon introducing a further phase in the brane parity, we show that its expectation value becomes non-zero in the insulator, while still vanishing at the transition to the superfluid phase. These quantities are directly accessible to experimental measures, thus providing an insightful signature of the Mott insulator.

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arXiv2016

Hidden Mott transition and large-$U$ superconductivity in the two-dimensional Hubbard model

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{\rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{\rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{\rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{\rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

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arXiv2016

Comment on "$Z_{2}$ spin liquid phase on the kagome lattice: a new saddle point", by Tao Li [arXiv:1601.02165 (2016)]

In a recent paper [arXiv:1601.02165], Tao Li claimed that a gapped $\mathbb{Z}_2$ spin liquid, obtained using projected Gutzwiller fermionic wave functions, can be stabilized in the Heisenberg model on the kagome lattice. We perform very accurate variational calculations and confirm with unprecedented accuracy the fact, that the $\mathbb{Z}_{2}$ spin liquid is a local energy minimum that goes away with system size, thus reaffirming the scenario of a gapless $U(1)$ Dirac spin liquid ground state.

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arXiv2016

Spin liquid nature in the Heisenberg $J_{1}$-$J_{2}$ triangular antiferromagnet

We investigate the spin-$\frac{1}{2}$ Heisenberg model on the triangular lattice in the presence of nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015)], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime $0.08\lesssim J_2/J_1\lesssim 0.16$, framed by $120^{\circ}$ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) $J_2/J_1$. By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless $U(1)$ Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped $\mathbb{Z}_{2}$ spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error-bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test-bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.

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arXiv2016

Spontaneous symmetry breaking in correlated wave functions

We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.

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arXiv2016

Assessing the orbital selective Mott transition with variational wave functions

We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes $t_1$ and $t_2$ for the two orbitals on the two-dimensional square lattice by using {\it non-magnetic} variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e., two electrons per site) as a function of $R=t_2/t_1$ and the on-site Coulomb repulsion $U$, for two values of the Hund's coupling $J=0$ and $J/U=0.1$. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of $U$, where both orbitals are itinerant; a Mott insulator, for large values of $U$, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of $R$ and intermediate $U$'s, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of $R$.

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arXiv2016

Variational wave functions for the $S=1/2$ Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders

By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification [Y. Zhou and X.-G. Wen, arXiv:cond-mat/0210662] and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for $J^\prime/J \le 1$, the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., $0.7 \lesssim J^\prime/J \lesssim 0.8$. In contrast, for $J/J^\prime \le 1$, a large spin-liquid region appears close to the limit of decoupled chains, i.e., for $J/J^\prime \lesssim 0.6$, while magnetically ordered phases with spiral order are stabilized close to the isotropic point.

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arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

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