arXiv subjects

Federico Becca

Publications and source records attributed to Federico Becca.

At least 73 records · Page 4Linked to original sources

arXiv2015

Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice

By using the variational Monte Carlo technique, we study the spin-$1/2$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids (with $U(1)$ or $Z_2$ symmetry) or magnetically ordered phases (with ${\bf q}=(0,0)$ or ${\bf q}=(4π/3,0)$). We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U(1)$ to $Z_2$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U(1)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.

cond-mat.str-el↗

arXiv2015

Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice

We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with $C=1/2$ fractionalized Chern number.

cond-mat.str-el↗

arXiv2015

Spin-$\frac{1}{2}$ Heisenberg $J_1$-$J_2$ antiferromagnet on the kagome lattice

We report variational Monte Carlo calculations for the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice in the presence of both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped $\mathbb{Z}_{2}$ spin liquid can be stabilized in the presence of a finite $J_2$ superexchange, with a substantial energy gain with respect to the gapless $U(1)$ Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit, implying that, at least within this approach, the $U(1)$ Dirac spin liquid remains stable in a relatively large region of the phase diagram. For $J_2/J_1 \gtrsim 0.3$, we find that a magnetically ordered state with ${\bf q}={\bf 0}$ overcomes the magnetically disordered wave functions, suggesting the end of the putative gapless spin-liquid phase.

cond-mat.str-el↗

arXiv2014

Lanczos steps to improve variational wave functions

Gutzwiller-projected fermionic states can be efficiently implemented within quantum Monte Carlo calculations to define extremely accurate variational wave functions for Heisenberg models on frustrated two-dimensional lattices, not only for the ground state but also for low-energy excitations. The application of few Lanczos steps on top of these states further improves their accuracy, allowing calculations on large clusters. In addition, by computing both the energy and its variance, it is possible to obtain reliable estimations of exact results. Here, we report the cases of the frustrated Heisenberg models on square and Kagome lattices.

cond-mat.str-el↗

arXiv2014

Superconductivity from spoiling magnetism in the Kondo lattice model

We find evidence that superconductivity intrudes into the paramagnetic-to-magnetic transition of the Kondo lattice model if magnetic frustration is added. Specifically, we study by variational method the model on a square lattice in the presence of both nearest- ($t$) and next-nearest-neighbor ($t^\prime$) hopping of the conduction electrons. We find that when $t^\prime/t$ is finite a $d$-wave superconducting dome emerges between the magnetic and paramagnetic metal phases and close to the compensated regime, i.e., the number of conduction electrons equal to the number of localized spin-1/2 moments. Superconductivity is further strengthened by a direct antiferromagnetic exchange between the localized moments, to such an extent that we even observe coexistence with magnetic order.

cond-mat.str-el↗

arXiv2014

One-dimensional spin liquid, collinear, and spiral phases from uncoupled chains to the triangular lattice

We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and $t^\prime$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t=t^\prime$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$ and substantial frustration, i.e., $0.3\lesssim t/t^\prime \lesssim 0.8$, the spin-liquid state is clearly favored over magnetic states. Spiral magnetic order is only stable in the vicinity of the isotropic point, while collinear order is obtained in a wide range of inter-chain hoppings from small to intermediate frustration.

cond-mat.str-el↗

arXiv2014

Spiral antiferromagnets beyond the spin-wave approximation: frustrated $XY$ and Heisenberg models in the honeycomb lattice

We examine the stability of classical states with a generic incommensurate spiral order against quantum fluctuations. Specifically, we focus on the frustrated spin-1/2 $XY$ and Heisenberg models on the honeycomb lattice with nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Our variational approach is based on the Jastrow wave functions, which include quantum correlations on top of classical spin waves. We perform a systematic optimization of wave vectors and Jastrow pseudo-potentials within this class of variational states and find that quantum fluctuations favor collinear states over generic coplanar spirals. The Néel state with ${\bf Q}=(0,0)$ extends its stability well beyond the classical value $J_2/J_1=1/6$. Most importantly, the collinear states with ${\bf Q}=(0,2π/\sqrt{3})$ (and the two symmetry-related states) are found to be stable in a large regime with intermediate frustration, while at the classical level they are limited to the point $J_2/J_1=0.5$. For large frustration, the $120^\circ$ state is stabilized for finite values of $J_2/J_1$ in both models.

cond-mat.str-el↗

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↗

arXiv2014

Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet

We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U(1)$ Dirac spin liquid state proposed by Y. Ran $et al.$ [Phys. Rev. Lett. $98$, $117205$ ($2007$)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed.

cond-mat.str-el↗

arXiv2014

Nature of the phases in the frustrated XY model on the honeycomb lattice

We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the spin-liquid state is based on a decomposition of the underlying bosonic particles in terms of spin-1/2 fermions (partons), with a Gutzwiller projection enforcing no single occupancy, as well as a long-range Jastrow factor.

cond-mat.str-el↗

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

Variational Monte Carlo approach to the two-dimensional Kondo lattice model

We study the phase diagram of the Kondo-lattice model with nearest-neighbor hopping in the square lattice by means of the variational Monte Carlo technique. Specifically, we analyze a wide class of variational wave functions that allow magnetic and superconducting order parameters, so to assess the possibility that superconductivity might emerge close to the magnetic instability, as often observed in heavy fermion systems. Indeed, we do find evidence of d-wave superconductivity in the paramagnetic sector, i.e., when magnetic order is not allowed in the variational wave function. However, when magnetism is allowed, it completely covers the superconducting region, which thus disappears from the phase diagram.

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↗

arXiv2013

Quantum quenches in one-dimensional gapless systems: Does bosonization work?

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. We show that important features are missed by the bosonization technique, which predicts the persistence of long-wavelength critical properties in the long-time evolution. Instead, numerical analysis provides puzzling evidences: while the momentum distribution appears to be consistent with the presence of a singularity at $k_F$, density-density correlations at small momenta clearly display a thermal-like behavior, namely ${\bar{N}}_q \simeq {\rm const}$ (where the overbar indicates the long-time average). This feature at small momenta is preserved in presence of an interaction term that breaks integrability, together with a rounding of the singularities at finite $q$'s, showing that the bosonization approach is not able to represent the time evolution of generic one-dimensional models after a quantum quench.

cond-mat.str-el↗

arXiv2013

Spin-liquid versus spiral-order phases in the anisotropic triangular lattice

We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters t and t' in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly-correlated regime and close to the isotropic limit t'/t=1. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) Néel and the (coplanar) 120° phases. The pitch vector of the spiral phase obtained from the unrestricted Hartree-Fock approximation is substantially renormalized in presence of electronic correlations, and the Néel phase is stabilized in a wide regime of the phase diagram, i.e., for t'/t < 0.75. We discuss these results in the context of organic charge-transfer salts.

cond-mat.str-el↗

arXiv2012

Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagome lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.

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

Strong renormalization of the Fermi-surface topology close to the Mott transition

The underlying Fermi surface is a key concept for strongly-interacting electron models and has been introduced to generalize the usual notion of the Fermi surface to generic (superconducting or insulating) systems. By using improved correlated wave functions that contain backflow and Jastrow terms, we examine the two-dimensional $t{-}t^\prime$ Hubbard model and find a non-trivial renormalization of the topology of the underlying Fermi surface close to the Mott insulator. Moreover, we observe a sharp crossover region, which arises from the metal-insulator transition, from a weakly interacting metal at small coupling to a resonating valence-bond superconductor at intermediate coupling. A violation of the Luttinger theorem is detected at low hole dopings.

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