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Luca Capriotti

Publications and source records attributed to Luca Capriotti.

At least 37 records · Page 2Linked to original sources
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↗
arXiv2005

Dissipation-driven phase transition in 2D Josephson arrays

We analyze the interplay of dissipative and quantum effects in the proximity of a quantum phase transition. The prototypical system is a resistively shunted two-dimensional Josephson junction array, studied by means of an advanced Fourier path-integral Monte Carlo algorithm. The reentrant superconducting-to-normal phase transition driven by quantum fluctuations, recently discovered in the limit of infinite shunt resistance, persists for moderate dissipation strength but disappears in the limit of small resistance. For large quantum coupling our numerical results show that, beyond a critical dissipation strength, the superconducting phase is always stabilized at sufficiently low temperature. Our phase diagram explains recent experimental findings.

cond-mat.stat-mech↗
arXiv2005

Quantum Heisenberg antiferromagnets: a survey of the activity in Firenze

Over the years the research group in Firenze has produced a number of theoretical results concerning the statistical mechanics of quantum antiferromagnetic models, which range from the theory of two-magnon Raman scattering to the characterization of the phase transitions in quantum low-dimensional antiferromagnetic models. Our research activity was steadily aimed to the understanding of experimental observations.

cond-mat.str-el↗
arXiv2004

Low temperature broken symmetry phases of spiral antiferromagnets

We study Heisenberg antiferromagnets with nearest- (J1) and third- (J3) neighbor exchange on the square lattice. In the limit of large spin S, there is a zero temperature (T) Lifshitz point at J3 = (1/4) J1, with long-range spiral spin order at T=0 for J3 > (1/4) J1. We present classical Monte Carlo simulations and a theory for T>0 crossovers near the Lifshitz point: spin rotation symmetry is restored at any T>0, but there is a broken lattice reflection symmetry for 0 <= T < Tc ~ (J3-(1/4) J1) S^2. The transition at T=Tc is consistent with Ising universality. We also discuss the quantum phase diagram for finite S.

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

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a Density Matrix Renormalization Group (DMRG) study of the ground-state properties of spin-1/2 frustrated $J_1-J_3$ Heisenberg $n_l$-leg ladders (with $n_l$ up to 8). For strong frustration ($J_3/J_1\simeq 0.5$), both even- and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.

cond-mat.str-el↗
arXiv2004

Berezinskii-Kosterlitz-Thouless transition in Josephson junction arrays

The quantum XY model shows a Berezinskii-Kosterlitz-Thouless (BKT) transition between a phase with quasi long-range order and a disordered one, like the corresponding classical model. The effect of the quantum fluctuations is to weaken the transition and eventually to destroy it. However, in this respect the mechanism of disappearance of the transition is not yet clear. In this work we address the problem of the quenching of the BKT in the quantum XY model in the region of small temperature and high quantum coupling. In particular, we study the phase diagram of a 2D Josephson junction array, that is one of the best experimental realizations of a quantum XY model. A genuine BKT transition is found up to a threshold value $g^\star$ of the quantum coupling, beyond which no phase coherence is established. Slightly below $g^\star$ the phase stiffness shows a reentrant behavior at lowest temperatures, driven by strong nonlinear quantum fluctuations. Such a reentrance is removed if the dissipation effect of shunt resistors is included.

cond-mat.mes-hall↗
arXiv2003

Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model

We study the thermodynamics of the spin-$S$ two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor couplings in its collinear phase ($J_2/J_1>0.5$), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio $J_2/J_1$ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li$_2$VOSiO$_4$ and related compounds.

cond-mat.str-el↗
arXiv2003

Reentrant behavior of the phase stiffness in Josephson junction arrays

The phase diagram of a 2D Josephson junction array with large substrate resistance, described by a quantum XY model, is studied by means of Fourier path-integral Monte Carlo. A genuine Berezinskii-Kosterlitz-Thouless transition is found up to a threshold value g* of the quantum coupling, beyond which no phase coherence is established. Slightly below g* the phase stiffness shows a reentrant behavior with temperature, in connection with a low-temperature disappearance of the superconducting phase, driven by strong nonlinear quantum fluctuations.

cond-mat.mes-hall↗
arXiv2003

Finite-size spin-wave theory of a collinear antiferromagnet

The ground-state and low-energy properties of the two-dimensional $J_1{-}J_2$ Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, {\em Europhys. Lett.} {\bf 21}, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half -- where the effects of quantization are the strongest -- the spin-wave expansion turns out to be quantitatively accurate for $J_2/J_1\gtrsim 0.8$. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, $m^\dagger\simeq 0.3$, is in remarkable agreement with recent neutron scattering measurements on ${\rm Li_2VOSiO_4}$.

cond-mat.str-el↗
arXiv2003

Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter.

cond-mat.str-el↗
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

Path integral Monte Carlo for dissipative many-body systems

We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the path-integral formalism through the inclusion of an influence action that is bilocal and quadratic in the system's coordinates. At a first sight the usual direct approach of discretizing the path integral could seem feasible, but complications arise when one tries to introduce a physically meaningful dissipation kernel: in particular its imaginary-time dependence turns out to be severely singular and difficult to evaluate analytically, in spite of the simple expressions for its Matsubara components. We therefore propose to face the numerical problem using Fourier path-integral Monte Carlo, that can be formulated in two different ways: transforming the continuous paths and then truncating the high Fourier components (with possible improvements upon the truncation procedure), or performing the Fourier transformation upon the discretized paths. The latter choice leads to a simpler formulation and allows for a better control of the extrapolation to the limit of infinite Trotter number. The method is implemented for a single nonlinear particle with Ohmic dissipation and for a phi^4 chain with Drude-like dissipation.

cond-mat.stat-mech↗
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↗
arXiv2001

Quantum Phase Transition in Coupled Spin Ladders

The ground state of an array of coupled, spin-half, antiferromagnetic ladders is studied using spin-wave theory, exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 256 sites). Our results clearly indicate the occurrence of a zero-temperature phase transition between a Néel ordered and a non-magnetic phase at a finite value of the inter-ladder coupling ($α_c\simeq0.3$). This transition is marked by remarkable changes in the structure of the excitation spectrum.

cond-mat.str-el↗
arXiv2001

Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and $J_1{-}J_2$ Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range Néel order.The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the $J_1{-}J_2$ Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at $J_2/J_1 \simeq 0.4$, marking the melting of the antiferromagnetic Néel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.

cond-mat.str-el↗
arXiv2001

Simulating Quantum Dissipation in Many-Body Systems

An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo sampling of the partition function after discretization and Fourier transformation in imaginary time of the dynamical variables. The method is tested extensively for model systems, using realistic dissipative kernels. Results are also compared with the predictions of a recently proposed semiclassical approximation, thus testing the reliability of the latter approach for weak quantum coupling. Our numerical method opens the possibility to quantitatively describe real quantum dissipative systems as, e.g., Josephson junction arrays.

cond-mat.stat-mech↗