arXiv subjects

Ruggero Vaia

Publications and source records attributed to Ruggero Vaia.

At least 37 records · Page 2Linked to original sources

arXiv2006

Steady states of the conserved Kuramoto-Sivashinsky equation

Recent work on the dynamics of a crystal surface [T.Frisch and A.Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved Kuramoto-Sivashinsky (CKS) equation: \partial_t u = -\partial_{xx}(u+u_{xx}+u_x^2), which displays coarsening. For a quantitative and qualitative understanding of the dynamics, the analysis of steady states is particularly relevant. In this paper we provide a detailed study of the stationary solutions and their explicit form is given. Periodic configurations form an increasing branch in the space wavelength-amplitude (lambda-A), with d(lambda)/dA>0. For large wavelength, lambda=4\sqrt{A} and the orbits in phase space tend to a separatrix, which is a parabola. Steady states are found up to an additive constant a, which is set by the dynamics through the conservation law \partial_t =0: a(lambda(t))=lambda^2(t)/48.

cond-mat.stat-mech↗

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

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

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

Detection of XY behaviour in weakly anisotropic quantum antiferromagnets on the square lattice

We consider the Heisenberg antiferromagnet on the square lattice with S=1/2 and very weak easy-plane exchange anisotropy; by means of the quantum Monte Carlo method, based on the continuous-time loop algorithm, we find that the thermodynamics of the model is highly sensitive to the presence of tiny anisotropies and is characterized by a crossover between isotropic and planar behaviour. We discuss the mechanism underlying the crossover phenomenon and show that it occurs at a temperature which is characteristic of the model. The expected Berezinskii-Kosterlitz-Thouless transition is observed below the crossover: a finite range of temperatures consequently opens for experimental detection of non-critical 2D XY behaviour. Direct comparison is made with uniform susceptibility data relative to the S=1/2 layered antiferromagnet Sr2CuO2Cl2.

cond-mat.stat-mech↗

arXiv2003

Quantum 2D Heisenberg antiferromagnet: bridging the gap between field-theoretical and semiclassical approaches

The field-theoretical result for the low-$T$ behaviour of the correlation length of the quantum Heisenberg antiferromagnet on the square lattice was recently improved by Hasenfratz [Eur. Phys. J. B {\bf 13}, 11 (2000)], who corrected for cutoff effects. We show that starting from his expression, and exploiting our knowledge of the classical thermodynamics of the model, it is possible to take into account non-linear effects which are responsible for the main features of the correlation length at intermediate temperature. Moreover, we find that cutoff effects lead to the appearance of an effective exchange integral depending on the very same renormalization coefficients derived in the framework of the semiclassical {\em pure-quantum self-consistent harmonic approximation}: The gap between quantum field-theoretical and semiclassical results is here eventually bridged.

cond-mat.stat-mech↗

arXiv2003

Anisotropy and Ising-like transition of the S=5/2 two-dimensional Heisenberg antiferromagnet Mn-formate di-Urea

Recently reported measurements of specific heat on the compound Mn-formate di-Urea (Mn-f-2U) by Takeda et al. [Phys. Rev. B 63, 024425 (2001)] are considered. As a model to describe the overall thermodynamic behavior of such compound, the easy-axis two-dimensional Heisenberg antiferromagnet is proposed and studied by means of the 'pure quantum self-consistent harmonic approximation' (PQSCHA). In particular it is shown that, when the temperature decreases, the compound exhibits a crossover from 2D-Heisenberg to 2D-Ising behavior, followed by a 2D-Ising-like phase transition, whose location allows to get a reliable estimate of the easy-axis anisotropy driving the transition itself. Below the critical temperature T_N=3.77 K, the specific heat is well described by the two-dimensional easy-axis model down to a temperature T*=1.47 K where a T^3-law sets in, possibly marking a low-temperature crossover of magnetic fluctuations from two to three dimensions.

cond-mat↗

arXiv2003

Field-induced XY behavior in the S=1/2 antiferromagnet on the square lattice

Making use of the quantum Monte Carlo method based on the worm algorithm, we study the thermodynamic behavior of the S=1/2 isotropic Heisenberg antiferromagnet on the square lattice in a uniform magnetic field varying from very small values up to the saturation value. The field is found to induce a Berezinskii-Kosterlitz-Thouless transition at a finite temperature, above which a genuine XY behavior in an extended temperature range is observed. The phase diagram of the system is drawn, and the thermodynamic behavior of the specific heat and of the uniform and staggered magnetization is discussed in sight of an experimental investigation of the field-induced XY behavior.

cond-mat.str-el↗

arXiv2002

Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice

We study the finite-temperature behaviour of two-dimensional S=1/2 Heisenberg antiferromagnets with very weak easy-axis and easy-plane exchange anisotropies. By means of quantum Monte Carlo simulations, based on the continuous-time loop and worm algorithm, we obtain a rich set of data that allows us to draw conclusions about both the existence and the type of finite-temperature transition expected in the considered models. We observe that the essential features of the Ising universality class, as well as those of the Berezinskii-Kosterlitz-Thouless (BKT) one, are preserved even for anisotropies as small as 10^{-3} times the exchange integral; such outcome, being referred to the most quantum case S=1/2, rules out the possibility for quantum fluctuations to destroy the long or quasi-long range order, whose onset is responsible for the Ising or BKT transition, no matter how small the anisotropy. Besides this general issue, we use our results to extract, out of the isotropic component, the features which are peculiar to weakly anisotropic models, with particular attention for the temperature region immediately above the transition. By this analysis we aim to give a handy tool for understanding the experimental data relative to those real compounds whose anisotropies are too weak for a qualitative description to accomplish the goal of singling out the genuinely two-dimensional critical behaviour.

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↗

arXiv2001

Quantum fluctuations in one-dimensional arrays of condensates

The effects of quantum and thermal fluctuations upon the fringe structure predicted to be observable in the momentum distribution of coupled Bose-Einstein condensates are studied by the effective-potential method. For a double-well trap, the coherence factor recently introduced by Pitaevskii and Stringari [Phys. Rev. Lett. 87, 180402 (2001)] is calculated using the effective potential approach and is found in good agreement with their result. The calculations are extended to the case of a one-dimensional array of condensates, showing that quantum effects are essentially described through a simple renormalization of the energy scale in the classical analytical expression for the fringe structure. The consequences for the experimental observability are discussed.

cond-mat.soft↗

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↗

arXiv2001

Quantum thermodynamics of systems with anomalous dissipative coupling

The standard {\em system-plus-reservoir} approach used in the study of dissipative systems can be meaningfully generalized to a dissipative coupling involving the momentum, instead of the coordinate: the corresponding equation of motion differs from the Langevin equation, so this is called {\em anomalous} dissipation. It occurs for systems where such coupling can indeed be derived from the physical analysis of the degrees of freedom which can be treated as a dissipation bath. Starting from the influence functional corresponding to anomalous dissipation, it is shown how to derive the effective classical potential that gives the quantum thermal averages for the dissipative system in terms of classical-like calculations; the generalization to many degrees of freedom is given. The formalism is applied to a single particle in a double-well and to the discrete $ϕ^4$ model. At variance with the standard case, the fluctuations of the coordinate are enhanced by anomalous dissipative coupling.

cond-mat.stat-mech↗

arXiv2000

Finite-temperature ordering in two-dimensional magnets

We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easy-axis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyse several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behaviour experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of $10^{-2}J$ ($J$ being the intra-layer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the {\it quasi}-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb$_2$MnF$_4$ shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.

cond-mat.stat-mech↗

arXiv2000

Effective potential approach to quantum dissipation in condensed matter systems

The effects of dissipation on the thermodynamic properties of nonlinear quantum systems are approached by the path-integral method in order to construct approximate classical-like formulas for evaluating thermal averages of thermodynamic quantities. Explicit calculations are presented for one-particle and many-body systems. The effects of the dissipation mechanism on the phase diagram of two-dimensional Josephson arrays is discussed.

cond-mat.stat-mech↗

arXiv2000

Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two dimensional Josephson arrays is studied by means of the mapping to the quantum XY model. The quantum effects onto the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the {\em pure-quantum self-consistent harmonic approximation}, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-to-insulator transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while the comparison with experimental data leads to conclude that the commonly assumed model is not suitable to describe in detail the real system.

cond-mat.mes-hall↗

arXiv1999

Semiclassical approach to the thermodynamics of spin chains

Using the PQSCHA semiclassical method, we evaluate thermodynamic quantities of one-dimensional Heisenberg ferro- and antiferromagnets. Since the PQSCHA reduces their evaluation to classical-like calculations, we take advantage of Fisher's exact solution to get all results in an almost fully analytical way. Explicitly considered here are the specific heat, the correlations length and susceptibility. Good agreement with Monte Carlo simulations is found for S>1 antiferromagnets, showing that the relevance of the topological terms and of the Haldane gap is significant only for the lowest spin values and temperatures.

cond-mat.stat-mech↗