arXiv subjects

Stefano Ruffo

Publications and source records attributed to Stefano Ruffo.

At least 37 records · Page 2Linked to original sources

arXiv2023

Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing

Thanks to their prominent collective character, long-range interactions promote information spreading and generate forms of entanglement scaling, which cannot be observed in traditional systems with local interactions. In this work, we study the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range hopping and pairing couplings decaying with a power law of the distance. We provide a fully-fledged analytical and numerical characterization of the asymptotic growth of the ground state entanglement in the large subsystem size limit, finding that the truly non-local nature of the model leads to an extremely rich phenomenology. Most significantly, in the strong long-range regime, we discovered that the system ground state may have a logarithmic, fractal, or volume-law entanglement scaling, depending on the value of the chemical potential and on the strength of the power law decay.

quant-ph↗

arXiv2023

Quantum heat engine with long-range advantages

The employment of long-range interactions in quantum devices provides a promising route towards enhancing their performance in quantum technology applications. Here, the presence of long-range interactions is shown to enhance the performances of a quantum heat engine featuring a many-body working substance. We focus on the paradigmatic example of a Kitaev chain undergoing a quantum Otto cycle and show that a substantial thermodynamic advantage may be achieved as the range of the interactions among its constituents increases. Interestingly, such an advantage is most significant for the realistic situation of a finite time cycle: the presence of long-range interactions reduces the non-adiabatic energy losses, by suppressing the detrimental effects of dynamically generated excitations. This effect allows mitigating the trade-off between power and efficiency, paving the way for a wide range of experimental and technological applications.

cond-mat.stat-mech↗

arXiv2023

Quantization of integrable and chaotic three-particle Fermi-Pasta-Ulam-Tsingou models

We study the transition from integrability to chaos for the three-particle Fermi-Pasta-Ulam- Tsingou (FPUT) model. We can show that both the quartic b-FPUT model ($α$ = 0) and the cubic one ($β$ = 0) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of $α$ and $β$, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincaré sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis.

cond-mat.stat-mech↗

arXiv2023

Modified Thirring model beyond the excluded-volume approximation

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d=1,2,3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.

cond-mat.stat-mech↗

arXiv2022

Fractional Dynamics and Modulational Instability in Long-Range Heisenberg Chains

We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent $α$. We add to the Hamiltonian an anisotropy in the $z$-direction. In the framework of a semiclassical approach, we use the Holstein-Primakoff transformation to derive an effective long-range discrete nonlinear Schrödinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schrödinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for $α< 3$. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent $α$.

cond-mat.stat-mech↗

arXiv2022

Villain model with long-range couplings

The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor $XY$ model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional $XY$ model has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, $σ$, in which there are a magnetized, a disordered and a critical phase (arXiv:2104.13217). Here we address the issue of whether the critical behavior of the two-dimensional $XY$ model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range $XY$ model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for $σ<2$ the two models no longer share the same universality class. Remarkably, within a large region of its phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with $1/r^2$ interactions.

cond-mat.stat-mech↗

arXiv2022

Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths

We study the nonequilibrium steady-state of a fully-coupled network of $N$ quantum harmonic oscillators, interacting with two thermal reservoirs. Given the long-range nature of the couplings, we consider two setups: one in which the number of particles coupled to the baths is fixed (intensive coupling) and one in which it is proportional to the size $N$ (extensive coupling). In both cases, we compute analytically the heat fluxes and the kinetic temperature distributions using the nonequilibrium Green's function approach, both in the classical and quantum regimes. In the large $N$ limit, we derive the asymptotic expressions of both quantities as a function of $N$ and the temperature difference between the baths. We discuss a peculiar feature of the model, namely that the bulk temperature vanishes in the thermodynamic limit, due to a decoupling of the dynamics of the inner part of the system from the baths. At variance with usual cases, this implies that the steady state depends on the initial state of the particles in the bulk. We also show that quantum effects are relevant only below a characteristic temperature that vanishes as $1/N$. In the quantum low-temperature regime the energy flux is proportional to the universal quantum of thermal conductance.

cond-mat.stat-mech↗

arXiv2022

Hydrodynamics and transport in the long-range-interacting $φ^4$ chain

We present a simulation study of the one-dimensional $φ^4$ lattice theory with long-range interactions decaying as an inverse power $r^{-(1+σ)}$ of the intersite distance $r$, $σ>0$. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for $0<σ\le 1$ analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for $σ>1$ and anomalous for $0<σ<1$ where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

cond-mat.stat-mech↗

arXiv2022

Tricritical point in the quantum Hamiltonian mean-field model

Engineering long-range interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian mean-field model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the many-body system through a first order quantum phase transition from an ordered to a disordered phase at zero temperature. At higher temperatures, the fluctuation-induced phase transition remains first order initially and switches to second order only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with long-range couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and mean-field theory.

cond-mat.stat-mech↗

arXiv2022

Energy fluctuation relations and repeated quantum measurements

In this review paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form $\langle e^{-βQ}\rangle = 1$, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies.

quant-ph↗

arXiv2022

Some considerations about reviewing and open-access in scientific publishing

Scientific research changed profoundly over the last 30 years, in all its aspects. Scientific publishing has changed as well, mainly because of the strong increased number of submitted papers and because of the appearance of Open Access journals and publishers. We propose some reflections on these issues.

cs.DL↗

arXiv2021

Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings

The Berezinskii-Kostelitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry-breaking, where a quasi-ordered phase, characterized by a power law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature $T_{\rm BKT}$. In this letter, we consider the effect of long-range decaying couplings $\sim r^{-2-σ}$ on this phenomenon. After pointing out the relevance of this non trivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features -- for $7/4<σ<2$ -- a quasi ordered phase in a finite temperature range $T_c < T < T_{\rm BKT}$, which occurs between a symmetry broken phase for $T T_{\rm BKT}$. The transition temperature $T_c$ displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in $2D$ atomic, molecular and optical quantum systems.

cond-mat.stat-mech↗

arXiv2021

Thermalization processes induced by quantum monitoring in multi-level systems

We study the heat statistics of a multi-level $N$-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number $M$ of measurements $(M \to \infty)$. In this context, the conditions allowing for an Infinite-Temperature Thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the non-equilibrium evolution of the system and its initial state. Exceptions to ITT, to which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasi-commuting) with the Hamiltonian of the quantum system, or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces ($N \to \infty$), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits $M\to\infty$ and $N\to\infty$ matters: when $N$ is fixed and $M$ diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A non trivial result is obtained fixing $M/N^2$ where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.

quant-ph↗

arXiv2021

Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point

The canonical phase diagram of the Blume-Emery-Griffiths (BEG) model with infinite-range interactions is known to exhibit a fourth order critical point at some negative value of the bi-quadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth order critical point is studied in detail revealing some distinct features from the canonical counterpart.

cond-mat.stat-mech↗

arXiv2021

Long-range interacting quantum systems

The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -- in some cases rigorously -- connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.

cond-mat.quant-gas↗

arXiv2021

Computation of microcanonical entropy at fixed magnetization without direct counting

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover, we apply the method to an Ising model with mean-field, nearest-neighbour and next-nearest-neighbour interactions, for which direct counting is not straightforward. For this model, we compare the solution obtained by our method with the one obtained from the formula for the entropy in terms of all correlation functions. This example shows that for general couplings our method is much more convenient than direct counting methods to compute the microcanonical entropy at fixed magnetization.

cond-mat.stat-mech↗

arXiv2021

Monte Carlo simulations in the unconstrained ensemble

The unconstrained ensemble describes completely open systems whose control parameters are chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up a new avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

cond-mat.stat-mech↗

arXiv2021

Fast collective oscillations and clustering phenomena in an antiferromagnetic mean-field model

We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a stationary state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performing a low kinetic energy approximation, we derive the explicit expression of the magnetization vector as a function of time. We find that the latter displays coherent oscillations, and we show numerically that the probability distribution for its phase is bimodal or quadrimodal. We then look at the individual rotator dynamics as a motion in an external time-dependent potential, given by the magnetization. This dynamics exhibits two distinct time scales, with the fast one associated to the oscillations of the global magnetization vector. Performing an average over the fast oscillations, we derive an expression for the effective force acting on the individual rotator. This force is always bimodal, and determines a low frequency oscillation of the rotators. Our approach leads to a self-consistent theory linking the time-dependence of the magnetization to the motion of the rotators, providing a heuristic explanation for the formation of the bicluster.

cond-mat.stat-mech↗