arXiv subjects

Nicolò Defenu

Publications and source records attributed to Nicolò Defenu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Observables in non-Hermitian systems: A methodological comparison

Despite acute interest in the dynamics of non-Hermitian systems, there is a lack of consensus in the mathematical formulation of non-Hermitian quantum mechanics in the community. Different methodologies are used in the literature to study non-Hermitian dynamics. This ranges from consistent frameworks like biorthogonal quantum mechanics and metric approach characterized by modified inner products, to normalization by time-dependent norms inspired by open quantum systems. In this work, we systematically explore the similarities and differences among these various methods. Utilizing illustrative models with exact solutions, we demonstrate that these methods produce not only quantitatively different results but also distinct physical interpretations. For dissipative systems where non-Hermiticity arises as an approximation, we find that simply dividing by the norm in the $\mathcal{PT}$-broken regime closely aligns with the full master equation solutions. In contrast, for quantum systems where non-Hermiticity can be engineered exactly, incorporating metric dynamics is crucial for the probabilistic interpretation of quantum mechanics, necessitating the generalizations of similarity transformations and unitarity to non-Hermitian systems. This study lays the groundwork for further exploration of non-Hermitian Hamiltonians, potentially leveraging generalized transformations for novel physical phenomena.

quant-ph↗

arXiv2024

The long-range origin of the black hole entropy

The Sachdev-Ye-Kitaev (SYK) model, has emerged as a powerful tool for exploring the quantum nature of black holes, particularly their residual entropy at zero temperature. In this work, we investigate the role of long-range interactions in a chain of SYK dots with power-law decaying couplings and demonstrate how these interactions can lead to finite residual entropy in the strong non-local case. Indeed, as a function of the interaction range, the black-hole phase, found in the isolated SYK, melts into a long-range Fermi-liquid phase in the weak long-range regime and finally reaches the non Fermi-liquid phase in the purely local case. Our results pave the way to the understanding of the role of the interaction range in black hole thermodynamics and quantum information.

cond-mat.str-el↗

arXiv2024

Ensemble inequivalence in long-range quantum systems

Ensemble inequivalence, i.e. the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in numerous classical systems. Here, an example of ensemble inequivalence of a long-range quantum ferromagnet is presented. While the $T=0$ microcanonical quantum phase-diagram coincides with that of the canonical ensemble, the phase-diagrams of the two ensembles are different at finite temperature. This is in contrast with the common lore of statistical mechanics of systems with short-range interactions where thermodynamic properties are bound to coincide for macroscopic systems described by different ensembles. The consequences of these findings in the context of atomic, molecular and optical (AMO) setups are delineated.

cond-mat.stat-mech↗

arXiv2024

Universality of critical dynamics on a complex network

We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically, we study the synchronization and entrainment transitions in the nonequilibrium dynamics of the Kuramoto model and the phase transition of the equilibrium dynamics of the classical $XY$ model, thereby covering a broad spectrum from nonlinear dynamics to statistical and condensed matter physics. Using linear theory, we obtain a general relationship between the dynamics occurring on the network and the underlying network properties. This yields the lower critical spectral dimension of the phase synchronization and entrainment transitions in the Kuramoto model as $d_s=4$ and $d_s=2$ respectively, whereas for the phase transition in the $XY$ model it is $d_s=2$. To test our theoretical hypotheses, we employ a network where any two nodes on the network are connected with a probability proportional to a power law of the distance between the nodes; this realizes any desired $d_s\in [1, \infty)$. Our detailed numerical study agrees well with the prediction of linear theory for the phase synchronization transition in the Kuramoto model. However, it shows a clear entrainment transition in the Kuramoto model and phase transition in the $XY$ model at $d_s \gtrsim 3$, not $d_s=2$ as predicted by linear theory. Our study indicates that network disorder in the region $2 \leq d_s \lesssim 3$ introduces strong finite-size fluctuations, which makes it extremely difficult to probe the existence of the ordered phase as predicted, affecting the dynamics profoundly.

cond-mat.stat-mech↗

arXiv2024

Freezing and Shielding under Global Quenches for Long-Range Interacting Many-Body Systems

We investigate the time evolution of a Fermi-Hubbard model with long range hopping following a sudden quench of the local interactions among different spin species. The quasi-particle spectrum consists of gapped low-energy levels while the high energy modes accumulate at a single point. When the low energy gaps are large enough, turning on the local interactions does not effectively mix high and low energy modes, leading to the freezing of the dynamical evolution. In general, the states within the excited subspace are shielded from the long-range signatures of the model, which are responsible for the low energy extended states, and the dynamics effectively look as if long-range hopping were absent. This cooperative shielding mechanism becomes evident in presence of disorder. It is shown that shielding and freezing are a universal feature of long-range interacting systems and conjecture that they are related to the existence of quasi-stationary states.

quant-ph↗

arXiv2024

Universal work statistics in long-range interacting quantum systems

We determine the conditions under which the presence of long-range interactions reduce the energy losses due to defect generation during non-adiabatic evolution, crucial for enhancing the power to efficiency ratio of quantum thermal devices. In order to do so, we investigate the response of long-range systems to diverse external drivings, emphasizing their robustness against dynamic excitation in comparison to generic local systems. This phenomenon is demonstrated through the study of the quantum work statistics, revealing insights into energy transfer efficiency and dynamical quantum criticality. Our results demonstrate the benefits of including a long-range interacting medium for quantum thermodynamics application, highlighting the potential to optimize finite-time quantum thermal cycles. Thanks to the effective dimension approach our findings can be drawn in full generality and, then, specified to different experimentally relevant scenarios.

cond-mat.stat-mech↗

arXiv2024

Universality in long-range interacting systems: the effective dimension approach

Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions $r^{d+σ}$ to a local system, i.e., with finite range interactions, in an effective fractal dimension $d_\mathrm{eff}$. This method simplifies the study of long-range models by leveraging known results from their local counterparts. While the validity of this approximation beyond the mean-field level has been long debated, we demonstrate that the effective dimension approach, while approximate for non-Gaussian fixed points, accurately estimates the critical exponents of long-range models with an accuracy typically larger than $97\%$. To do so, we review perturbative RG results, extend the approximation's validity using functional RG techniques, and compare our findings with precise numerical data from conformal bootstrap for the two-dimensional Ising model with long-range interactions.

cond-mat.stat-mech↗

arXiv2024

Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions

Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.

cond-mat.quant-gas↗

arXiv2024

Universal scaling in real dimension

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension $d_{s}$, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously also to noninteger values and to find the universal exponents as continuous functions of the dimension. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of $O(\mathcal{N})$ symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.

cond-mat.stat-mech↗

arXiv2024

Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range

The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data.

quant-ph↗

arXiv2024

Melting of the two-dimensional solid phase in the Gaussian-core model

A general theory for the melting of two dimensional solids explaining the universal and non-universal properties is an open problem up to date. Although the celebrated KTHNY theory have been able to predict the critical properties of the melting transition in a variety cases, it is already known that it is not able to capture the occurrence of first order transitions observed in certain systems as well as it doesn't provide a clear way to calculate the melting temperature for a specific model. In the present work we have developed an analytical method that combines Self Consistent Variational Approximation with the Renormalization Group in order to deal simultaneously with the phonon fluctuations and the topological defects present in the melting process of two dimensional crystals. The method was applied with impressive success to the study of the phase diagram of the Gaussian-core model, capturing not only the reentrant feature of its 2D solid phase, but also the related critical temperatures as a function of the density in quantitative detail. The developed method can be directly applied to study the melting of any hexagonal simple crystal formed by particles interacting through any finite pairwise interaction potential. Additionally, it has the potential to explain the occurrence of first order transitions in the melting process of two dimensional crystals.

cond-mat.stat-mech↗

arXiv2023

$BKT$ transitions in classical and quantum long-range systems

In the past decades considerable efforts have been made in order to understand the critical features of both classical and quantum long-range interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the $2d$ classical $XY$ model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper we discuss a field theoretical treatment of the $2d$ $XY$ model with long-range couplings and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power-law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of long-range interactions. We also discuss the Villain approximation for the $2d$ $XY$ model with power-law couplings, providing hints that, in the long-range regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the long-range quantum XXZ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.

cond-mat.stat-mech↗

arXiv2023

Fractal nature of high-order time crystal phases

Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline phases display critical behaviour of different order, i.e., oscillations whose period is a multiple $p > 2$ of the Floquet driving period. Here, we introduce a new, experimentally-accessible, order parameter which is able to unambiguously detect crystalline phases regardless of the value of $p$ and, at the same time, is a useful tool for chaos diagnostic. This new paradigm allows us to investigate the phase diagram of the long-range (LR) kicked Ising model to an unprecedented depth, unveiling a rich landscape characterized by self-similar fractal boundaries. Our theoretical picture describes the emergence of DFTCs phase both as a function of the strength and period of the Floquet drive, capturing the emergent $\mathbb{Z}_p$ symmetry in the Floquet-Bloch waves.

cond-mat.stat-mech↗

arXiv2023

Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems

Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly solvable non-Hermitian system, hosting both $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken modes subject to a linear quench. Employing a fully consistent framework, in which the Hilbert space is endowed with a nontrivial dynamical metric, we analyze the dynamics of the generated defects. In contrast to Hermitian systems, our study reveals that PT -broken time evolution leads to defect freezing and hence the violation of adiabaticity. This physics necessitates the so-called metric framework, as it is missed by the oft used approach of normalizing quantities by the time-dependent norm of the state. Our results are relevant for a wide class of experimental systems.

quant-ph↗

arXiv2023

Generalized Higgs mechanism in long-range interacting quantum systems

The physics of long-range interacting quantum systems is currently living through a renaissance driven by the fast progress in quantum simulators. In these systems many paradigms of statistical physics do not apply and also the universal long-wavelength physics gets substantially modified by the presence of long-ranged forces. Here we explore the low-energy excitations of several long-range interacting quantum systems, including spin models and interacting Bose gases, in the ordered phase associated with the spontaneous breaking of U(1) and SU(2) symmetries. Instead of the expected Goldstone modes, we find three qualitatively different regimes, depending on the range of the interaction. In one of these regimes the Goldstone modes are gapped, via a generalization of the Higgs mechanism. Moreover, we show how this effect is realized in current experiments with ultracold atomic gases in optical cavities.

cond-mat.quant-gas↗

arXiv2023

Vortex supersolid in the XY model with tunable vortex fugacity

In this paper, we investigate the XY model in the presence of an additional potential term that independently tunes the vortex fugacity favouring their nucleation. By increasing the strength of this term and thereby the vortex chemical potential μ, we observe significant changes in the phase diagram with the emergence of a normal vortex-antivortex lattice as well as a superconducting vortex-antivortex crystal (lattice supersolid) phase. We examine the transition lines between these two phases and the conventional non-crystalline one as a function of both the temperature and the chemical potential. Our findings suggest the possibility of a peculiar tricritical point where second-order, first-order, and infinite-order transition lines meet. We discuss the differences between the present phase diagram and previous results for two-dimensional Coulomb gas models. Our study provides important insights into the behaviour of the modified XY model and opens up new possibilities for investigating the underlying physics of unconventional phase transitions.

cond-mat.str-el↗

arXiv2023

Softening of Majorana edge states by long-range couplings

The inclusion of long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. By means of the scattering approach, we prove that the Majorana states \textit{soften}, becoming increasingly delocalised at a universal rate which is only determined by the interaction range. This edge mechanism can be related to a change in the value of the bulk topological index at criticality, upon careful redefinition of the latter. The critical point turns out to be topologically akin to the trivial phase rather than interpolating between the two phases. Our treatment moreover showcases how various topological aspects of quantum models can be investigated analytically.

cond-mat.mes-hall↗

arXiv2023

Universal defects statistics with strong long-range interactions

Quasi-static transformations, or slow quenches, of many-body quantum systems across quantum critical points create topological defects. The Kibble-Zurek mechanism regulates the appearance of defects in a local quantum system through a classical combinatorial process. However, long-range interactions disrupt the conventional Kibble-Zurek scaling and lead to a density of defects that is independent of the rate of the transformation. In this study, we analytically determine the complete full counting statistics of defects generated by slow annealing a strong long-range system across its quantum critical point. We demonstrate that the mechanism of defect generation in long-range systems is a purely quantum process with no classical equivalent. Furthermore, universality is not only observed in the defect density but also in all the moments of the distribution. Our findings can be tested on various experimental platforms, including Rydberg gases and trapped ions.

quant-ph↗