arXiv subjects

Antonello Scardicchio

Publications and source records attributed to Antonello Scardicchio.

At least 19 recordsLinked to original sources

arXiv2026

Vanishing spin stiffness in weakly disordered two-dimensional Heisenberg ferromagnets

We show that a small fraction of antiferromagnetic bonds qualitatively alters the long-wavelength dynamics of two-dimensional Heisenberg ferromagnets. Although the classical ground state remains magnetized, weak bond frustration generates logarithmically correlated spatial fluctuations of the local spin stiffness, despite the microscopic disorder being short ranged. A replica field theory calculation shows that the effective disorder strength grows under coarse graining, while the spin stiffness decreases, yielding anomalously soft magnons with a scale-dependent dynamical exponent $z > 2$. Numerical diagonalization of the semiclassical spin-wave Hamiltonian confirms the anomalous low-energy scaling. The flow is toward an infinite-disorder, zero stiffness regime.

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arXiv2026

Quantum Spin Glass in the Two-Dimensional Disordered Heisenberg Model via Foundation Neural-Network Quantum States

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.

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arXiv2026

Semiclassical picture of the Heisenberg spin glass in two dimensions: from weak localization to hydrodynamics

The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of its spectrum and eigenfunctions. We find that the nature of the spin-wave excitations, whether they are hydrodynamic or localized modes, depends crucially on the relevance/irrelevance -- in the renormalization group sense -- of the correlations induced by the underlying classical order in the spin-wave Hamiltonian matrix elements: low-energy excitations around magnetically ordered states are delocalized, whereas those around spin-glass ordered states are localized, albeit weakly. We interpret this phenomenology by relating the spontaneous breaking of spin-rotation symmetry in the original Heisenberg model to the symmetry and universality class of the resulting quadratic spin-wave Hamiltonian. We conjecture that the hydrodynamic picture can be recovered through the inclusion of interactions among the spin-wave excitations at higher order in the semiclassical expansion, favoring the onset of ergodic behavior.

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arXiv2025

Scaling theory of fading ergodicity

In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $ν=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems.

cond-mat.stat-mech↗

arXiv2025

Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain

We analyze the spectral properties of the Heisenberg spin-1/2 chain with random fields in light of recent works of the renormalization-group flow of the Anderson model in infinite dimension. We reconstruct the beta function of the order parameter from the numerical data, and show that it does not admit a one-parameter scaling form and a simple Wilson-Fisher fixed point. Rather, it is compatible with a two-parameter, Berezinskii-Kosterlitz-Thouless-like flow with a line of fixed points (the many-body localized phase), which terminates into the localization transition critical point. Therefore, we argue that previous studies, which assumed the existence of an isolated Wilson- Fisher fixed point and performed one-parameter finite-size scaling analysis, could not explain the numerical data in a coherent way.

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arXiv2025

Exact results on the hydrodynamics of certain kinetically-constrained hopping processes

We consider a model of interacting random walkers on a triangular chain and triangular lattice, where a particle can move only if the other two sites of the triangle are unoccupied -- a kinetically-constrained hopping process (KCHP) recently introduced in the context of non-linear diffusion cascades. Using a classical-to-quantum mapping -- where the rate matrix of the stochastic KCHP corresponds to a spin Hamiltonian, and the equilibrium probability distribution to the quantum ground state -- we develop a systematic perturbation theory to calculate the diffusion constant; the hydrodynamics of the KCHPs is determined by the low-energy properties of the spin Hamiltonian, which we analyse with the standard Holstein-Primakoff spin-wave expansion. For the triangular hopping we consider, we show that \textit{non-interacting} spin-wave theory predicts the \textit{exact} diffusion constant. We conjecture this holds for all KCHPs with (i) hard-core occupancy, (ii) parity-symmetry, and (iii) where the hopping processes are given by three-site gates -- that is, where hopping between two sites is conditioned on the occupancy of a third. We further show that there are corrections to the diffusion constant when the KCHP is described by \textit{four}-site gates, which we calculate at leading order in the semi-classical $1/S$ expansion. We support all these conclusions with numerical simulations.

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arXiv2025

Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians

Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we propose Foundation Neural-Network Quantum States (FNQS) as an integrated paradigm for studying quantum many-body systems. FNQS leverage key principles of foundation models to define variational wave functions based on a single, versatile architecture that processes multimodal inputs, including spin configurations and Hamiltonian physical couplings. Unlike specialized architectures tailored for individual Hamiltonians, FNQS can generalize to physical Hamiltonians beyond those encountered during training, offering a unified framework adaptable to various quantum systems and tasks. FNQS enable the efficient estimation of quantities that are traditionally challenging or computationally intensive to calculate using conventional methods, particularly disorder-averaged observables. Furthermore, the fidelity susceptibility can be easily obtained to uncover quantum phase transitions without prior knowledge of order parameters. These pretrained models can be efficiently fine-tuned for specific quantum systems. The architectures trained in this paper are publicly available at https://huggingface.co/nqs-models, along with examples for implementing these neural networks in NetKet.

quant-ph↗

arXiv2025

Condensation of vanishing photon emission rates in random atomic clouds

In the collective photon emission from atomic clouds both the atomic transition frequency and the decay rate are modified compared to a single isolated atom, leading to the effects of superradiance and subradiance. In this article, we analyse the properties of the Euclidean random matrix associated to the radiative dynamics of a cold atomic cloud, previously investigated in the contexts of photon localization and Dicke super- and subradiance. We present evidence of a new type of phase transition, surprisingly controlled by the cooperativeness parameter, rather than the spatial density or the diagonal disorder. The numerical results corroborate the occurrence of such a phase transition at a critical value of the cooperativeness parameter, above which the lower edge of the spectrum vanishes exhibiting a macroscopic accumulation of eigenvalues. Independent evaluations based on the two phenomena provide the same value of the critical cooperativeness parameter.

quant-ph↗

arXiv2025

Scaling analysis and renormalization group on the mobility edge in the quantum random energy model

Building on recent progress in the study of Anderson and many-body localization via the renormalization group (RG), we examine the scaling theory of localization in the quantum Random Energy Model (QREM). The QREM is known to undergo a localization-delocalization transition at finite energy density, while remaining fully ergodic at the center of the spectrum. At zero energy density, we show that RG trajectories consistently flow toward the ergodic phase, and are characterized by an unconventional scaling of the fractal dimension near the ergodic fixed point. When the disorder amplitude is rescaled, as suggested by the forward scattering approximation approach, a localization transition emerges also at the center of the spectrum, with properties analogous to the Anderson transition on expander graphs. At finite energy density, a localization transition takes place without disorder rescaling, and yet it exhibits a scaling behavior analogous to the one observed on expander graphs. The universality class of the model remains unchanged under the rescaling of the disorder, reflecting the independence of the RG from microscopic details. Our findings demonstrate the robustness of the scaling behavior of random graphs and offer new insights into the many-body localization transition.

cond-mat.dis-nn↗

arXiv2025

A kinetically constrained model exhibiting non-linear diffusion and jamming

We present a classical kinetically constrained model of interacting particles on a triangular ladder, which displays diffusion and jamming and can be treated by means of a classical-quantum mapping. Interpreted as a theory of interacting fermions, the diffusion coefficient is the inverse of the effective mass of the quasiparticles which can be computed using mean-field theory. At a critical density \r{ho} = 2/3, the model undergoes a dynamical phase transition in which exponentially many configurations become jammed while others remain diffusive. The model can be generalized to two dimensions.

cond-mat.stat-mech↗

arXiv2025

Many-Body Localization in the Age of Classical Computing

Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. Persistent finite size drifts towards ergodicity consistently emerge in spectral properties of disordered many-body systems, excluding naive single-parameter scaling hypothesis and preventing comprehension of the status of the MBL phase. The drifts are related to tendencies towards thermalization and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength suggests the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.

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arXiv2024

Renormalization group for Anderson localization on high-dimensional lattices

We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $β$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson transition on random regular graphs. We show how in the delocalized region, including the transition point, the one-parameter scaling part of the $β$-function for the fractal dimension $D_{1}$ evolves smoothly from its $d=2$ form, in which $β_2\leq 0$, to its $β_\infty\geq 0$ form, which is represented by the regular random graph (RRG) result. We show how the $ε=d-2$ expansion and the $1/d$ expansion around the RRG result can be reconciled and how the initial part of a renormalization group trajectory governed by the irrelevant exponent $y$ depends on dimensionality. We also show how the irrelevant exponent emerges out of the high-gradient terms of expansion in the nonlinear sigma-model and put forward a conjecture about a lower bound for the fractal dimension. The framework introduced here may serve as a basis for investigations of disordered many-body systems and of more general non-equilibrium quantum systems.

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arXiv2024

Renormalization Group Analysis of the Anderson Model on Random Regular Graphs

We present a renormalization group analysis of the problem of Anderson localization on a Random Regular Graph (RRG) which generalizes the renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The renormalization group equations necessarily involve two parameters (one being the changing connectivity of sub-trees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the non-monotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of Many-Body Localization.

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arXiv2023

Subdiffusive spin transport in disordered classical Heisenberg chains

We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics, and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution. We propose a solvable phenomenological model that correctly yields the subdiffusive exponent, thereby linking local fluctuations in the coupling strengths to the long-time, large-distance behaviour. It also yields the finite-time corrections to the asymptotic scaling, which can be important in fitting the numerical data. We show how such exponents undergo transitions as the distribution of the coupling gets wider, marking the passage from diffusion to a regime of slow diffusion, and finally to subdiffusion.

cond-mat.stat-mech↗

arXiv2023

Stability of many-body localization in Floquet systems

We study many-body localization (MBL) transition in disordered Floquet systems using a polynomially filtered exact diagonalization (POLFED) algorithm. We focus on disordered kicked Ising model and quantitatively demonstrate that finite size effects at the MBL transition are less severe than in the random field XXZ spin chains widely studied in the context of MBL. Our conclusions extend also to other disordered Floquet models, indicating smaller finite size effects than those observed in the usually considered disordered autonomous spin chains. We observe consistent signatures of the transition to MBL phase for several indicators of ergodicity breaking in the kicked Ising model. Moreover, we show that an assumption of a power-law divergence of the correlation length at the MBL transition yields a critical exponent $ν\approx 2$, consistent with the Harris criterion for 1D disordered systems.

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arXiv2023

Universality in Anderson localization on random graphs with varying connectivity

We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder $W_{E}$ which is strictly less than the Anderson localization critical disorder $W_C$, and that of other works which suggest that there is no such region. We find that, although no separate $W_{E}$ exists from $W_C$, the length scale at which fully developed ergodicity is found diverges like $|W-W_C|^{-1}$, while the critical length over which delocalization develops is $\sim |W-W_C|^{-1/2}$. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.

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arXiv2023

Interface dynamics in the two-dimensional quantum Ising model

In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this paper, we elaborate more on the issue. First, we discuss two classes of initial states on the square lattice, the dynamics of which is driven by complementary terms in the effective Hamiltonian and may be solved exactly: (a) strips of consecutive neighbouring spins aligned in the opposite direction of the surrounding spins, and (b) a large class of initial states, characterized by the presence of a well-defined "smooth" interface separating two infinitely extended regions with oppositely aligned spins. The evolution of the latter states can be mapped onto that of an effective one-dimensional fermionic chain, which is integrable in the infinite-coupling limit. In this case, deep connections with noteworthy results in mathematics emerge, as well as with similar problems in classical statistical physics. We present a detailed analysis of the evolution of these interfaces both on the lattice and in a suitable continuum limit, including the interface fluctuations and the dynamics of entanglement entropy. Second, we provide analytical and numerical evidence supporting the conclusion that the observed non-ergodicity -- arising from Stark localization of the effective fermionic excitations -- persists away from the infinite-Ising-coupling limit, and we highlight the presence of a timescale $T\sim e^{c L\ln L}$ for the decay of a region of large linear size $L$. The implications of our work for the classic problem of the decay of a false vacuum are also discussed.

cond-mat.stat-mech↗

arXiv2023

Slow melting of a disordered quantum crystal

The melting of the corner of a crystal is a classical, real-world, non-equilibrium statistical mechanics problem which has shown several connections with other branches of physics and mathematics. For a perfect, classical crystal in two and three dimensions the solution is known: the crystal melts reaching a certain asymptotic shape, which keeps expanding ballistically. In this paper, we move onto the quantum realm and show that the presence of quenched disorder slows down severely the melting process. Nevertheless, we show that there is no many-body localization transition, which could impede the crystal to be completely eroded. We prove such claim both by a perturbative argument, using the forward approximation, and via numerical simulations. At the same time we show how, despite the lack of localization, the erosion dynamics is slowed from ballistic to logarithmic, therefore pushing the complete melting of the crystal to extremely long timescales.

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