arXiv subjects

Federico Balducci

Publications and source records attributed to Federico Balducci.

At least 19 recordsLinked to original sources

arXiv2026

Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets

The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.

cond-mat.quant-gas↗

arXiv2026

(Non-)Traversable Quantum Phase Transitions

Quantum phase transitions manifest as an abrupt change in the ground state of a many-body system; yet it is an open question whether this sudden change necessarily precludes a continuous dynamical connection between the two phases. We introduce a classification of quantum phase transitions based on this geometric aspect of the ground-state manifold, that differs from known classifications. By leveraging the framework of counterdiabatic driving, we explicitly construct schedules that dynamically connect one phase to another. This strategy allows us to uncover a large class of quantum phase transitions, where the states on both sides are separated only by a finite geometric distance in the thermodynamic limit. We term such transitions traversable, since exact counterdiabatic driving links the two phases via a finite dynamical protocol in the thermodynamic limit. We show that multiple known transitions fall into this class -- e.g., symmetry-breaking transitions obeying hyperscaling and discontinuous transitions with an enhanced continuous symmetry. We further show the existence of quantum phase transitions that cannot be crossed dynamically even with the help of nonlocal counterdiabatic driving, as they would require divergent amplitudes and frequencies. Geometrically, these nontraversable transitions correspond to an infinite distance separating the two phases of matter; we show that the class comprises continuous transitions exhibiting mean-field universality, and discontinuous transitions arising from the competition between metastable minima. Our geometric classification goes beyond the known taxonomy, is independent of local order parameters and renormalization group fixed points, and has direct implications for the complexity of state preparation and adiabatic quantum computation.

quant-ph↗

arXiv2026

Perspective: Interactions and Nonlinearity in Non-Hermitian Physics

For decades, Hermiticity was considered an immutable axiom of quantum mechanics, essential for ensuring real energies and unitary evolution. This perspective has shifted radically, driven by the realization that non-Hermitian Hamiltonians provide a powerful effective description of open quantum systems, granting access to unique phenomena such as Exceptional Points and the Non-Hermitian Skin Effect. In this Perspective, we chart the trajectory of this field, moving from its established foundations in single-particle, linear models to the emerging frontier of interacting many-body systems. We first clarify the physical origins of non-Hermitian dynamics, distinguishing between mean-field approximations, conditional "no-click" evolution, and exact Liouvillian dynamics. We then focus on the rich phenomenology arising from the interplay of non-Hermiticity and interactions. We discuss interaction-induced topological phases, the generalization of skin effects to the many-body Hilbert space, and the distinct signatures of dissipative quantum chaos and complexity. Finally, we highlight collective phenomena in nonlinear regimes, including skin solitons and dissipative phase transitions. We also comment on measurement-induced entanglement transitions and their relation to non-Hermitian spectra and topology. By synthesizing these diverse developments, we provide a roadmap for the future of non-Hermitian physics.

quant-ph↗

arXiv2025

The deep Hilbert space of all-to-all interacting SU(3) atoms: from quantum to classical

We study the emergence of chaos in multilevel atoms with all-to-all interactions, inspired by cavity QED. Focusing on a 3-level Tavis-Cummings model in a far detuned limit, we detail its deep Hilbert space structure -- i.e. we enumerate all distinct dynamical sectors, beyond the totally symmetric subspace -- by using the Schur-Weyl duality, which is applicable thanks to the permutation symmetry in the all-to-all Hamiltonian. Strong Hilbert space fragmentation ensues from the non-abelian nature of the symmetry, with some sectors displaying regular dynamics and others being chaotic. We uncover that many permutation symmetry sectors contribute to the dynamics in the classical limit, in addition to the commonly studied totally symmetric subspace. To elucidate the dynamical responses in each of the symmetry sectors, we propose a semiclassical description in terms of spin coherent states, which is also able to explain the origin of chaotic or regular dynamics with a simple geometrical argument. Our work contributes to the study of the quantum-classical correspondence in chaotic systems, and uncovers a rich structure in multilevel all-to-all interacting models.

quant-ph↗

arXiv2025

Domain coarsening in fractonic systems: a cascade of critical exponents

We study the dynamics of domain growth when multipole moments of the order parameter are conserved. Following a quench into the ordered phase of the Ising model, the typical size of domains grows with time as $R(t) \sim t^{1/2}$ in the absence of conserved quantities. When the order parameter is conserved, the domain growth slows to $R(t) \sim t^{1/3}$. Conservation of higher moments of the order parameter fundamentally modifies this behavior: coarsening proceeds via anomalously slow growth. We analytically and numerically show that conservation of the $m$-th multipole moment causes domains to grow as $R(t) \sim t^{1/(2m+3)}$. This cascade of dynamical critical exponents characterizes a new family of non-equilibrium universality classes for fractonic systems.

cond-mat.stat-mech↗

arXiv2025

Symmetry re-breaking in an effective theory of quantum coarsening

We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [T. Manovitz et al., Nature \textbf{638}, 86 (2025)]: an apparent speeding up of the coarsening process as the phase transition is approached; and persistent oscillations of the order parameter after quenches within the ordered phase. Our theory, based on the Hamiltonian structure of the equations of motion in the classical limit of the quantum model, finds a speeding up already deep within the ordered phase, with subsequent slowing down as the domain wall tension vanishes upon approaching the critical line. Further, the oscillations are captured within a mean-field treatment of the order parameter field. For quenches within the ordered phase, small spatially-varying fluctuations in the initial mean-field lead to a remarkable long-time effect, wherein the system dynamically destroys its long-range order and has to coarsen to re-establish it. We term this phenomenon \emph{symmetry re-breaking}, as the resulting late-time magnetization can have a sign opposite to the initial magnetization.

cond-mat.stat-mech↗

arXiv2025

Non-Hermitian Multipole Skin Effects Challenge Localization

We study the effect of quenched disorder on the non-Hermitian skin effect in systems that conserve a U(1) charge and its associated multipole moments. In particular, we generalize the Hatano-Nelson argument for a localization transition in disordered, non-reciprocal systems to the interacting case. When only U(1) charge is conserved, we show that there is a transition between a skin effect phase, in which charges cluster at a boundary, and a many-body localized phase, in which charges localize at random positions. In the dynamics of entanglement, this coincides with an area to volume law transition. For systems without boundaries, the skin effect becomes a delocalized phase with a unidirectional current. If dipoles or higher multipoles are conserved, we show that the non-Hermitian skin effect remains stable to arbitrary disorder. Counterintuitively, the system is therefore always delocalized under periodic boundary conditions, regardless of disorder strength.

cond-mat.dis-nn↗

arXiv2025

Finite steady-state current defies non-Hermitian many-body localization

Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a non-commutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understand localization in non-Hermitian settings.

cond-mat.dis-nn↗

arXiv2025

Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model

We study the crossing of the quantum phase transition in the transverse-field Ising model after modulating the magnetic field at an arbitrary rate, exploring the critical dynamics from the slow to the sudden quench regime. We do so by analyzing the defect density, the complete kink number distribution, and its cumulants upon completion of a linearized quench. Our analysis relies on the diagonalization of the model using the standard Jordan-Wigner and Fourier transformations, along with the exact solution of the time evolution in each mode in terms of parabolic cylinder functions. The free-fermion nature of the problem dictates that the kink number distribution is associated with independent and distinguishable Bernoulli variables, each with a success probability $p_k$. We employ a combination of convergent and asymptotic series expansions to characterize $p_k$ without restrictions on the driving rate. When the latter is approximated by the Landau-Zener formula, the kink density is described by the Kibble-Zurek mechanism, and higher-order cumulants follow a universal power-law behavior, as recently predicted theoretically and verified in the laboratory. By contrast, for moderate and sudden driving protocols, the cumulants exhibit a nonuniversal behavior that is not monotonic on the driving rate and changes qualitatively with the cumulant order. The kink number statistics remain sub-Poissonian for any driving rate, as revealed by an analysis of the cumulant rations that vary nonmonotonically from the sudden to the slow-driving regime. Thanks to the determination of $p_k$ for an arbitrary rate, our study provides a complete analytical understanding of kink number statistics from the slow driving regime to the sudden quench limit.

cond-mat.stat-mech↗

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↗

arXiv2024

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.

cond-mat.dis-nn↗

arXiv2024

Fighting Exponentially Small Gaps by Counterdiabatic Driving

We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through exponentially small gaps. First, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving a fully adiabatic evolution remains challenging. Extending our investigation to realistic NP-hard spin-glass problems -- specifically, the $3$-regular \textsc{Max Cut} and $3$-\textsc{XORSAT} -- we find again that local CD expansions lead to negligible improvements in the final ground state fidelity. These results highlight the limited impact of local CD methods in overcoming the bottlenecks associated with first-order quantum phase transitions. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which employs the approximate full CD connecting the ground state and the first excited state at a single parameter value close to the critical point. In the minimal spin-glass model, QBCD enables exponentially faster adiabatic evolution than the local strategies. To alleviate the challenges of its experimental and classical implementation for realistic \textsc{NP}-hard problems, we exponentially reduce the non-locality of the QBCD Hamiltonian by sparsifying its matrix elements to the density of the local expansions. Despite this drastic simplification, sparsified QBCD maintains finite ground-state fidelity at driving times exponentially shorter than in local strategies and counterdiabatic optimized local driving (COLD).

quant-ph↗

arXiv2024

Non-Adiabatic Quantum Optimization for Crossing Quantum Phase Transitions

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model.

quant-ph↗

arXiv2023

Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition

Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized (MBL) phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. Through the use of the singular value decomposition and the introduction of new diagnostic tools complementing the singular-value statistics, namely, the singular form factor, the inverse participation ratio, and entanglement entropy for singular vectors, we provide a positive answer. Our method is illustrated in an XXZ Hamiltonian with random local dissipation.

quant-ph↗

arXiv2023

Large Deviations Beyond the Kibble-Zurek Mechanism

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.

quant-ph↗

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

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.

cond-mat.dis-nn↗