arXiv subjects

Vincenzo Alba

Publications and source records attributed to Vincenzo Alba.

At least 19 recordsLinked to original sources

arXiv2026

Out-of-equilibrium inhomogeneous XX chains: Exact results and the hydrodynamic limit

We study the out-of-equilibrium dynamics in the XX chain with step-like magnetic field, which maps to an inhomogeneous tight-binding chain after Jordan-Wigner transformation. We obtain exact analytic expressions for the fermionic two-point correlation function after a quantum quench from several initial product states, both homogeneous and inhomogeneous ones. This is achieved by using a combination of Fourier and Laplace transforms, which al low us to map the problem to a standard Riemann-Hilbert problem on the unit circle. For arbitrary positions and times the correlators are not expressed in terms of elementary functions. However, in the hydrodynamic limit $x,y,t\to\infty$ with fixed ratios, we provide explicit formulas that depend only on the effective transmission coefficient across the origin. We benchmark our analytic predictions against exact numerical simulations and find excellent agreement in the hydrodynamic limit, apart from finite-time corrections.

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arXiv2026

Fate of entanglement in quadratic Markovian dissipative systems

We develop a hydrodynamic description for the driven-dissipative dynamics of the entanglement negativity, which quantifies the genuine entanglement in mixed-state systems. We focus on quantum quenches in fermionic and bosonic systems subject to linear dissipation, as described by quadratic Lindblad master equations. In the spirit of hydrodynamics, we divide the system into mesoscopic cells. At early times, correlations are generated in each cell by the unitary component of the evolution. Correlations are then transported across different cells via ballistic quasiparticle propagation, while simultaneously evolving under the action of the environment. We show that in the hydrodynamic limit the negativity can be reconstructed from the correlations between the independently propagating quasiparticles. We benchmark our approach considering quenches from both homogeneous and inhomogeneous initial states in the Kitaev chain, the tight-binding chain, and the harmonic chain in the presence of gain/loss dissipation.

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arXiv2026

Inhomogeneous quenches and GHD in the $ν= 1$ QSSEP model

We investigate the dynamics of the $ν=1$ Quantum Symmetric Simple Exclusion Process starting from spatially inhomogeneous initial states. This one-dimensional system of free fermions has time-dependent stochastic hopping amplitudes that are uniform in space. We focus on two paradigmatic setups: domain-wall melting and the expansion of a trapped gas. Both are investigated by extending the framework of quantum generalized hydrodynamics to account for the underlying stochastic dynamics. We derive the evolution of the local quasiparticle occupation function, which characterizes the system at large space-time scales, and analyze the resulting entanglement spreading. By incorporating quantum fluctuations of the occupation function and employing conformal field theory techniques, we obtain the exact contribution to the entanglement entropy for each individual noise realization. Averaging over these realizations then yields the full entanglement statistics in the hydrodynamic regime. Our theoretical predictions are confirmed by exact numerical calculations. The results presented here constitute the first application of quantum generalized hydrodynamics to stochastic quantum systems, demonstrating that this framework can be successfully extended beyond purely unitary dynamics to include stochastic effects.

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arXiv2026

Dynamics of entanglement fluctuations and quantum Mpemba effect in the $ν=1$ QSSEP model

We study the out-of-equilibrium dynamics of entanglement fluctuations in the $ν=1$ Quantum Symmetric Simple Exclusion Process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous work showed that the average entanglement growth after a quantum quench can be explained in terms of pairs of entangled quasiparticles performing random walks, leading to diffusive entanglement spreading. By incorporating the noise-induced statistical correlations between the quasiparticles, we extend this description to the full-time probability distribution of the entanglement entropy. Our generalized quasiparticle picture allows us to compute the average time evolution of a generic function of the reduced density matrix of a subsystem. We also apply our result to the entanglement asymmetry. This allows us to investigate the restoration of particle-number symmetry in the dynamics from initial states with no well-defined particle number. Regarding the possible existence of the quantum Mpemba effect, our analysis indicates that its occurrence is an extremely fine-tuned phenomenon, requiring very specific conditions and therefore being rather difficult to observe in practice.

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arXiv2026

$ν$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems

We investigate out-of-equilibrium entanglement dynamics in a generalization of the so-called $QSSEP$ model, which is a free-fermion chain with stochastic in space and time hopping amplitudes. In our setup, the noisy amplitudes are spatially-modulated satisfying a $ν$-site translation invariance but retaining their randomness in time. For each noise realization, the dynamics preserves Gaussianity, which allows to obtain noise-averaged entanglement-related quantities. The statistics of the steady-state correlators satisfy nontrivial relationships that are of topological nature. They reflect the Haar invariance under multiplication with structured momentum-dependent random $SU(ν)$ matrices. We discuss in detail the case with $ν=1$ and $ν=2$. For $ν=1$, i.e., spatially homogeneous noise we show that the entanglement dynamics is describable by a stochastic generalization of the quasiparticle picture. Precisely, entanglement is propagated by pairs of quasiparticles. The entanglement content of the pairs is the same as for the deterministic chain. However, the trajectories of the quasiparticles are random walks, giving rise to diffusive entanglement growth.

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arXiv2026

Entanglement dynamics after quenches with inhomogeneous Hamiltonians

We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schrödinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.

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arXiv2026

Smearing of dynamical quantum phase transitions in dissipative free-fermion systems

We investigate the Lindblad dynamics of the reduced Loschmidt echo (RLE) in dissipative quadratic fermion systems. Focusing on the case of gain and loss dissipation, we derive general conditions for the persistence of nonanalyticities (so-called dynamical quantum phase transitions) in the time evolution of the RLE. We show that nonanalyticities that are present in the corresponding unitary dynamics can survive under purely gain or purely loss processes, but are completely smeared out as soon as both channels are active, even if one is infinitesimally small. These results hold for generic dissipative Gaussian evolutions, and are illustrated explicitly for the quench from the Néel state in the tight-binding chain, as well as for the quantum Ising chain. We also show that the subtle interplay between dissipative and unitary dynamics gives rise to a nested lightcone structure in the dynamics of the RLE, even in cases where this structure is not present in the corresponding unitary evolution, due to coherent cancellations in the phase structure of the wavefunction.

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arXiv2026

The non-stabilizerness of fermionic Gaussian states

We introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states, overcoming the long-standing challenge posed by their extensive entanglement. Using a perfect sampling scheme based on an underlying determinantal point process, we compute the Stabilizer Renyi Entropies (SREs) for systems with hundreds of qubits. Benchmarking on random Gaussian states with and without particle conservation, we reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections. We support these findings with analytical calculations for a set of related quantities, the participation entropies in the computational (or Fock) basis, for which we derive an exact formula. We also investigate the time evolution of non-stabilizerness in a random unitary circuit with Gaussian gates, observing that it converges in a time that scales logarithmically with the system size. Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in non-stabilizerness at the phase boundaries, highlighting the power of our approach in exploring different phases of quantum many-body systems, even in higher dimensions.

quant-ph↗

arXiv2026

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains

We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different macrostates. In the former case, focusing on thermal states we numerically show that matrix elements are compatible with the exponential decay as $\exp(-L |{M}^{\scriptscriptstyle{\mathcal{O}}}_{ij}|)$. The probability distribution functions of ${M}_{ij}^{\scriptscriptstyle{\mathcal{O}}}$ depend on the observable and on the macrostate, and are well described by Gumbel distributions. On the other hand, matrix elements between eigenstates in different macrostates decay faster as $\exp(-|{M'}_{ij}^{\scriptscriptstyle{\mathcal{O}}}|L^2)$, with ${M'}_{ij}^{\scriptscriptstyle \mathcal{O}}$, again, compatible with a Gumbel distribution.

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arXiv2026

Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect

We investigate the out-of-equilibrium dynamics after a quantum quench of the reduced fidelities between the states of a subregion $A$ at different times. Precisely, we consider the fidelity between the time-dependent state of $A$ and its initial value, as well as with the state at infinite time. We denote these fidelities as the reduced Loschmidt echo (RLE) and the final-state fidelity (FSF), respectively. If region $A$ is the full system, the RLE coincides with the standard Loschmidt echo. We focus on quenches from Gaussian states in several instances of the XY spin chain. In the hydrodynamic limit of long times and large sizes of $A$, with their ratio fixed, the reduced fidelities admit a quasiparticle picture interpretation. Interestingly, for some quenches in the hydrodynamic regime the RLE features a complicated structure with an infinite sequence of nested lightcones, corresponding to quasiparticles with arbitrary large group velocities. This leads to a ''staircase'' of cusp-like singularities in the time-derivative of the fidelity. At the sub-hydrodynamic regime for some quenches the RLE exhibits cusp-like singularities, similar to the so-called dynamical quantum phase transitions (DQPT). We conjecture a criterion for the occurrence of the DQPT and for the ''critical'' times at which the singularities occur. Finally, we discuss the hydrodynamic limit of the FSF. In particular, we show that it provides a valuable tool to detect the so-called quantum Mpemba effect.

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arXiv2025

Universality of equilibration dynamics after quantum quenches

We investigate the distribution of the eigenvalues of the reduced density matrix (entanglement spectrum) after a global quantum quench. We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits ``universality''. In the scaling limit and at asymptotically long times the distribution of the entanglement spectrum depends on two parameters that can be determined from the Rényi entropies. We show that two typical scenarios occur. In the first one, the distribution of the entanglement spectrum levels is similar to the one describing the ground-state entanglement spectrum in Conformal Field Theories. In the second scenario, the lower levels of the entanglement spectrum are highly degenerate and their distribution is given by a series of Dirac deltas. We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.

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arXiv2025

More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking

We investigate the dynamics of the Rényi Operator Space Entanglement ($OSE$) entropies $S_n$ across several one-dimensional integrable and chaotic models. As a paradigmatic integrable system, we first consider the so-called rule $54$ chain. Our numerical results reveal that the Rényi $OSE$ entropies of diagonal operators with nonzero trace saturate at long times, in contrast with the behavior of von Neumann entropy. Oppositely, the Rényi entropies of traceless operators exhibit logarithmic growth with time, with the prefactor of this growth depending in a nontrivial manner on $n$. Notably, at long times, the complete operator entanglement spectrum ($ES$) of an operator can be reconstructed from the spectrum of its traceless part. We observe a similar pattern in the $XXZ$ chain, suggesting universal behavior. Additionally, we consider dynamics in nonintegrable deformations of the $XXZ$ chain. Finite-time corrections do not allow to access the long-time behavior of the von Neumann entropy. On the other hand, for $n>1$ the growth of the entropies is milder, and it is compatible with a sublinear growth, at least for operators associated with global conserved quantities. Finally, we show that in finite-size integrable systems, $S_n$ exhibit strong revivals, which are washed out when integrability is broken.

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arXiv2025

Free fermions with dephasing and boundary driving: Bethe Ansatz results

By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe ansatz to diagonalize the Liouvillian ${\mathcal L}^{\scriptscriptstyle(2)}$ governing the dynamics of the correlator. The majority of its energy levels are complex. Precisely, $L(L-1)/2$ complex energies do not depend on dephasing, apart for a trivial shift. The remaining complex levels are perturbatively related to the dephasing-independent ones for large $L$. The long-time dynamics is governed by a band of real energies, which contains an extensive number of levels. They give rise to diffusive scaling at intermediate times, when boundaries can be neglected. Moreover, they encode the breaking of diffusion at asymptotically long times. Interestingly, for large loss rate two boundary modes appear in the spectrum. The real energies correspond to string solutions of the Bethe equations, and can be treated effectively for large chains. This allows us to derive compact formulas for the dynamics of the fermionic density. We check our results against exact diagonalization, finding perfect agreement.

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arXiv2024

Bound-state confinement after trap-expansion dynamics in integrable systems

Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$ anisotropic Heisenberg chain ($XXZ$ chain). Specifically, we consider the sudden vacuum expansion of a finite region $A$ prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of $A$. Since region $A$ is finite, at asymptotically long times bound states are "liberated" after the "evaporation" of all the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the $p$-Néel states, which are obtained by repetition of a unit cell with $p$ up spins followed by $p$ down spins. Upon increasing $p$, the bound-state content is enhanced. In the limit $p\to\infty$ one obtains the domain-wall initial state. We show that for $p<4$, only bound states with $n>p$ are confined at large chain anisotropy. For $p\gtrsim 4$, also bound states with $n=p$ are confined, consistent with the absence of transport in the limit $p\to\infty$. The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.

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arXiv2024

Steady-state entanglement scaling in open quantum systems: A comparison between several master equations

We investigate the scaling of the fermionic logarithmic negativity (FLN) between complementary intervals in the steady state of a driven-dissipative tight-binding critical chain, coupled to two thermal reservoirs at its edges. We compare the predictions of three different master equations, namely a nonlocal Lindblad equation, the Redfield equation, and the recently proposed universal Lindblad equation (ULE). Within the nonlocal Lindblad equation approach, the FLN grows logarithmically with the subsystem size $\ell$, for any value of the system-bath coupling and of the bath parameters. This is consistent with the logarithmic scaling of the mutual information analytically demonstrated in [Phys. Rev. B 106, 235149 (2022)]. In the ultraweak-coupling regime, the Redfield equation and the ULE exhibit the same logarithmic increase; such behavior holds even when moving to moderately weak coupling and intermediate values of $\ell$. However, when venturing beyond this regime, the FLN crosses over to superlogarithmic scaling for both equations.

quant-ph↗

arXiv2024

Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems

Recently, the entanglement asymmetry emerged as an informative tool to understand dynamical symmetry restoration in out-of-equilibrium quantum many-body systems after a quantum quench. For integrable systems the asymmetry can be understood in the space-time scaling limit via the quasiparticle picture, as it was pointed out in Ref. [1]. However, a quasiparticle picture for quantum quenches from generic initial states was still lacking. Here we conjecture a full-fledged quasiparticle picture for the charged moments of the reduced density matrix, which are the main ingredients to construct the asymmetry. Our formula works for quenches producing entangled multiplets of an arbitrary number of excitations. We benchmark our results in the $XX$ spin chain. First, by using an elementary approach based on the multidimensional stationary phase approximation we provide an $\textit{ab initio}$ rigorous derivation of the dynamics of the charged moments for the quench treated in [2]. Then, we show that the same results can be straightforwardly obtained within our quasiparticle picture. As a byproduct of our analysis, we obtain a general criterion ensuring a vanishing entanglement asymmetry at long times. Next, by using the Lindblad master equation, we study the effect of gain and loss dissipation on the entanglement asymmetry. Specifically, we investigate the fate of the so-called quantum Mpemba effect (QME) in the presence of dissipation. We show that dissipation can induce QME even if unitary dynamics does not show it, and we provide a quasiparticle-based interpretation of the condition for the QME.

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arXiv2023

Negative tripartite mutual information after quantum quenches in integrable systems

We build the quasiparticle picture for the tripartite mutual information (TMI) after quantum quenches in spin chains that can be mapped onto free-fermion theories. A nonzero TMI (equivalently, topological entropy) signals quantum correlations between three regions of a quantum many-body system. The TMI is sensitive to entangled multiplets of more than two quasiparticles, i.e., beyond the entangled-pair paradigm of the standard quasiparticle picture. Surprisingly, for some nontrivially entangled multiplets the TMI is negative at intermediate times. This means that the mutual information is monogamous, similar to holographic theories. Oppositely, for multiplets that are "classically" entangled, the TMI is positive. Crucially, a negative TMI reflects that the entanglement content of the multiplets is not directly related to the Generalized Gibbs Ensemble (GGE) that describes the post-quench steady state. Thus, the TMI is the ideal lens to observe the weakening of the relationship between entanglement and thermodynamics. We benchmark our results in the XX chain and in the transverse field Ising chain. In the hydrodynamic limit of long times and large intervals, with their ratio fixed, exact lattice results are in agreement with the quasiparticle picture.

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arXiv2023

Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

We derive the quasiparticle picture for the fermionic logarithmic negativity in a tight-binding chain subject to gain and loss dissipation. We focus on the dynamics after the quantum quench from the fermionic Néel state. We consider the negativity between both adjacent and disjoint intervals embedded in an infinite chain. Our result holds in the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed. Additionally, we consider the weakly-dissipative limit, in which the dissipation rates are inversely proportional to the size of the intervals. We show that the negativity is proportional to the number of entangled pairs of quasiparticles that are shared between the two intervals, as is the case for the mutual information. Crucially, in contrast with the unitary case, the negativity content of quasiparticles is not given by the Rényi entropy with Rényi index 1/2, and it is in general not easily related to thermodynamic quantities.

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