arXiv subjects

Mohammad Javad Vasli

Publications and source records attributed to Mohammad Javad Vasli.

10 recordsLinked to original sources

arXiv2026

Krylov-Space Memory Cores

We introduce Krylov-space memory cores as stationary, depth-resolved structures that reveal how anomalous initial-state memory is organized inside the Krylov space of otherwise thermalizing nonintegrable systems. The stationary occupation profile identifies where late-time probability is concentrated along the Krylov chain, while complementary diagnostics of residual equilibration fluctuations, deviation from the Gibbs reference, and long-time Krylov-current fluctuations determine the physical character of that region. Across weak thermalization, confinement-induced anomalous dynamics, and many-body scarring, anomalous initial states develop compact low-depth memory cores that carry appreciable residual fluctuations, Gibbs mismatch, and persistent current-fluctuation activity. These cores are often embedded within substantially broader stationary occupation halos. The reference states considered, by contrast, do not exhibit a comparable combination of signal strength and spatial compactness. An auxiliary integrable comparison further shows that compact Krylov memory is state selective rather than a generic consequence of integrability. Krylov-space memory cores therefore provide a stationary framework for identifying where structured quantum memory resides and how it remains dynamically encoded.

hep-th↗

arXiv2026

Krylov Distribution and Spectral Convergence of Quantum Fisher Information

We establish a direct correspondence between the Krylov hierarchy of quantum Fisher information (QFI) and a Krylov-resolved decomposition of the symmetric logarithmic derivative (SLD). Building on the existing Krylov formulation of QFI, we show that the metrological information resolved at each Krylov level is exactly encoded in the incremental gain of the Lanczos hierarchy, giving the Krylov distribution a direct information-theoretic interpretation. A dual spectral formulation distinguishes the Hilbert--Schmidt geometry used to construct the computational Lanczos hierarchy from the state-dependent geometry in which the SLD and QFI are naturally defined, and relates their associated Liouville measures. This distinction clarifies the origin of different convergence regimes: we recover exponential convergence for gapped spectra and derive an exact algebraic hard-edge convergence law for the Jacobi class, including the exact finite-order error and the marginal case separating finite from divergent QFI.

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arXiv2026

Eigenstate Thermalization Hypothesis: A Primer

How does an isolated quantum system evolve toward thermal equilibrium from a far-from-equilibrium initial state-for instance, one prepared by a global quantum quench? This question has attracted significant interest in recent years. The Eigenstate Thermalization Hypothesis (ETH) provides a compelling framework for addressing it, with far-reaching implications from high-energy physics to condensed matter. This primer offers a pedagogical introduction to quantum equilibrium and ETH for a broad physics audience, particularly high-energy physicists seeking a comprehensive understanding of these topics. We assume only basic knowledge of quantum mechanics and statistical mechanics.

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arXiv2026

Krylov Distribution

We introduce the Krylov distribution $\mathcal{D}(ξ)$, a static Krylov-space diagnostic that characterizes how inverse-energy response is organized in Hilbert space. The central object is the resolvent-dressed state $(H-ξ)^{-1}|ψ_0\rangle$, whose decomposition in the Krylov basis generated from a reference state defines a normalized distribution over Krylov levels. Unlike conventional spectral functions, which resolve response solely along the energy axis, the Krylov distribution captures how the resolvent explores the dynamically accessible subspace as the spectral parameter $ξ$ is varied. Using asymptotic analysis, exact results in solvable models, and numerical studies of an interacting spin chain, we identify three universal regimes: saturation outside the spectral support, extensive growth within continuous spectra, and sublinear or logarithmic scaling near spectral edges and quantum critical points. We further show that fidelity susceptibility and the quantum geometric tensor admit natural decompositions in terms of Krylov-resolved resolvent amplitudes.

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arXiv2025

On Krylov Complexity as a Probe of the Quantum Mpemba Effect

We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional diagnostics such as the trace distance, while offering a complementary interpretation in terms of Hilbert-space exploration and dynamical delocalization. In $U(1)$-symmetric systems, we confirm that the recently proposed symmetric component of Krylov complexity serves as a robust and reliable indicator of the QME, capturing anomalous relaxation even in cases where the total complexity fails to do so.

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arXiv2025

Krylov Complexity as a Probe for Chaos

In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner in which complexity saturates reveals the chaotic nature of the system. In particular, we show that the dynamics towards saturation precisely distinguish between chaotic and integrable systems. For chaotic models, the saturation value of complexity reaches its infinite time average at a finite saturation time. In this case, depending on the initial state, it may also exhibit a peak before saturation. In contrast, in integrable models, complexity approaches the infinite time average value from below at a much longer timescale. We confirm this distinction using numerical results for specific spin models.

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arXiv2025

Holographic Study of Reflected Entropy in Anisotropic Theories

We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using this prescription, we study in detail the effect of anisotropy on reflected entropy and other holographic entanglement measures. In particular, we study the discontinuous phase transition of this quantity for a symmetric configuration consisting of two disjoint strips. We find that in the specific regimes of the parameter space the critical separation is an increasing function of the anisotropy parameter and hence the correlation between the subregions becomes more pronounced. We carefully examine how these results are consistent with the behavior of other correlation measures including the mutual information. Finally, we show that the structure of the universal terms of entanglement entropy is corrected depending on the orientation of the entangling region with respect to the anisotropic direction.

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arXiv2025

Thermalization in Krylov Basis

We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix are exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity.

quant-ph↗

arXiv2024

Entanglement in Lifshitz Fermion Theories

We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys. 11, no.2, 031 (2021)] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed.

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arXiv2021

Entanglement Wedge Cross Section in Holographic Excited States

We evaluate the entanglement wedge cross section (EWCS) in asymptotically AdS geometries which are dual to boundary excited states. We carry out a perturbative analysis for calculating EWCS between the vacuum and other states for a symmetric configuration consisting of two disjoint strips and obtain analytical results in the specific regimes of the parameter space. In particular, when the states described by purely gravitational excitations in the bulk we find that the leading correction to EWCS is negative and hence the correlation between the boundary subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. Our study reveals some generic properties of boundary information measures dual to EWCS, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.

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