arXiv subjects

Jovan Odavić

Publications and source records attributed to Jovan Odavić.

7 recordsLinked to original sources

arXiv2026

Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems

We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as our non-stabilizerness monotone, we derive the average and the variance for U(1)-constrained Haar random states. We show that the presence of a conserved charge leads to a substantial suppression of non-stabilizerness (magic) compared to the unconstrained case, and identify a qualitative difference between entanglement and magic response. In the thermodynamic limit, stabilizer entropy exhibits a different leading-order scaling close to a vanishing relative charge density, implying that magic is more robust to charge density fluctuations than entanglement entropy. We test our analytical predictions against midspectrum eigenstates of two chaotic many-body systems with conserved U(1) charge: the complex-fermion Sachdev-Ye-Kitaev (cSYK) model and a Heisenberg XXZ chain with next-to-nearest-neighbour couplings and conserved magnetization. We find an excellent agreement for the non-local cSYK model and systematic deviations for the local XXZ chain, highlighting the role of interaction locality.

quant-ph↗

arXiv2026

Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to study the chaotic content of a Hamiltonian $H$ via its associated random walk seen as a fractal, using the tools of fractal geometry. In particular we conjecture that for chaotic Hamiltonians the Hausdorff dimension of the frontier of the corresponding random walk approaches the universal value $d_F=4/3$ -- the same value obtained when the random walk describes a Wiener process. Our numerical simulations for non-integrable models confirm this expectation while for quasi-free integrable models we obtain a value $d_F = 1$. Additionally, we numerically show that ``Bethe Ansatz walkers'' fall into a category similar to the non-integrable walkers. To motivate this conjecture we consider many-body Hamiltonians with degenerate but rationally independent eigenvalues. We prove that if the degeneracies satisfy certain Lyapunov conditions, the random walk becomes a Wiener process, $d_F=4/3$, and the distribution of the SFF becomes Gaussian. This is the familiar Gaussian approximation for the SFF which we show to be violated at very low temperature. We also compute the moments of the SFF exactly under milder hypotheses thus solving the classical problem of determining the moments of a random walker taking steps of unequal lengths. Finally, we consider quasi-free Fermionic models with possibly degenerate but rationally independent one-particle spectra. We show that in this case the distribution of the SFF becomes log-Normal and also give the exact form of the moments under milder hypotheses.

quant-ph↗

arXiv2025

Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a microscopic theory of two-dimensional gravity. We study the interplay between Stabilizer Rényi Entropy (SRE) and entanglement entropy in both the ground state and highly excited states of the SYK4+SYK2 model interpolating the highly chaotic four-body interactions model with the integrable two-body interactions one. The interplay between these quantities is assessed also through universal statistics of the entanglement spectrum and its anti-flatness. We find that SYK4 is indeed characterized by a complex pattern of both entanglement and non-stabilizer resources while SYK2 is non-universal and not complex. We discuss the fragility and robustness of these features depending on the interpolation parameter.

quant-ph↗

arXiv2025

Stabilizer entropy in non-integrable quantum evolutions

Entanglement and stabilizer entropy are both involved in the onset of complex behavior in quantum many-body systems. Their interplay is at the root of complexity of simulability, scrambling, thermalization and typicality. In this work, we study the dynamics of entanglement, stabilizer entropy, and the anti-flatness of the entanglement spectrum after a quantum quench in a spin chain. We find that free-fermion theories show a gap in the long-time behavior of these resources compared to their random matrix theory value while non-integrable models saturate it.

quant-ph↗

arXiv2025

Long-distance genuine multipartite Entanglement between Magnetic Defects in Spin Chains

We investigate the emergence and properties of long-distance genuine multipartite entanglement, induced via three localized magnetic defects, in a one-dimensional transverse-field XX spin-$1/2$ chain. Using both analytical and numerical techniques, we determine the conditions for the existence of bound states localized at the defects. We find that the reduced density matrix (RDM) of the defects exhibits long-distance genuine multipartite entanglement (GME) across the whole range of the Hamiltonian parameter space, including regions where the two-qubit concurrence is zero. We quantify the entanglement by using numerical lower bounds for the GME concurrence, as well as by analytically deriving the GME concurrence in regions where the RDM is of rank two. Our work provides insights into generating multipartite entanglement in many-body quantum systems via local control techniques.

quant-ph↗

arXiv2023

Long-range entanglement and topological excitations

Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement (LRE) carried by a single, fractionalized excitation. We show this by considering a quantum, delocalized domain wall excitation that can be introduced into a system by inducing topological frustration in an antiferromagnetic spin chain. Furthermore, we study the resilience of LRE against a quantum quench and the introduction of disorder, thus establishing the existence of a phase with topological features despite not being a typical topological order or symmetry-protected one.

cond-mat.str-el↗

arXiv2020

Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of $10^4$ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.

cond-mat.str-el↗