Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators

• URL: http://arxiv.org/abs/2601.02877v1
• Date: Tue, 06 Jan 2026 10:04:29 GMT
• Title: Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators
• Authors: Akshay Kulkarni, Rahul Nigam,
• Abstract summary: We map a Yukawa-type interaction to an effective harmonic oscillator system with controlled anharmonic perturbations.<n>We compute the leading non-Gaussian correction from the quartic interaction $4$, which appears at order $2$ in the expansion of the Yukawa-like potential.<n>Our results clarify the roles of harmonic renormalization and genuinely non-Gaussian interactions in generating entanglement.
• Score: 0.03437656066916039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate interaction-induced corrections to entanglement entropy by mapping a screened Yukawa-type interaction to an effective harmonic oscillator system with controlled anharmonic perturbations. Starting from a one-dimensional interaction $V(x) = -g^2 e^{-αm x}/x$, we reformulate the problem in terms of a four-dimensional radial oscillator, where the finite screening length generates a systematic hierarchy of polynomial interactions in the radial coordinate. This mapping enables a controlled Rayleigh-Schrodinger perturbative treatment of the ground-state wavefunction and an explicit spectral analysis of the reduced density matrix. Working in the weak-screening regime, we compute the leading non-Gaussian correction arising from the quartic interaction $ρ^4$, which appears at order $α^2$ in the expansion of the Yukawa-like potential. We obtain closed analytic expressions for the resulting small eigenvalues of the reduced density matrix and evaluate their contribution to the von Neumann entanglement entropy. We show that the entropy receives analytic corrections at order $α^2$, originating both from explicit anharmonic state-mixing effects and from the implicit $α$ dependence of the Gaussian width parameter. Our results clarify the distinct roles of harmonic renormalization and genuinely non-Gaussian interactions in generating entanglement, establish a systematic power-counting and normalization scheme for higher-order $ρ^{2n}$ perturbations, and provide a transparent oscillator-based framework for computing entanglement entropy in weakly interacting low-dimensional and field-theoretic systems.

Related papers

• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Numerical study of non-relativistic quantum systems and small oscillations induced in a helically twisted geometry [0.0]
  We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry.<n>The dynamics is described by the Schrdinger equation on a curved spatial background.<n>We compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem.
  arXiv  Detail & Related papers  (2026-02-18T18:39:54Z)
• Perturbative Input-Output Theory of Floquet Cavity Magnonics and Magnon Energy Shifts [0.0]
  We compute reflectance and transmittance spectra of cavity magnonics systems subject to a Floquet modulation.<n>We reproduce the characteristic sideband structure observed in recent Floquet cavity electromagnonics experiments.
  arXiv  Detail & Related papers  (2025-12-13T00:29:45Z)
• Parametric resonant enhancement of motional entanglement under optimal control: an analytical study [45.88028371034407]
  We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction.<n>We perform a detailed analysis of the parametric resonance induced by temporal modulation of the coupling strength, based on the system's coupled nonlinear, nonhomogeneous dynamical equations.<n>We demonstrate that a stationary nonequilibrium entangled state is realized as a result of the competition between parametric gain and decoherence.
  arXiv  Detail & Related papers  (2025-10-21T09:01:19Z)
• Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow [44.500314182711236]
  We derive explicit ordinary equations govern the evolution of mean, covariance, and mass under HK-Boltzmann flow.<n>We demonstrate exponential convergence to equilibrium through constructing a gradient structure associated with a Polyak-Lojasiewicz-type inequalities.<n>We extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity.
  arXiv  Detail & Related papers  (2025-04-29T03:54:56Z)
• Momentum-Resolved Probing of Lorentz-Violating Dispersion Relations via Unruh-DeWitt Detector [6.034968381804006]
  We probe Lorentz symmetry violation via modified dispersion relations $omega_|textbfk|$.<n>We employ an Unruh-DeWitt detector to probe energy-dependent modifications to the dispersion relations.<n>Our approach offers a scalable method to test Lorentz symmetry violation across energy scales, and establishes a foundation for experimental verification of Planck-scale relics.
  arXiv  Detail & Related papers  (2025-03-22T12:43:49Z)
• Measurement-induced Lévy flights of quantum information [35.31418199674737]
  We explore a model of free fermions in one dimension subject to frustrated local measurements across adjacent sites.<n>For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate.<n>Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians.
  arXiv  Detail & Related papers  (2025-01-22T14:29:13Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations.<n>Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM)<n>By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems [0.0]
  We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds for their entanglement entropy. Our methods result in a logarithmically corrected area law for the entanglement of eigenstates, corresponding to one excitation.
  arXiv  Detail & Related papers  (2024-04-08T13:51:02Z)
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model [0.0]
  We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$frac12$ XYZ chain. We find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that universally of quantum-chaotic interacting models.
  arXiv  Detail & Related papers  (2023-11-17T19:00:09Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Entanglement in interacting quenched two-body coupled oscillator system [0.653972432012203]
  We use the invariant operator method, under a perturbative framework, for computing the ground state of this system. We show the analytical calculation of two entanglement measures viz., Von Neumann entanglement entropy using replica trick and Renyi entanglement entropy. We comment on the variation of these entanglement measures for different orders of coupling strength.
  arXiv  Detail & Related papers  (2022-04-11T18:00:03Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.