Entanglement Entropy for Screened Interactions via Dimensional Mapping to Harmonic Oscillators

Chisanupong Puttarprom, Monsit Tanasittikisol, Sikarin Yoo-Kong

Akshay Kulkarni, Rahul Nigam

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.

M. Ghasemi Nezhadhaghighi, M. A. Rajabpour

We study different aspects of quantum von Neumann and R\'enyi entanglement entropy of one-dimensional long-range harmonic oscillators that can be described by well-defined nonlocal field theories. We show that the entanglement entropy of one interval with respect to the rest changes logarithmically with the number of oscillators inside the subsystem. This is true also in the presence of different boundary conditions. We show that the coefficients of the logarithms coming from different boundary conditions can be reduced to just two different universal coefficients. We also study the effect of the mass and temperature on the entanglement entropy of the system in different situations. The universality of our results is also confirmed by changing different parameters in the coupled harmonic oscillators. We also show that more general interactions coming from general singular Toeplitz matrices can be decomposed to our long-range harmonic oscillators. Despite the long-range nature of the couplings, we show that the area law is valid in two dimensions and the universal logarithmic terms appear if we consider subregions with sharp corners. Finally, we study analytically different aspects of the mutual information such as its logarithmic dependence to the subsystem, effect of mass, and influence of the boundary. We also generalize our results in this case to general singular Toeplitz matrices and higher dimensions.

K. M. R. Audenaert, Jens Eisert, Martin Bodo Plenio

Nicolás Quesada

Arash Jafarizadeh, M. A. Rajabpour

We study general entanglement properties of the excited states of the one-dimensional translational invariant free fermions and coupled harmonic oscillators. In particular, using the integrals of motion, we prove that these Hamiltonians independent of the gap (mass) have infinite excited states that can be described by conformal field theories with integer or half-integer central charges. In the case of free fermions, we also show that because of the huge degeneracy in the spectrum, even a gapless Hamiltonian can have excited states with an area law. Finally, we study the universal average entanglement entropy over eigenstates of the Hamiltonian of the free fermions introduced recently in Vidmar et al. [Phys. Rev. Lett. 119, 020601 (2017)]. In particular, using a duality relation, we map the average bipartite entanglement entropy over all the exponential numbers of eigenstates of a generic free fermion Hamiltonian to the problem of the calculation of the average multibipartite entanglement entropy over a single eigenstate of the $\mathit{XX}$ chain. This relation can be useful for experimental measurement of the universal average entanglement entropy. Part of our conclusions can be extended to the quantum spin chains that are associated with the free fermions via Jordan-Wigner transformation.