Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2604.14103

Chiral Fermion Localization in Two-Kink Scalar Backgrounds: Tunable Brane Positioning and Universal Divergence at the Single-Kink Limit

H. P. Pinheiro·C. A. S. Almeida
View original source ↗Read source document ↗Export metadata ↓

Abstract

The localization of chiral fermionic zero modes in scalar field backgrounds with domain wall structure is a central mechanism in brane-world scenarios. We investigate this mechanism in a system that provides an effective realization of the $(1+1)$-dimensional Jackiw--Rebbi model, using a two-kink scalar background generated by the deformation method applied to the $\varphi^4$ model. The two-kink profile introduces two physically distinct parameters: an asymmetry parameter $a_2$ controlling the left-right symmetry of the scalar background, and an inter-kink separation parameter $b$ controlling the distance between the constituent domain walls. We establish two independent scaling laws. First, the collective center-of-mass position of the chiral zero modes responds linearly to $a_2$, providing a mechanism for continuously tuning the effective brane position in the extra dimension. Second, the differential spatial separation between the two chiral modes diverges as the two-kink background collapses into a simple kink, following a power law in $(b-1)$ with exponent statistically consistent with $-1$. These two results are physically independent and each admits a precise interpretation in the language of brane-world scenarios. The mechanism is realized concretely in bilayer graphene under an asymmetric two-kink electrostatic potential, providing a tunable platform for probing extra-dimensional localization physics.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

H. P. Pinheiro, C. A. S. Almeida. 2026-04-15. Chiral Fermion Localization in Two-Kink Scalar Backgrounds: Tunable Brane Positioning and Universal Divergence at the Single-Kink Limit. https://arxiv.org/abs/2604.14103

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer R\'enyi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer R\'enyi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

hep-th↗
arXiv2026

Landau-Ginzburg description of an exceptional ${\mathcal N}=1$ minimal model

The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-\epsilon$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(\epsilon)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.

hep-th↗
arXiv2026

Detecting one-dimensional bosonic SPT phases via twisted entropic order parameter

Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.

hep-th↗