Symmetric Mass Generation of Kähler-Dirac Fermions from the Perspective of Symmetry-Protected Topological Phases

Yuxuan Guo; Yi-Zhuang You

Home/Archive/arXiv

arXiv · 2306.17420

Symmetric Mass Generation of Kähler-Dirac Fermions from the Perspective of Symmetry-Protected Topological Phases

Yuxuan Guo·Yi-Zhuang You

View original source ↗Read source document ↗Export metadata ↓

Abstract

The Kähler-Dirac fermion, recognized as an elegant geometric approach, offers an alternative to traditional representations of relativistic fermions. Recent studies have demonstrated that symmetric mass generation (SMG) can precisely occur with two copies of Kähler-Dirac fermions across any spacetime dimensions. This conclusion stems from the study of anomaly cancellation within the fermion system. Our research provides an alternative understanding of this phenomenon from a condensed matter perspective, by associating the interacting Kähler-Dirac fermion with the boundary of bosonic symmetry-protected topological (SPT) phases. We show that the low-energy bosonic fluctuations in a single copy of the Kähler-Dirac fermion can be mapped to the boundary modes of a $\mathbb{Z}_2$-classified bosonic SPT state, protected by an inversion symmetry universally across all dimensions. This implies that two copies of Kähler-Dirac fermions can always undergo SMG through interactions mediated by these bosonic modes. This picture aids in systematically designing SMG interactions for Kähler-Dirac fermions in any dimension. We present the exact lattice Hamiltonian of these interactions and validate their efficacy in driving SMG.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yuxuan Guo, Yi-Zhuang You. 2024-05-19. Symmetric Mass Generation of Kähler-Dirac Fermions from the Perspective of Symmetry-Protected Topological Phases. https://arxiv.org/abs/2306.17420

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

KEEP EXPLORING

Related papers

arXiv2026

Real-space determination of orbital states driving successive phase transitions in FeV2O4

Direct experimental access to orbital states in strongly correlated materials remains a major challenge, despite their central role in driving coupled structural and magnetic phase transitions. In systems where electronic correlations, electron-lattice coupling, and relativistic spin-orbit interactions compete on comparable energy scales, even first-principles calculations often yield multiple metastable solutions, hindering the unambiguous identification of the ground state. Here, we demonstrate that the orbital states of the spinel oxide FeV2O4, which possesses active orbital degrees of freedom on both Fe and V ions, are uniquely resolved by combining valence electron density (VED) analysis based on state-of-the-art synchrotron x-ray diffraction with spin-polarized density-functional-theory calculations. Our results reveal that temperature-dependent rearrangements of orbital occupations drive successive structural transitions that accompany collinear and noncoplanar ferrimagnetic orders, establishing a direct correspondence between orbital anisotropy and spin structure. More broadly, this work shows that experimentally determined VED provides a decisive real-space constraint on competing theoretical solutions, offering a powerful and broadly applicable framework for elucidating the microscopic mechanisms of complex phase transitions in strongly correlated electron systems.

cond-mat.str-el↗

arXiv2026

Macroscopic Zero-Mode Manifold Isolated by Quantum Chaos

Chaotic many-body spectra are expected to densely fill their energy window. We show that constrained spin chains with chiral symmetry evade this expectation by hosting an exponentially large manifold of symmetry-protected exact zero modes separated from the surrounding spectrum by a sharp gap at zero energy. The gap is generated by chaotic level repulsion, with width set by the number of zero modes times the mean level spacing. We verify this mechanism in an East-West kinetically constrained chain, develop a minimal random-matrix description, and show how the gap can be detected through linear-response spectroscopy.

cond-mat.str-el↗

arXiv2026

Textures as a phase-transition probe for quantum spin chains

The idea of quantum texture has been recently proposed and used as a tool for quantifying coherences and for quantum gate identification. In this work we offer a study on its usage to quantum phase transitions, demonstrating the rugosity metric as a simple tool for effective phase-transition probing. We establish the link between rugosity in the computational basis and the hierarchy of spin correlators, and analyze rugosities defined in the global ground-state and in ground-states belonging to different magnetization sectors (to which we refer to as global vs symmetry-resolved rugosities) to study the phase diagram of the Heisenberg XXZ model. We find distinct rugosity signatures at both transition points. In particular, a sharp feature appears at $Δ=1$ already for small systems, revealing a pronounced sensitivity of the correlation hierarchy encoded by the texture to this point. Since the BKT transition coincides with the isotropic $SU(2)$ point of the XXZ model, this behavior may reflect a particular sensitivity of rugosity to the structure of the spin-correlation hierarchy at isotropy.

cond-mat.str-el↗