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Abstract:

We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric ${\mathsf{Z}}_2$ and $\mathsf{U}\left(1\right)$ QSLs on the trillium lattice. We find two ${\mathsf{Z}}_2$ spin-liquids, and a single $\mathsf{U}\left(1\right)$ spin-liquid that is proximate to one of the ${\mathsf{Z}}_2$ states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two ${\mathsf{Z}}_2$ QSLs is nodal, while the $\mathsf{U}\left(1\right)$ case hosts a spinon Fermi surface. One of our ${\mathsf{Z}}_2$ spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.

Abstract:

SciPost Submission Detail Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

Abstract:

We explore the phase diagrams of moiré materials in search of a class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper [Kwan , .], breaks valley <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>U</mi> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </math> symmetry in a nontrivial fashion wherein the valley order parameter is forced to texture in momentum space as a consequence of band topology. Using detailed Hartree-Fock studies, we establish that the CTI emerges as an energetically competitive intermediate-coupling ground state in several moiré systems that lack a twofold rotation symmetry that forbids the single-particle topology essential to the formation of the CTI valley texture. Published by the American Physical Society 2025