Siddharth Parameswaran

Abstract:

<jats:p>We introduce an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>SU</a:mi><a:mo>(</a:mo><a:mi>M</a:mi><a:mo>)</a:mo></a:mrow></a:math>-symmetric disordered bipartite spin model with unusual characteristics. Although superficially similar to the Sachdev-Ye (SY) model, it has several markedly different properties for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>M</b:mi><b:mo>≥</b:mo><b:mn>3</b:mn></b:mrow></b:math>. In particular, it has a large nontrivial nullspace whose dimension grows exponentially with system size. The states in this nullspace are frustration-free and are ground states when the interactions are ferromagnetic. The exponential growth of the nullspace leads to Hilbert-space fragmentation and a violation of the eigenstate thermalization hypothesis. We demonstrate that the commutant algebra responsible for this fragmentation is a nontrivial subalgebra of the Read-Saleur commutant algebra of certain nearest-neighbor models such as the spin-1 biquadratic spin chain. We also discuss the low-energy behavior of correlations for the disordered version of this model in the limit of a large number of spins and large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>M</c:mi></c:math>, using techniques similar to those applied to the SY model. We conclude by generalizing the Shiraishi-Mori embedding formalism to nonlocal models, and apply it to turn some of our nullspace states into quantum many-body scars.</jats:p> <jats:sec> <jats:title/> <jats:supplementary-material> <jats:permissions> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material> </jats:sec>

Abstract:

Recent scanning tunneling microscopy experiments in twisted bilayer [K. P. Nuckolls et al., Nature (London) 620, 525 (2023)] and trilayer [H. Kim et al., Nature (London) 623, 942 (2023)] graphene have revealed the ubiquity of Kekulé charge-density wave order in magic-angle graphene. Most samples are moderately strained and show “incommensurate Kekulé spiral” (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultralow strain bilayer samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor 𝜈=−2, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at |𝜈|=2 with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.