Siddharth Parameswaran

Abstract:

We show that Hubbard models with nearest-neighbor hopping and a nearest-neighbor hardcore constraint exhibit “maximal” Hilbert space fragmentation in many lattices of arbitrary dimension 𝑑. Focusing on the 𝑑 =1 rhombus chain and the 𝑑 =2 Lieb lattice, we demonstrate that the fragmentation is strong for all fillings in the thermodynamic limit, and explicitly construct all emergent integrals of motion, which include an extensive set of higher-form symmetries. Blockades consisting of frozen particles partition the system in real space, leading to anomalous dynamics. Our results are potentially relevant to optical lattices of dipolar and Rydberg-dressed atoms.

Abstract:

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at nonzero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic 𝑝-wave instability of the Kohn-Luttinger type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behavior seen in experiments.

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>