From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects

SciPost Physics Stichting SciPost 16:5 (2024) 127

Authors:

Luisa Eck, Paul Fendley

Abstract:

<jats:p>Strongly interacting models often possess “dualities” subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy.</jats:p>

Conformal field theory approach to parton fractional quantum Hall trial wave functions

Physical Review B American Physical Society (APS) 109:20 (2024) 205128

Authors:

Greg J Henderson, GJ Sreejith, Steven H Simon

Chern-Simons Modified-RPA Eliashberg theory of the ν = 1/2 + 1/2 quantum Hall bilayer

Physical Review Letters American Physical Society 132 (2024) 176502

Authors:

Tevz Lotric, Steven Simon

Abstract:

The ν = 1/2 + 1/2 quantum Hall bilayer has been previsously modeled using Chern-Simons-RPAEliashberg (CSRPAE) theory to describe pairing between the two layers. However, these approaches are troubled by a number of divergences and ambiguities. By using a “modified” RPA approximation to account for mass renormalization, we can work in a limit where the cyclotron frequency is taken to infinity, effectively projecting to a single Landau level. This, surprisingly, controls the important divergences and removes ambiguities found in prior attempts at CSRPAE. Examining BCS pairing of composite fermions we find that the angular momentum channel l = +1 dominates for all distances d between layers and at all frequency scales. Examining BCS pairing of composite fermion electrons in one layer with composite fermion holes in the opposite layer, we find the l = 0 pairing channel dominates for all d and all frequencies. The strength of the pairing in these two different descriptions of the same phase of matter is found to be almost identical. This agrees well with our understanding that these are two different but dual descriptions of the same phase of matter.

Double-dome Unconventional Superconductivity in Twisted Trilayer Graphene

(2024)

Authors:

Zekang Zhou, Jin Jiang, Paritosh Karnatak, Ziwei Wang, Glenn Wagner, Kenji Watanabe, Takashi Taniguchi, Christian Schönenberger, SA Parameswaran, Steven H Simon, Mitali Banerjee

Free fermions beyond Jordan and Wigner

SciPost Physics SciPost 16:4 (2024) 102

Authors:

Paul Fendley, Balazs Pozsgay

Abstract:

The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows from the eigenvalues of a matrix whose size grows only linearly with the volume of the system. However, several Hamiltonians that do not admit a Jordan-Wigner transformation to fermion bilinears still have the same type of free-fermion spectra. The spectra of such "free fermions in disguise" models can be found exactly by an intricate but explicit construction of the raising and lowering operators. We generalise the methods further to find a family of such spin chains. We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.