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

Abstract

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.

41 pages

References in corpus (17)

• Probing many-body dynamics on a 51-atom quantum simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Interacting anyons in topological quantum liquids: The golden chain
• Competing density-wave orders in a one-dimensional hard-boson model
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Topological Defects on the Lattice: Dualities and Degeneracies
• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Dualities in one-dimensional quantum lattice models: topological sectors
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Building models of topological quantum criticality from pivot Hamiltonians
• Critical lines and ordered phases in a Rydberg-blockade ladder
• All local conserved quantities of the XXZ model
• A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states

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• Additivity, Haag duality, and non-invertible symmetries
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Global symmetries of quantum lattice models under non-invertible dualities
• Duality-preserving deformation of 3+1d lattice ${\mathbb{Z}}_2$ gauge theory with exact gapped ground states
• Isolated zero mode in a quantum computer from a duality twist
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Dualities between 2+1d fusion surface models from braided fusion categories
• Intertwined order of generalized global symmetries
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra