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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Eck, Luisa, Fendley, Paul
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866907904831913984
author Eck, Luisa
Fendley, Paul
author_facet Eck, Luisa
Fendley, Paul
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2302_14081
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
Eck, Luisa
Fendley, Paul
Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
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.
title From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
topic Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2302.14081