Integrable models on Rydberg atom chains
arXiv:2405.15848 · doi:10.21468/SciPostPhys.18.4.139
Abstract
We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert space, and formulate an integrability condition. This enables us to construct new integrable models with fixed interaction ranges. We classify all time- and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. At range 3, we find a single family of integrable Hamiltonians: the so-called RSOS quantum chains, which are related to the well-known RSOS models of Andrews, Baxter, and Forrester. At range 4 we find two families of models, the first of which is the constrained XXZ model. We also find a new family of models depending on a single coupling . We provide evidence of two critical points related to the golden ratio , at and . We also perform a partial classification of integrable Hamiltonians for range 5.
40 pages, 11 figures. v2: added references. v3: fixed typos
References in corpus (46)
- Probing many-body dynamics on a 51-atom quantum simulator
- Quantum many-body scars
- Observation of Rydberg blockade between two atoms
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- Interacting anyons in topological quantum liquids: The golden chain
- Emergent SU(2) dynamics and perfect quantum many-body scars
- Competing density-wave orders in a one-dimensional hard-boson model
- Signatures of integrability in the dynamics of Rydberg-blockaded chains
- Hilbert-Space Fragmentation from Strict Confinement
- Interacting Fibonacci anyons in a Rydberg gas
- A short introduction to Fibonacci anyon models
- Many-body spin interactions and the ground state of a dense Rydberg lattice gas
- Quantum scars as embeddings of weakly "broken" Lie algebra representations
- Collective states of interacting Fibonacci anyons
- The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
- Liquid ground state, gap and excited states of a strongly correlated spin chain
- Microscopic models of interacting Yang-Lee anyons
- Free fermions in disguise
- The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
- Superdiffusive Energy Transport in Kinetically Constrained Models
- Fragmentation and emergent integrable transport in the weakly tilted Ising chain
- Yang-Baxter and the Boost: splitting the difference
- Classifying nearest-neighbour interactions and deformations of AdS
- Classifying integrable spin-1/2 chains with nearest neighbour interactions
- Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays
- New exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states
- Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
- Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
- On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex -matrix: Relations with Zamolodchikov's tetrahedral algebra
- One dimensional strongly interacting Luttinger liquid of lattice spinless fermions
- R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
- Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
- RSOS Quantum Chains Associated with Off-Critical Minimal Models and Parafermions
- Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
- Wrapping corrections for long range spin chains
- Exactly solvable interacting vertex models
- Fifteen-vertex models with non-symmetric matrices
- Thermodynamics and short-range correlations of the XXZ chain close to its triple point
- The solutions of the Yang-Baxter equation for the -vertex models through a differential approach
- 3-state Hamiltonians associated to solvable 33-vertex models
- Lifting integrable models and long-range interactions
- Superdiffusive to Ballistic Transports in Nonintegrable Rydberg Chains
- Solutions to the constant Yang-Baxter equation in all dimensions
- New spectral-parameter dependent solutions of the Yang-Baxter equation
- Novel approach of exploring ASEP-like models through the Yang Baxter Equation