Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities

Abstract

We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of current interest in the context of topological quantum order. These include Kitaev's toric code and honeycomb models, a vector exchange model, and a Clifford gamma model on a triangular lattice.

12 pages, 5 figures

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Cited by in corpus (79)

• Quantum Spin Liquid States
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Hilbert Space Fragmentation and Commutant Algebras
• Symmetry and Topological Order
• Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
• Dualities and the phase diagram of the $p$-clock model
• The Bond-Algebraic Approach to Dualities
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Unified approach to Quantum and Classical Dualities
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Holographic Symmetries and Generalized Order Parameters for Topological Matter
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Free fermions behind the disguise
• Phonon renormalization in the Kitaev quantum spin liquid
• Effective and exact holographies from symmetries and dualities
• Thermal transport in a two-dimensional ${\mathbb{Z}}_2$ spin liquid
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Quantum Phase Transition in the One-Dimensional Extended Quantum Compass Model in a Transverse Field
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
• An Exact Chiral Amorphous Spin Liquid
• Kitaev model and dimer coverings on the honeycomb lattice
• Manipulating unpaired Majorana fermions in a quantum spin chain
• Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Heat transport in the anisotropic Kitaev spin liquid
• Duality as a Feasible Physical Transformation
• Reduced fidelity in Kitaev honeycomb model
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Geometric Criterion for Solvability of Lattice Spin Systems
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface
• (SPT-)LSM theorems from projective non-invertible symmetries
• Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System
• Thermal Transport in a one-dimensional Z${}_2$ Spin Liquid
• Flux mobility delocalization in the Kitaev spin ladder
• Gauging non-invertible symmetries on the lattice
• Generalised Onsager Algebra in Quantum Lattice Models
• Gapped Quantum Criticality Gains Long Time Quantum Correlations
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Equivalence of Topological Insulators and Superconductors
• State selection in frustrated magnets
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Integrable spin chains and the Clifford group
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations
• Bosonization of Majorana modes and edge states
• Topological Phase Transition in the Extended Cluster Compass Ladder
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Additivity, Haag duality, and non-invertible symmetries
• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Topological aspects of an exactly solvable spin chain
• The non-Abelian Duality Problem
• Robust Topological Degeneracy of Classical Theories
• Emergent magnetic order in the antiferromagnetic Kitaev model with a [111] field
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Majorana corner states in square and Kagome quantum spin liquids
• Finite temperature topological order in 2D topological color codes
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Two-triplon excitations of the Kitaev-Heisenberg-Bilayer
• Finite-momentum energy dynamics in a Kitaev magnet
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Divergent Thermopower without a Quantum Phase Transition
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Giant magnetoresistance of edge current between fermion and spin topological systems