Linked Cluster Expansions via Hypergraph Decompositions
arXiv:2202.03366 · doi:10.1103/PhysRevE.105.064110
Abstract
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.
arXiv comment12 pages, 7 figures
References in corpus (67)
- Fault-tolerant quantum computation by anyons
- Persistent entanglement in arrays of interacting particles
- String-net condensation: A physical mechanism for topological phases
- Local stabilizer codes in three dimensions without string logical operators
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- Fractons
- Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
- Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
- Robustness of a perturbed topological phase
- Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
- Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
- Numerical Linked-Cluster Approach to Quantum Lattice Models
- Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
- Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model
- Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
- Error Threshold for Color Codes and Random 3-Body Ising Models
- One- and Two-Triplon Spectra of a Cuprate Ladder
- The Structure of Operators in Effective Particle-Conserving Models
- Fractional excitations in foliated fracton phases
- String and Membrane condensation on 3D lattices
- Observation of two-magnon bound states in the two-leg ladders of (Ca,La)14Cu24O41
- Topological Phase Transitions in the Golden String-Net Model
- X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
- Fractional and Integer Excitations in Quantum Antiferromagnetic Spin 1/2 Ladders
- Strong-Coupling Expansions for Multiparticle Excitations: Continuum and Bound States
- Series Expansions for Excited States of Quantum Lattice Models
- Correlation function diagnostics for type-I fracton phases
- Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
- Spectral Properties of Magnetic Excitations in Cuprate Two-Leg Ladder Systems
- Linked Cluster Series Expansions for Two-Particle Bound States
- The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
- Geometrical String and Spin Systems
- Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
- Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
- Raman Response in Antiferromagnetic Two-Leg S=1/2 Heisenberg Ladders
- Systematic Mapping of the Hubbard Model to the Generalized t-J Model
- Self-Avoiding Gonihedric Srting and Spin Systems
- Effective models for gapped phases of strongly correlated quantum lattice models
- Fate of the cluster state on the square lattice in a magnetic field
- Slow dynamics of Ising models with energy barriers
- Plaquette Ising models, degeneracy and scaling
- Optimizing linked cluster expansions by white graphs
- Quantum criticality and excitations of a long-range anisotropic -chain in a transverse field
- Robustness of a topological phase: Topological color code in parallel magnetic field
- Ising anyons with a string tension
- Interaction Hierarchy. Gonihedric String and Quantum Gravity
- GEOMETRICAL STRING and DUAL SPIN SYSTEMS
- Quantum robustness of fracton phases
- Theoretical analysis of magnetic Raman scattering in La2CuO4: two-magnon intensity with the inclusion of ring exchange
- Low temperature expansion of the gonihedric Ising model
- Raman Response of Magnetic Excitations in Cuprate Ladders and Planes
- Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
- Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase
- Slow dynamics in the 3--D gonihedric model
- High temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high temperature series expansion study
- Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
- Quantum robustness and phase transitions of the 3D Toric Code in a field
- Linked-cluster expansions for quantum magnets on the hypercubic lattice
- Baxter-Wu model in a transverse magnetic field
- Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
- A generalized perspective on non-perturbative linked cluster expansions
- High-Temperature Series Expansion for Spin-1/2 Heisenberg Models
- Competing topological orders in three dimensions: X-cube versus toric code
- Dynamic structure factor of disordered quantum spin ladders
- Fine-Grained Tensor Network Methods
- Bounds on universal quantum computation with perturbed 2d cluster states
- Non-perturbative linked-cluster expansions in long-range ordered quantum systems