Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations

DOI10.1063/1.5084136zbMath1427.82055arXiv1707.02446OpenAlexW3102884857MaRDI QIDQ5228057

Yingkai Ouyang

Publication date: 8 August 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02446

zbMATH Keywords

algorithmsexact solutionsspectral gapgraphsspectral graph theorymean field modelisoperimetric boundslower bounds on the spectrumcombinatorial optimization algorithmgraph diametersSobolev inequalities on graphsbounds on largest eigenvaluesHeisenberg Hamiltonian (HH)Heisenberg spectrumHeisenberg spin 1/2 ferromagnetic model (HM)symmetric powers of graphs

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Interacting particle systems in time-dependent statistical mechanics (82C22) Estimates of eigenvalues in context of PDEs (35P15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Statistical mechanics of magnetic materials (82D40) Software, source code, etc. for problems pertaining to statistical mechanics (82-04)

Related Items

Quantitatively improved finite-size criteria for spectral gaps ⋮ On the Connectivity of Token Graphs of Trees ⋮ On the spectra of token graphs of cycles and other graphs ⋮ The automorphism groups of some token graphs ⋮ Spectral properties of token graphs ⋮ Entanglement entropy bounds in the higher spin XXZ chain ⋮ The edge-connectivity of token graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model
• Symmetric squares of graphs
• Eigenvalues and expanders
• On a problem of Kleitman and West
• Some simplified NP-complete graph problems
• Laplacian matrices of graphs: A survey
• Combinatorial optimization. Polyhedra and efficiency (3 volumes)
• Permutationally invariant codes for quantum error correction
• Upper bounds for eigenvalues of the discrete and continuous Laplace operators
• Token graphs
• Edge isoperimetric inequalities for product graphs
• Swapping labeled tokens on graphs
• Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet
• Permutation-invariant qudit codes from polynomials
• The connectivity of token graphs
• Fast linear algebra is stable
• Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
• Vertex Bisection is Hard, too
• Sobolev spaces on graphs
• Proof of Aldous’ spectral gap conjecture
• Association schemes and coding theory
• Eigenvalues of Graphs and Sobolev Inequalities
• Isoperimetric Inequalities and Their Applications