Assuming unique gapped ground states on finite open chains with boundary fields, the infinite S=1 AF Heisenberg chain is proven to have a nontrivial SPT topological index.
Ground State Properties of Antiferromagnetic Chains with Unrestricted Spin: Integer Spin Chains as Realisations of the O(3) Non-Linear Sigma Model
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abstract
A continuum limit treatment of planar spin chains with arbitrary S is presented. The difference between integer and half-integer spins is emphasised. While isotropic half-integer spin chains are gapless,and have power-law decay of correlations at T = 0 with exponent eta = 1, integer spin systems have a singlet ground state with a gap for S=1 excitations and exponential decay of correlations. The easy-plane to easy-axis transition is described. Note: this is a verbatim transcription of ILL preprint SP-81/95, which is cited in a number of places, but was rejected for publication in 1981, and remained unpublished in this original form, which gives somewhat different arguments for the central result as compared to the later paper finally published in Phys. Lett. 93A, 464 (1983); many thanks to Jeno Solyom for preserving this historical document.
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Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Hopf terms govern phases in 2D metals near fluctuating magnetic and spin loop-current orders, realizing an SU(2)-protected topological phase with gapped bulk, chiral edges, and quantized spin-Hall conductance.
A quantum channel applied near the entanglement cut maps the reduced density matrix of trivial gSPT states to non-trivial ones, thereby predicting their boundary CFT entanglement spectra.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
Conjectures an asymptotic formula for the Haldane gap at large integer spins and reports that topological order in the spin-1 chain vanishes smoothly in ladders without a phase transition.
citing papers explorer
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The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
Assuming unique gapped ground states on finite open chains with boundary fields, the infinite S=1 AF Heisenberg chain is proven to have a nontrivial SPT topological index.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Hopf symmetry protected topological phases in the vicinity of spin orders
Hopf terms govern phases in 2D metals near fluctuating magnetic and spin loop-current orders, realizing an SU(2)-protected topological phase with gapped bulk, chiral edges, and quantized spin-Hall conductance.
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A Framework for Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension
A quantum channel applied near the entanglement cut maps the reduced density matrix of trivial gSPT states to non-trivial ones, thereby predicting their boundary CFT entanglement spectra.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states
Conjectures an asymptotic formula for the Haldane gap at large integer spins and reports that topological order in the spin-1 chain vanishes smoothly in ladders without a phase transition.