2005/02/28 by A. M. M. Pruisken, Ravi Shankar, R. Shankar +1
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.72.035329
published as Phys. Rev. B 72, 035329 (2005) · Title changed, Section 2 and Appendix expanded, an error in the expression for theta corrected
openalex publication_date 2005/07/14 · arxiv created 2005/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concept of superuniversality in quantum Hall liquids and spin liquids. This concept has emerged from previous studies of the quantum Hall effect and states that all the fundamental features of the quantum Hall effect are generically displayed as general topological features of the \ensuremathθ parameter in nonlinear \ensuremathσ models in two dimensions. To establish superuniversality in spin liquids we revisit the mapping by Haldane who argued that the antiferromagnetic Heisenberg spin-s chain in 1+1 space-time dimensions is effectively described by the O(3) nonlinear \ensuremathσ model with a \ensuremathθ term. By combining the path integral representation for the dimerized spin s=1∕2 chain with renormalization-group decimation techniques we generalize the Haldane approach to include a more complicated theory, the fermionic rotor chain, involving four different renormalization-group parameters. We show how the renormalization-group calculation technique can be used to build a bridge between the fermionic rotor chain and the O(3) nonlinear \ensuremathσ model with the \ensuremathθ term. As an integral and fundamental aspect of the mapping we establish the topological significance of the dangling spin at the edge of the chain. The edge spin in spin liquids is in all respects identical to the massless chiral edge excitations in quantum Hall liquids. We consider various different geometries of the spin chain such as open and closed chains, chains with an even and odd number of sides. We show that for each of the different geometries the \ensuremathθ term has a distinctly different physical meaning. We compare each case with a topologically equivalent quantum Hall liquid.