Supersymmetric Valence Bond Solid States
arXiv:0901.1498 · doi:10.1103/PhysRevB.79.224404
Abstract
In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states, and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states (RVB). The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.
21 pages, 8 figures, 1 table, minor corrections
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- Critical theory of the topological quantum phase transition in a spin-2 chain
- Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
- Graded Hopf Maps and Fuzzy Superspheres
- Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
- Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
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- The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
- Exact renormalization in quantum spin chains
- Spin-spin correlation functions of the q-VBS state of an integer spin model
- Topological Quantum Phase Transition from Fermionic Integer Quantum Hall Phase to Bosonic Fractional Quantum Hall Phase through P-Wave Feshbach Resonance
- Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
- Interrelations among frustration-free models via Witten's conjugation
- Deconfined quantum criticality with internal supersymmetry
- A brief note on the G Affleck-Kennedy-Lieb-Tasaki chain