Condensation of Anyons in Frustrated Quantum Magnets

Abstract

We derive the exact ground space of a family of spin-1/2 Heisenberg chains with uniaxial exchange anisotropy (XXZ) and interactions between nearest and next-nearest-neighbor spins. The Hamiltonian family, H(Q), is parametrized by a single variable Q. By using a generalized Jordan-Wigner transformation that maps spins into anyons, we show that the exact ground states of H(Q) correspond to a condensation of anyons with statistical phase phi=-4Q. We also provide matrix-product state representations of some ground states that allow for the efficient computation of spin-spin correlation functions.

5 pages and 3 Figs

References in corpus (6)

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• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
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Cited by in corpus (8)

• Correlation functions of one-dimensional strongly interacting two-component gases
• Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Anyonic Liquids in Nearly Saturated Spin Chains
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• All product eigenstates in Heisenberg models from a graphical construction
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons