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arXiv:0712.1264

Theoretical construction of 1D anyon models

Ren-Gui Zhu, An Min Wang

Published Dec 8, 2007• 4 citations
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Abstract

One-dimensional anyon models are renewedly constructed by using path integral formalism. A statistical interaction term is introduced to realize the anyonic exchange statistics. The quantum mechanics formulation of statistical transmutation is presented.
DOI
10.48550/arxiv.0712.1264

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Anyons exhibit a non-trivial interplay between local exclusion rules and non-local braiding and exchange phases, making a consistent commutation algebra and second-quantized formulation challenging. We develop an algebraic framework for Abelian anyons in one dimension with statistical phase θθθ = πππ/N that enforces a finite on-site occupancy of N-1 anyons with the exchange phase θθθ between different sites. Moreover, we introduce an exact Jordan-Wigner duality between πππ/3 anyons and spin-1 operators, allowing us to map a tight-binding anyon model to an XY-like spin-1 model. The model exhibits anyon-density-dependent flux, incompressible or gapless regions, and critical points with level crossings that appear as discontinuities in ground-state currents, momenta, fidelities, and correlation functions. Our second-quantization formalism establishes a novel spin anyon duality, offering a conceptually new route to realize anyons from spin Hamiltonians and to engineer corresponding device architectures.