We investigated a one-dimensional system of anyons that interact with each other under a local three-body term. Using a fractional Jordan-Wigner transformation, we arrived at a modified Bose-Hubbard model, which exhibits gapped and gapless phases. We built the phase diagram of the system fixing the hopping parameter or the statistics, showing the evolution of the critical points, which were estimated with von Neumann block entropy. A superfluid to Mott insulator quantum phase transition with one particle per site can be driven by the statistics or the interaction. Specifically, we show that for larger angles there is a finite critical value of the interaction at which the Mott phase appears. Also, we found that the critical angles increase with the hopping. Diverse gapless phases were observed away from the pseudofermion limit.We investigated a one-dimensional system of anyons that interact with each other under a local three-body term. Using a fractional Jordan-Wigner transformation, we arrived at a modified Bose-Hubbard model, which exhibits gapped and gapless phases. We built the phase diagram of the system fixing the hopping parameter or the statistics, showing the evolution of the critical points, which were estimated with von Neumann block entropy. A superfluid to Mott insulator quantum phase transition with one particle per site can be driven by the statistics or the interaction. Specifically, we show that for larger angles there is a finite critical value of the interaction at which the Mott phase appears. Also, we found that the critical angles increase with the hopping. Diverse gapless phases were observed away from the pseudofermion limit.

arXiv:1702.04412Physical Review AFeb 22, 201815 citations

Universal momentum tail of identical one-dimensional anyons with two-body interactions

Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume

Nonrelativistic anyons in one dimension possess generalized exchange statistics in which the exchange of two identical anyons generates a phase that is governed by the spatial ordering of the particles and the statistical parameter $\ensuremath{\alpha}$. Working in the continuum, we demonstrate the existence of two distinct types of one-dimensional (1D) anyons, namely, bosonic anyons and fermionic anyons. We identify a many-body Hamiltonian with additive two-body zero-range interactions that supports bosonic and fermionic anyon eigenstates, which are, for arbitrary interaction strength, related through a generalized bosonic-anyon--fermionic-anyon mapping, an extension of the celebrated Bose-Fermi mapping for zero-range interacting 1D systems. The momentum distributions of bosonic and fermionic anyons are distinct: while both feature ${k}^{\ensuremath{-}2}$ and ${k}^{\ensuremath{-}3}$ tails, the associated prefactors differ. Our work reveals intricate connections between the generalized exchange statistics, the universal two- and three-body Tan contacts of systems consisting of $N$ identical particles, and the emergence of statistics-induced chiral symmetry breaking.Nonrelativistic anyons in one dimension possess generalized exchange statistics in which the exchange of two identical anyons generates a phase that is governed by the spatial ordering of the particles and the statistical parameter $\ensuremath{\alpha}$. Working in the continuum, we demonstrate the existence of two distinct types of one-dimensional (1D) anyons, namely, bosonic anyons and fermionic anyons. We identify a many-body Hamiltonian with additive two-body zero-range interactions that supports bosonic and fermionic anyon eigenstates, which are, for arbitrary interaction strength, related through a generalized bosonic-anyon--fermionic-anyon mapping, an extension of the celebrated Bose-Fermi mapping for zero-range interacting 1D systems. The momentum distributions of bosonic and fermionic anyons are distinct: while both feature ${k}^{\ensuremath{-}2}$ and ${k}^{\ensuremath{-}3}$ tails, the associated prefactors differ. Our work reveals intricate connections between the generalized exchange statistics, the universal two- and three-body Tan contacts of systems consisting of $N$ identical particles, and the emergence of statistics-induced chiral symmetry breaking.

arXiv:2505.17669Physical Review AOct 16, 20252 citations

Anyons in a weakly interacting system

G. Rosenberg, Babak Seradjeh, Conan Weeks +1 more

Bulletin of the American Physical SocietyMar 8, 20070 citations

N

identical particles, and the emergence of statistics-induced chiral symmetry breaking.