Discrete scale-invariant boson-fermion duality in one dimension

Ohya, Satoshi

doi:10.1103/physreva.105.033312

Cited by 4 publications

(1 citation statement)

References 37 publications

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“…Q, points of X that differ by a permutation of labels are collapsed to same point in Q. Unless X excludes all two-body coincidences, the quotient space Q is not naturally a manifold and is better described as an orbifold [16,17,[60][61][62][63]. An advantage of the intrinsic approach is that, unlike a symmetry, true indistinguishability cannot be broken; the intrinsic approach treats particle labels as a gauge structure imposed on indistinguishable particles, not as a symmetry of configuration space [25,64].…”

Section: Discussionmentioning

confidence: 99%

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Nagies,

Wang,

Knapp

et al. 2024

SciPost Phys.

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Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.

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Section: Discussionmentioning

confidence: 99%

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Nagies,

Wang,

Knapp

et al. 2024

SciPost Phys.

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Topological exchange statistics in one dimension

Harshman

Knapp

2022

Phys. Rev. A

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Efimov effect for two particles on a semi-infinite line

Ohya

2022

American Journal of Physics

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The Efimov effect (in a broad sense) refers to the onset of a geometric sequence of many-body bound states as a consequence of the breakdown of continuous scale invariance to discrete scale invariance. While originally discovered in three-body problems in three dimensions, the Efimov effect has now been known to appear in a wide spectrum of many-body problems in various dimensions. Here, we introduce a simple, exactly solvable toy model of two identical bosons in one dimension that exhibits the Efimov effect. We consider the situation where the bosons reside on a semi-infinite line and interact with each other through a pairwise δ-function potential with a particular position-dependent coupling strength that makes the system scale invariant. We show that, for sufficiently attractive interaction, the bosons are bound together, and a new energy scale emerges. This energy scale breaks continuous scale invariance to discrete scale invariance and leads to the onset of a geometric sequence of two-body bound states. We also study the two-body scattering off the boundary and derive the exact reflection amplitude that exhibits discrete scale invariance.

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Discrete scale-invariant boson-fermion duality in one dimension

Cited by 4 publications

References 37 publications

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Topological exchange statistics in one dimension

Efimov effect for two particles on a semi-infinite line

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