A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism

Ohya, Satoshi

doi:10.48550/arxiv.2105.04288

Cited by 1 publication

(3 citation statements)

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“…It should be emphasized that, if Ψ, , and Θ are normalized solutions to the equations (28a)-(28c), then Eqs. (29a) and (29b) automatically become the normalized eigenfunctions of the Hamiltonians (14) with the eigenvalue = cm + rel . Now, it is well-known in the context of 1/ 2 potential that infinitely many discrete energy levels appear if…”

Section: From Continuous To Discrete Scale Invariancementioning

confidence: 99%

“…The simplest application of this equivalence to many-body problems is the well-known boson-fermion duality between the Lieb-Liniger model [12] of identical spinless bosons and the Cheon-Shigehara model [13] of identical spinless fermions. Recently, it has been shown [14] that this duality can be further generalized because one-dimensional two-body contact interactions have much more variety than previously investigated. And most importantly, this generalization includes scale-invariant two-body contact interactions which-at least at the formal level-renders the system invariant under continuous scale transformation.…”

Section: Introductionmentioning

confidence: 99%

“…The key to this achievement is the configuration-space approach to identical particles [15][16][17][18]. Before going to discuss scale-invariance breaking, let us first briefly review the boson-fermion duality in [14] from the viewpoint of the configuration-space approach.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Scale-Invariant Boson-Fermion Duality in One Dimension

Ohya

2021

Preprint

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We introduce models of one-dimensional (≥ 3)-body problems that undergo phase transition from a continuous scale invariant phase to a discrete scale invariant phase. In this paper, we focus on identical spinless particles that interact only through two-body contacts. We first classify all possible scale-invariant two-body contact interactions for identical particles in one dimension. We then present a criterion for the breakdown of continuous scale invariance to discrete scale invariance. Under the assumption that the criterion is met, we solve the many-body Schrödinger equation exactly; we obtain the exact -body bound-state spectrum as well as the exact -body Smatrix elements for arbitrary ≥ 3, all of which enjoy discrete scale invariance or log-periodicity. Thanks to the boson-fermion duality, these results can be applied equally well to both bosons and fermions. Finally, we demonstrate how the criterion is met in the case of = 3; we determine the exact phase diagram for the scale-invariance breaking in the three-body problem of identical bosons and fermions. The zero-temperature transition from the unbroken phase to the broken phase is the Berezinskii-Kosterlitz-Thouless-like transition discussed in the literature.

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Section: From Continuous To Discrete Scale Invariancementioning

confidence: 99%