Discrete Scale-Invariant Boson-Fermion Duality in One Dimension
- URL: http://arxiv.org/abs/2110.09723v2
- Date: Tue, 22 Mar 2022 08:00:00 GMT
- Title: Discrete Scale-Invariant Boson-Fermion Duality in One Dimension
- Authors: Satoshi Ohya
- Abstract summary: We introduce models of one-dimensional $n(geq3)$-body problems that undergo phase transition from a continuous scale-invariant phase to a discrete scale-invariant phase.
Thanks to the boson-fermion duality, these results can be applied equally well to both bosons and fermions.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce models of one-dimensional $n(\geq3)$-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. Without assuming any particular
cluster-decomposition property, we first classify all possible scale-invariant
two-body contact interactions that respect unitarity, permutation invariance,
and translation invariance 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
Schr\"{o}dinger equation exactly; we obtain the exact $n$-body bound-state
spectrum as well as the exact $n$-body S-matrix elements for arbitrary
$n\geq3$, 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 $n=3$; 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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