Abstract
We study a tight binding model of \mathbb{Z}_3ℤ3-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge \boldsymbol{c=2}𝐜=2, and two gapless phases with central charge \boldsymbol{c=1}𝐜=1. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.
Highlights
Particles in three dimensions are known to be either bosons or fermions, distinguished by the symmetry or antisymmetry of their wave functions Ψ(x1, x2) under particle exchange, ie, Ψ(x1, x2) = ±Ψ(x2, x1)
Since low-dimensional systems are ubiquitous in condensed-matter physics—think of two-dimensional systems like graphene [1] or two-dimensional electron gases in quantum Hall transistors [2], one-dimensional quantum wires [3], or the dimensional restriction of ultracold atomic gases in optical lattices [4, 5]—non-trivial quantum statistics has to be considered in these contexts
The aim of our work is to extend the analysis to g = 0 and study the effect of the additional pair hopping on the phase diagram
Summary
The idea is to ask how the number of available quantum states D will change if ∆N particles are added to the system, with the statistical parameter α being defined as ∆D = −α∆N In principle this concept can be defined in any spatial dimension, with bosons (α = 0) and fermions (α = 1) as special cases. Due to the relations (4) it is not possible to interpret γ†j as a particle creation operator at site j Very recently this limitation was overcome by Cobanera and Ortiz [30] who introduced the so-called Fock parafermions (FPFs).
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