Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

Abstract

The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied by calculating the persistent current in small quantum rings and by exact simulations of the timeevolution of the many-particle state in two cases: Expansion of a localized cloud, and collisions in a Newtons cradle. We consider three different lattices which in the tight binding model exhibit flat bands. The physical realization is considered to be an optical lattice with bosonic or fermionic atoms. The atoms are assumed to interact with a repulsive short range interaction. The different statistics of bosons and fermions lead to different dynamics. Spinless fermions are easily trapped in the flat-band states due to the Pauli exclusion principle, which prevents them from interacting, while bosons are able to push each other out from the flat-band states.

Parity-time symmetry in a flat-band system

“…Using φ (2) 2 in the expression above leads to the same result. Previously we have mentioned that the numerically obtained slope in this case is 0.708, calculated using κ + (τ = 0.1) ≈ κ+(τ ) τ τ =0.1…”

“…Systems that exhibit flat bands have attracted considerable interest in the past few years, including optical [1,2] and photonic lattices [3][4][5][6], graphene [7,8], superconductors [9][10][11][12], fractional quantum Hall systems [13][14][15] and exciton-polariton condensates [16,17]. One interesting consequence of a flat band is the different scaling properties of its localization length when compared with a dispersive band [18][19][20], due to a multitude of degenerate states in the flat band.…”

Simple method to construct flat-band lattices

“…In Ref. [30] authors describe a collection of FB lattices to study bosons and fermions dynamics. They briefly mention that an important condition is that the wave-function may be zero at some connecting sites, in order to make impossible the transport across the lattice.…”

Flat bands andPTsymmetry in quasi-one-dimensional lattices

“…On the other hand, hermitian systems that exhibit flat bands have attracted considerable interest in the past few years, including optical [18,19] and photonic lattices [20][21][22], graphene [23,24], superconductors [25][26][27][28], fractional quantum Hall systems [29][30][31] and excitonpolariton condensates [32,33]. The presence of a flat band in the spectrum of a hermitian lattice implies the existence of entirely degenerate states, whose superposition displays no dynamical evolution.…”