Universal scaling behavior of coupled chains of interacting fermions

TL;DR

This paper investigates the universal scaling behavior of single-particle hopping in coupled chains of interacting fermions, revealing a transition from single-particle to two-particle hopping regimes through finite-size scaling analysis.

Contribution

It provides the first numerical evidence of a change in scaling law indicating the onset of coherent transverse two-particle hopping in coupled fermionic chains.

Findings

Single-particle transverse hopping scales as t_perp^{alpha/(1-alpha)} for alpha<alpha_{tp}.

Finite-size effects are described by a universal scaling function in this regime.

Transition to two-particle hopping occurs at alpha>alpha_{tp}, changing the scaling law.

Abstract

The single-particle hopping between two chains is investigated by exact-diagonalizations techniques supplemented by finite-size scaling analysis. In the case of two coupled strongly-correlated chains of spinless fermions, the Taylor expansion of the expectation value of the single-particle interchain hopping operator of an electron at momentum k_F in powers of the interchain hopping t_perp is shown to become unstable in the thermodynamic limit. In the regime alpha<alpha_{tp} (alpha_{tp} simeq 0.41) where transverse two-particle hopping is less relevant than single-particle hopping, the finite-size effects can be described in terms of a universal scaling function. From this analysis it is found that the single-particle transverse hopping behaves as t_perp^{alpha/(1-alpha)} in agreement with a RPA-like treatment of the interchain coupling. For alpha>alpha_{tp}, the scaling law is proven to change its functional form, thus signaling, for the first time numerically, the onset of coherent transverse two-particle hopping.