Scaling Theory of Few-Particle Delocalization

TL;DR

This paper develops a scaling theory for how few-particle states in disordered quantum systems become delocalized due to interactions, extending known localization results to multi-particle scenarios and providing experimental relevance.

Contribution

It introduces a hypothesis that multi-particle delocalization occurs when the sum of spatial dimension and particle number exceeds four, supported by exact calculations and mapping to symplectic symmetry problems.

Findings

3-particle states in 1D with repulsion delocalize at Wc ≈ 1.4t

Localization length critical exponent found as ν = 1.5 ± 0.3

Delocalization transition mapped to a symplectic symmetry problem

Abstract

We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion will delocalize with $W_c \approx 1.4t$ and with localization length critical exponent $\nu = 1.5 \pm 0.3$. The delocalization transition can be understood by means of a mapping onto a non-interacting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.