Universal fluctuations of localized two interacting particles in one dimension

TL;DR

This paper explores how disorder and interactions influence the universal fluctuation behavior of two particles in a one-dimensional disordered system, revealing a transition between fluctuation universality classes.

Contribution

It demonstrates that random potentials and long-range interactions lead to different fluctuation universality classes, connecting Fock space fluctuations to directed polymer models.

Findings

Random potentials produce fluctuation growth exponent 1/2.

Long-range interactions induce KPZ universality class with exponent 1/3.

Complex polymer models confirm the role of disorder structure in fluctuation universality.

Abstract

We investigate the universal fluctuations of localized wavefunction in the Fock space of two interacting particles in one-dimensional disordered systems, focusing on the interplay between random potentials and random long-range interactions. By mapping the system onto a directed polymer problem, we show that random potentials alone produce correlated energies for the sites in the Fock space, giving rise to the fluctuation growth exponent 1/2. Introducing random long-range interactions alters these correlations and drives the system's fluctuations into the Kardar-Parisi-Zhang universality class in (1+1)D with the exponent 1/3. To validate the universality of the observed fluctuation scaling, we study a complex directed polymer model with competing point and columnar disorder. Our results confirm that columnar disorder corresponds to on-site energies in the Fock space from the random potentials, while point disorder models the effects of random long-range interactions between the two particles. These findings provide new insights into the Fock-space perspective for examining disordered quantum many-body systems, and emphasize the critical role of disorder structure in determining the universality class of fluctuations in localized quantum systems.