Strongdeco: Expansion of analytical, strongly correlated quantum states into a many-body basis

TL;DR

This paper introduces a Mathematica code that decomposes strongly correlated quantum states into many-body Fock states, enabling analysis of their properties and overlaps, with applications to quantum Hall states like Laughlin and Pfaffian.

Contribution

The paper presents a novel computational tool for decomposing analytical quantum states into many-body basis, facilitating analysis of strongly correlated systems in ultracold gases.

Findings

Enabled calculation of overlaps with Laughlin and Pfaffian states

Read off angular momentum distributions from decompositions

Computed normalization factors for quasi-particle/quasi-hole excitations

Abstract

We provide a Mathematica code for decomposing strongly correlated quantum states described by a first-quantized, analytical wave function into many-body Fock states. Within them, the single-particle occupations refer to the subset of Fock-Darwin functions with no nodes. Such states, commonly appearing in two-dimensional systems subjected to gauge fields, were first discussed in the context of quantum Hall physics and are nowadays very relevant in the field of ultracold quantum gases. As important examples, we explicitly apply our decomposition scheme to the prominent Laughlin and Pfaffian states. This allows for easily calculating the overlap between arbitrary states with these highly correlated test states, and thus provides a useful tool to classify correlated quantum systems. Furthermore, we can directly read off the angular momentum distribution of a state from its decomposition. Finally we make use of our code to calculate the normalization factors for Laughlin's famous quasi-particle/quasi-hole excitations, from which we gain insight into the intriguing fractional behavior of these excitations.