# Interaction-dependent anisotropy of fractional quantum Hall states

## TL;DR

This study explores how anisotropy in the band mass of particles influences the geometric and physical properties of fractional quantum Hall states, revealing non-analytic responses and dependence on interaction type, filling, and symmetry.

## Contribution

It provides a detailed numerical analysis of how anisotropy transfers from single-particle properties to many-body FQH states across various interactions and symmetries.

## Key findings

- Non-analytic response at a filling-dependent power law exponent.
- Interaction effectively becomes zero-range above a critical exponent.
- Different effects observed for $C_4$-symmetric distortions.

## Abstract

A fractional quantum Hall (FQH) system with broken rotational symmetry exploits its geometric degree of freedom to minimize its ground state energy. The mass anisotropy of bare particles interacting isotropically is partially inherited by the many-body FQH state, and the extent to which it does so depends on the type of interaction, filling fraction and ground state phase. Using numerical infinite density matrix renormalization group simulations, we investigate the transference of elliptical ($C_2$-symmetric) anisotropy from the band mass of the bare particles to the FQH states, for various power law interactions. We map out the response of FQH states to small anisotropy as a function of power law exponent, filling, and statistics (bosonic or fermionic) of the constituents. Interestingly, we find a non-analyticity in the linear response of the FQH state at a special filling-dependent value of the power law exponent, above which the interaction effectively becomes zero-range (point-like). We also investigate the the effect of $C_4$-symmetric band distortions, where we observe a strikingly different dependence on filling.