Interaction-dependent anisotropy of fractional quantum Hall states

Abstract

In the absence of rotational symmetry, a fractional quantum Hall (FQH) system can exploit a 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, to an extent that 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 (C2-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 nonanalyticity in the linear response of the FQH state at a special filling-dependent value of the power-law exponent, above which the interactions effectively become zero-range (pointlike). We also investigate the effect of C4-symmetric band distortions, where we observe a strikingly different dependence on filling.