Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator

TL;DR

This paper investigates the effects of electron correlations in fractional topological insulators with spin-dependent holomorphicity, revealing that strong correlations lead to spin separation due to spontaneous symmetry breaking.

Contribution

It demonstrates that fractional topological insulators with spin-dependent holomorphicity cannot be simply viewed as two independent fractional quantum Hall states, highlighting intrinsic spin interactions.

Findings

Strong correlations prevent FTI from being two independent FQHSs.

Half-filled spin-holomorphic FTI is an insulator.

Spontaneous spin separation occurs at half filling.

Abstract

Motivated by the close analogy with the fractional quantum Hall states (FQHSs), fractional Chern insulators (FCIs) are envisioned as strongly correlated, incompressible states emerging in a fractionally filled, (nearly) flat band with non-trivial Chern number. Built upon this vision, fractional topological insulators (FTIs) have been proposed as being composed of two independent copies of the FCI with opposite Chern numbers for different spins, preserving the time-reversal symmetry as a whole. An important question is if the correlation between electrons with different spins can be really ignored. To address this question, we investigate the effects of correlation in the presence of spin-dependent holomorphicity, i.e., electrons of one spin species reside in the holomorphic lowest Landau level, while those of the other in the antiholomorphic counterpart. By constructing and performing exact diagonalization of an appropriate model Hamiltonian, here, we show that generic, strongly correlated, fractionally filled states with spin-dependent holomorphicity cannot be described as two independent copies of the FQHS, suggesting that FTIs in the lattice cannot be described as those of the FCI either. Fractionally filled states in this system are generally compressible except at half filling, where an insulating state called the half-filled spin-holomorphic FTI occurs. It is predicted that the half-filled spin-holomorphic FTI is susceptible to an inherent spontaneous symmetry breaking, leading to the spatial separation of spins.