Real-space entanglement spectra of parton states in fractional quantum Hall systems

Abstract

Real-space entanglement spectra (RSES) capture characteristic features of the topological order encoded in the fractional quantum Hall (FQH) states. In this work, we numerically compute, using Monte Carlo methods, the RSES and the counting of edge excitations of non-Abelian FQH states constructed using the parton theory. Efficient numerical computation of RSES of parton states is possible, thanks to their product-of-Slater-determinant structure, allowing us to compute the spectra in systems of up to 80 particles. Specifically, we compute the RSES of the parton states ${\varphi }_2^2$, ${\varphi }_2^3$, and ${\varphi }_3^2$, where ${\varphi }_n$ is the wave function of $n$ filled Landau levels, in the ground state as well as in the presence of bulk quasihole states. We then explicitly demonstrate a one-to-one correspondence of RSES of the parton states with representations of the Kac-Moody algebras satisfied by their edge currents. We also show that for the lowest Landau level projected version of these parton states, the spectra match with that obtained from the edge current algebra. We also perform a computation of spectra of the overlap matrices corresponding to the edge excitations of the parton states with a constrained number of particles in the different parton Landau levels. Counting in these matches the individual branches present in RSES, providing insight about how different branches are formed.

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• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride