Real Space Entanglement Spectrum of Fractional Hall States

Antoine Sterdyniak

Hui Li, F. D. M. Haldane

Jérôme Dubail, N. Read, Edward H. Rezayi

We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely related particle entanglement spectrum and carry out the Schmidt decomposition of the Laughlin state analytically at large size.

Li-Xia Wei, Na Jiang, Qi Li +1 more

The edge of the electronic fractional quantum Hall (FQH) system obeys the law of the chiral Luttinger liquid theory due to its intrinsic topological properties and the relation of bulk-edge correspondence. However, in a realistic experimental system, such as the usual Hall bar setup, the softening of the background confinement potential can induce the reconstruction of the edge spectrum, which breaks the chirality and universality of the FQH edge. The entanglement spectrum (ES) of the FQH ground state has the same counting structure as that of the energy spectrum indicating the topological characters of the quantum state. In this work, we report that the ES can also have an edge reconstruction while sweeping the area of the subsystem in real space cut. Moreover, we found that the critical area of the subsystem matches accurately with the intrinsic building block of the FQH liquids, namely the correlation hole of the FQH liquids. The above results seem to be universal after our study of a series of typical FQH states, such as two Laughlin states at $\ensuremath{\nu}=1/3$ and $1/5$, and the Moore-Read state for $\ensuremath{\nu}=5/2$.

Ivan Dario Jimenez Rodriguez, Simon C. Davenport, Steven H. Simon +1 more

We study the entanglement spectra of many-particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall effect. We identify a set of entanglement wave functions (EWFs), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWFs for the Laughlin and Jain states can be recognized as composite fermion states. These states provide an exact description of the low angular-momentum sectors of the real-space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states.

Edward H. Rezayi