Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator

The multiscale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with a finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wave function with a nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

Figure 1

Berry curvature of the renormalized wave function in the interaction picture at different scales $u$, drawn schematically in momentum space. The blue arrow corresponds to the direction of the reversed cMERA circuit. The area contributing to the Chern number expands as one approaches the UV scale.

Figure 2

A scheme to engineer the cMERA circuit in the interaction picture. The two excited states are coupled by spin-orbit interaction to each other and by off-resonant lasers to the two ground states.