2D Entanglement from a Twisted Motzkin Spaghetto

While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their 2D counterparts were only recently found, with rather sophisticated interactions involving at least 4 neighboring degrees of freedom. Here, we show that similar 2D entanglement properties can be realized by twisting a single 1D chain embedded on a 2D lattice. The interaction to generate such 2D entanglement is much simpler than the previous 2D construction by coupling orthogonal arrays of 1D highly entangled chains. The new construction exhibits an entanglement phase transition with enhanced entanglement entropy at the critical point compared to the previous bona fide 2D models, but the spectral gap in the highly entangled phase decays faster. The tensor network representation of the new ground state is composed of tensors with lower rank, showing a similar global geometry as those of the old ones.