The Motzkin Spaghetto

Abstract

While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four neighboring degrees of freedom. Here, we show that similar bipartite entanglement properties can be realized on a square lattice with anisotropic interactions in four different quadrants. The interaction to generate such entanglement is much simpler than the previous constructions by coupling orthogonal arrays of highly entangled chains. The new construction exhibits an entanglement phase transition with different scalings of entanglement entropy at the critical point and in the lowly entangled phase, and faster decay of the spectral gap in the highly entangled phase. The tensor network representation of the new ground state consists of tensors with lower rank, while preserving a global geometry similar to that of the original networks.