Fig. 3: Mean-field striated versus entangled nematic phase.

a Density-density correlation functions of the mean-field and exact striated ground state, both at (δ, R_b) = (3.1, 1.5); these agree, confirming the mean-field nature of the striated phase. (b) Density-density correlation functions for the entangled nematic phase ground state and two different mean-field ground states (from a 6 × 3 unit cell and a 3 × 4 unit cell) at (δ, R_b) = (5.0, 2.3). In (a, b), 2-fold/4-fold degeneracy of a peak is indicated by 2/4 horizontal dots distributed around the proper distance coordinate. 8-fold degeneracy in (a) is shown as two rows of 4 dots. The non-mean-field (entangled) character of the nematic phase is evident. c Structure of the nematic state in terms of classical configurations constructed via compositions of 3 individual column states \(\left|a\right\rangle,\left|b\right\rangle,\left|c\right\rangle\). In the classical limit, there are 4 distinct sets of low-energy configurations, all characterized by the absence of adjacent columns in the same state (e.g., \(\left|aa...\right\rangle\)) and large degeneracies due to permutational symmetry between \(\left|a\right\rangle\), \(\left|b\right\rangle\), and \(\left|c\right\rangle\). The lowest in energy is 6-fold degenerate, corresponding to the 3-star state. However, in the quantum nematic state the configurations that are slightly higher in energy have much larger wavefunction coefficients. The most relevant classical states in the wavefunction are those with the greatest number of possible single full column hops (e.g., a → b) without introducing unfavorable states like \(\left|aa...\right\rangle\), revealing the role of itinerancy in the nematic phase. d Bipartite entanglement entropy for each possible bipartition of the 12 × 9 supercell nematic ground state. One inset shows the path that the partition location axis follows through the supercell MPS, while the other shows the entanglement spectrum at a central cut.