Quantum phase transitions in entanglement complexity in Rokhsar-Kivelson-type wave functions

We study the behavior of families of states in the Rokhsar-Kivelson form under the Metropolis entanglement cooling algorithm introduced in [1]. We show the existence of two quantum phases. In the disordered phase, the algorithm is completely incapable of disentangling, thus revealing a complex pattern of entanglement, while in the ordered phase a finite amount of disentanglement is possible. We construct an order parameter from the relative effective disentangling performance and show an order-disorder quantum phase transition with universal critical indexes. In addition, we show that the disordered phase has complex pattern of entanglement as revealed by the Wigner-Dyson distribution for the gaps in the entanglement spectrum of Haar-random matrices. In contrast, states in the ordered phase stray away from the universal distribution.

[1] D. Shaffer, C. Chamon et al., Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits, J. Stat. Mech. (2014) P12007