Quantum entanglement and fixed-point bifurcations (9 pages)

Maria Carolina Nemes, K. Furuya, G. Q. Pellegrino +3 more

Andrew P. Hines, Ross H. McKenzie, Gerard J Milburn

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state---the ground state---achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Tobias Brandes, Clive Emary, Neill Lambert

Jonathan F. San Miguel, Arpit Dua, Dominic J. Williamson

We introduce the subsystem symmetry-preserving real-space entanglement renormalization group and apply it to study bifurcating flows generated by linear and fractal subsystem symmetry-protected topological phases in two spatial dimensions. We classify all bifurcating fixed points that are given by subsystem symmetric cluster states with two qubits per unit cell. In particular, we find that the square lattice cluster state is a quotient-bifurcating fixed point, while the cluster states derived from Yoshida's first-order fractal spin liquid models are self-bifurcating fixed points. We discuss the relevance of bifurcating subsystem symmetry-preserving renormalization group fixed points for the classification and equivalence of subsystem symmetry-protected topological phases.

Barry C. Sanders, Shohini Ghose

Stein Olav Skrøvseth