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Recently, there is an increasing interest in realizing new phases of matters by non-unitary dynamics, where different phases are classified by their entanglement properties. In this talk, I will present our recent three works of using solvable SYK chains to understand such entanglement transitions. For non-interacting models, the system shows a critical phase, which can be understood as emergent replica conformal symmetry due to spontaneous symmetry breaking of the O(2) group. The entanglement entropy corresponds to the energy of a half-vortex pair. When interaction is added, the O(2) group is replaced by the C4 group, and the vortex pair is replaced by domain walls. We also study the phase diagram when long-range coupling exists, and find a novel fractal phase with sub-volume entanglement.
Pengfei Zhang is now a postdoc in Caltech. He got his B.Sc. in the Department of Physics, Tsinghua University in 2015. He got his Ph.D. in the Institute for Advanced Study, Tsinghua University in 2019 under the supervision of Prof. Hui Zhai. He then went to Caltech as a Burke Fellow postdoc with Prof. Alexei Kitaev. His main research area is information scrambling and SYK models, quantum gases, and quantum machine learning.