Interacting thermofield doubles and critical behavior in random regular graphs

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2021. Vol. 103. No. 10. Article 106013.

Valba O. V., Gorsky A.

We discuss numerically the nonperturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for C4 μ4 and degree preserving constraint is clarified. The first order phase transition at critical value of chemical potential for C4 μRRG 4 into bipartite phase with a formation of fixed number of bipartite clusters is found for ensemble of random regular graphs (RRG). We consider the similar phase transition in mean field version of combinatorial quantum gravity based of the Ollivier graph curvature for RRG supplemented with hard-core constraint and show that a order of a phase transition at μCRRG 4 and the structure of emerging phase depend on a vertex degree d in RRG. For d ¼ 3 the bipartite closed ribbon emerges at μ4 > μCRRG 4 while for d > 3 the ensemble of isolated or weakly interacting hypercubes supplemented with the bipartite closed ribbon gets emerged at the first order phase transition with a clearcut hysteresis. If the additional connectedness condition is imposed the phase at μ4 > μCRRG 4 gets identified as the closed chain of weakly coupled hypercubes. Since the ground state of isolated hypercube is the thermofield double we suggest that the dual holographic picture involves multiboundary wormholes. Treating RRG as a model of a Hilbert space for a interacting many-body system we discuss the patterns of the Hilbert space fragmentation at the phase transition. We also briefly comment on a possible relation of the found phase transition to the problem of holographic interpretation of a partial deconfinement transition in the gauge theories.

Keywords: random networks, critical behavior, phase transition

Publication based on the results of: Критические явления в сложных сетях (2020)