2016/10/31 by Sumilan Banerjee, Ehud Altman · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.dis-nn #hep-th #msc:82B26 #msc:81Q50 #msc:82B44 #msc:82C10
paper · pdf · doi:10.1103/physrevb.95.134302
published as Phys. Rev. B 95, 134302 (2017) · 20 pages, 12 figures, added the calculation for Lyapunov exponent away from the particle-hole symmetric situation
arxiv created 2016/11/07 · arxiv updated 2017/04/21
We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi liquid like state, while still allowing an exact solution in a suitable large N limit. The extended model involves coupling the interacting N-site SYK model to a new set of pN peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low energy phase below a critical ratio of peripheral sites p<pc(n) that depends on the fermion filling n. The scrambling dynamics throughout the non-Fermi liquid phase is characterized by a universal Lyapunov exponent λL→ 2πT in the low temperature limit, however the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point pc. The residual entropy at T→ 0, non zero in the NFL, also vanishes continuously at the critical point. For p>pc the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low temperature and frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent λL∝ T2.