PT対称性障害による同一モデルの連結(Connecting identical models via PT-symmetric disorder)


多自由度系での量子通信の可能性を探る研究者たち Researchers ponder the possibility of quantum communication in systems with many degrees of freedom

2022-03-24 大韓民国・基礎科学研究院(IBS)



PT対称Sachdev-Ye-Kitaevモデルにおけるレプリカ非対角配置の優勢と相転移 Dominance of Replica Off-Diagonal Configurations and Phase Transitions in a PT Symmetric Sachdev-Ye-Kitaev Model

Antonio M. García-García, Yiyang Jia (贾抑扬), Dario Rosa, and Jacobus J. M. Verbaarschot
Published 22 February 2022 DOI:


We show that, after ensemble averaging, the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, non-Hermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices is dominated by saddle points that couple replicas and conjugate replicas. This results in a nearly flat free energy that terminates in a first-order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relation between both configurations. For a nonchaotic SYK, the results are qualitatively different: the spectrum is gapless in the low temperature phase and there is an infinite number of second order phase transitions unrelated to the restoration of replica symmetry.
PT対称性障害による同一モデルの連結(Connecting identical models via PT-symmetric disorder)

Figure 1

The eigenvalue density, obtained from exact diagonalization, for one realization of the q=4k=1 non-Hermitian SYK model with N/2=30, compared to a circle (red curve).


Figure 2

The temperature dependence of the free energy of the non-Hermitian SYK model for N/2=30q=4, and k=1 (blue curve) compared to the analytical result (16). The value of E0 is the radius of the circle in Fig. 1.


Figure 3

Top: GLR(τ) from the solution of the Schwinger-Dyson equations for the SYK model (9) with q=4T=0.0005, and k=0.5 fitted by (17). Middle: the order parameter GLR(0), versus temperature for k=0.5. Bottom: the energy gap Eg for T=0.0005Tc as a function of k from the fit (17).


Figure 4

Derivative of the free energy for the non-Hermitian q=2k=1 SYK model. On the way to T=0, the system undergoes infinitely many second order phase transitions. For T>1/π, it becomes a constant which is a typical feature of free fermions.