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)

＜関連情報＞

• https://www.ibs.re.kr/cop/bbs/BBSMSTR_000000000738/selectBoardArticle.do?nttId=21140&pageIndex=1&searchCnd=&searchWrd=#toggle
• https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.081601

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:https://doi.org/10.1103/PhysRevLett.128.081601

ABSTRACT

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.

Figure 1

The eigenvalue density, obtained from exact diagonalization, for one realization of the $q=4$, $k=1$ 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 $N/2=30$, $q=4$, and $k=1$ (blue curve) compared to the analytical result (16). The value of $E_0$ is the radius of the circle in Fig. 1.

Figure 3

Top: $G_{LR}\left(\tau \right)$ from the solution of the Schwinger-Dyson equations for the SYK model (9) with $q=4$, $T=0.0005$, and $k=0.5$ fitted by (17). Middle: the order parameter $G_{LR}\left(0\right)$, versus temperature for $k=0.5$. Bottom: the energy gap $E_g$ for $T=0.0005\ll T_c$ as a function of $k$ from the fit (17).

Figure 4

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