AI 中文总结
该研究针对PT对称非厄米多通道近藤模型，发现零模与局域矩相的杂质熵非单调，打破了RG不可逆性的单调熵流规律。
AI 中文摘要
我们研究了一个PT对称的非厄米多通道近藤模型，该模型由一对自旋为1/2的杂质通过复共轭近藤耦合与n个传导电子通道耦合而成。杂质的重整化群（RG）流由近藤标度T_K和无量纲非厄米性参数α表征。随着α增大，精确的Bethe Ansatz解呈现出四种杂质相：过屏蔽近藤相、零模相、Yu-Shiba-Rusinov（YSR）相和局域矩相。近藤相、零模相和局域矩相是PT未破缺的，而YSR相自发破缺PT对称性。我们利用广义热力学Bethe Ansatz确定了PT未破缺各相中的杂质自由能和Affleck-Ludwig g函数。在近藤相中，缺陷RG流连接紫外和红外共形不动点，杂质熵从2ln2流向2ln[2cos(π/(n+2))]，与缺陷共形场论一致。在零模相中，零能杂质弦将能谱重组为多个激发塔；在局域矩相中，RG流变为循环，回到未屏蔽的局域矩不动点。我们推测RG不可逆性及广义Affleck-Ludwig g定理在近藤相中依然成立，但精确解表明，与缺陷共形场论一致的实能谱和缺陷熵并不保证RG不可逆性：零模相和局域矩相中的杂质熵均为非单调的。
英文摘要
We study a $\mathscr{PT}$-symmetric non-Hermitian multichannel Kondo model consisting of a pair of spin-$\frac12$ impurities coupled to $n$ conduction-electron channels through complex-conjugate Kondo couplings. The impurity renormalization-group (RG) flow is characterized by the Kondo scale $T_K$ and a dimensionless non-Hermiticity parameter $α$. As $α$ increases, the exact Bethe Ansatz solution exhibits four impurity phases: overscreened Kondo, zero mode, Yu--Shiba--Rusinov (YSR), and local moment. The Kondo, zero-mode, and local-moment phases are $\mathscr{PT}$-unbroken, whereas the YSR phase spontaneously breaks $\mathscr{PT}$ symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck--Ludwig $g$-function throughout the $\mathscr{PT}$-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from $2\ln2$ to $2\ln\left[2\cos\left(\fracπ{n+2}\right)\right]$, in agreement with defect conformal field theory. In the zero-mode phase, zero-energy impurity strings reorganize the spectrum into multiple excitation towers, while in the local-moment phase, the RG flow becomes cyclic, returning to the unscreened local-moment fixed point. We conjecture that RG irreversibility, and hence a generalized Affleck--Ludwig $g$-theorem, survives throughout the Kondo phase. Our exact solution nevertheless shows that a real spectrum and defect entropies consistent with defect CFT do not guarantee RG irreversibility: the impurity entropy is non-monotonic in both the zero-mode and local-moment phases.
CommentsThe arXiv abstract has been shortened to comply with the abstract length limit; the full abstract appears in the manuscript, some typos corrected
