Agrawal Utkarsh, Gopalakrishnan Sarang, Vasseur Romain
Department of Physics, University of Massachusetts, Amherst, Massachusetts, 01003, USA.
Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York, 10314, USA.
Nat Commun. 2020 May 6;11(1):2225. doi: 10.1038/s41467-020-15760-5.
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.
准周期系统是非周期性但具有确定性的，因此它们的临界行为也不同于纯净系统和无序系统。准周期临界性此前仅在耦合遵循离散准周期序列的特殊极限情况下被理解。在这里，我们考虑一般的准周期调制；我们显著地发现，对于一大类自旋链，一般的准周期调制在实空间重整化群变换下流向离散序列。因此，这些离散序列是泛函重整化群的不动点。这一观察结果使得对临界点进行渐近精确处理成为可能。我们使用这种方法来分析准周期海森堡、伊辛和Potts自旋链，以及准周期多体局域化转变的一个唯象模型。
