For a quasi-two-dimensional nonlinear sigma model on the real Stiefel manifolds with a generalized (anisotropic) metric, the equations of a two-charge renormalization group (RG) for the homothety and anisotropy of the metric as effective couplings are obtained in a one-loop approximation. Normal coordinates and the curvature tensor are exploited for the renormalization of the metric. The RG trajectories are investigated and the presence of a fixed point common to four critical lines or four phases (tetracritical point) in the general case, or its absence in the case of an Abelian structure group, is established. For the tetracritical point, the critical exponents are evaluated and compared with those known earlier for a simpler particular case.
Research Institute for Innovation and Co-Creation, Osaka Metropolitan University（大阪公立大学创新与共创研究院）；Department of Physics, Osaka Metropolitan University（大阪公立大学物理系）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南部阳一郎理论与实验物理研究所）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）
Renormalization group analysis of the quantum non-linear sigma model with a damping term
研究了d维零温量子非线性西格玛模型在阻尼项f（w）~ |w| ^alpha存在下的行为，其中1 \le alpha <2. We find two fixed points: a spin-wave fixed point FP1 showing a dynamic scaling exponent z=1 and a dissipative fixed point FP2 with z>1.在ε-展开的框架中，可以看出，存在值α_*（d）\le α \le 2的范围，其中点FP 1相对于FP 2是稳定的，使得即使在存在耗散项的情况下，系统也实现z=1的量子临界行为。然而，合理的论证表明，在d=2时，这个范围非常窄。在对称性破缺阶段，我们讨论了一种唯象标度方法，将阻尼视为有序基态的微扰。这些结果与欠掺杂层状铜氧化物中观察到的赝能隙效应的关系进行了讨论。
