Discrete symmetry breaking defines the Mott quartic fixed point
Discrete symmetry breaking defines the Mott quartic fixed point
复制标题
DOI：
10.1038/s41567-022-01529-8
复制
发表时间：
2022-03-21
期刊：
影响因子：
19.6
通讯作者：
Phillips, Philip W.
中科院分区：
文献类型：
--
作者：
Huang, Edwin W.;La Nave, Gabriele;Phillips, Philip W.
由于费米液体本质上是物质的非相互作用状态，所有低于化学势的电子能级都被双重占据。因此，打破费米液体理论的最简单方法是设计一个模型，其中一些状态被单独占据，保持时间反演不变性不变。我们证明，打破一个被忽视的费米液体的（1）局部动量空间Z（2）对称性正是这样做的。因此，虽然费米液体的莫特跃迁被正确地认为是在不破坏任何连续对称性的情况下发生的，但离散对称性被破坏了。这种对称性破缺是莫特物理学的一个组织原则，无论它是来自易于处理的Hatsugai-Kohmoto模型还是难以处理的Hubbard模型。通过重整化群分析，我们建立了两者都由同一个不动点控制。这个固定点的一个实验表现是粒子-空穴不对称性的开始，这是强关联系统中广泛观察到的（2-10）现象。从理论上讲，光谱的单占据区域产生单粒子绿色函数的零表面，表示为Luttinger表面。使用K-同调，我们证明了Bott拓扑不变量保证了该曲面对局部扰动的稳定性。证明了强耦合不动点只对应于余维p + 1且p为奇数的Luttinger曲面，并得出结论：Hubbard和Hatsugai-Kohmoto模型都属于同一个高温普适类，且都受Z（2）对称破缺的四次不动点控制.
Because Fermi liquids are inherently non-interacting states of matter, all electronic levels below the chemical potential are doubly occupied. Consequently, the simplest way of breaking the Fermi-liquid theory is to engineer a model in which some of those states are singly occupied, keeping time-reversal invariance intact. We show that breaking an overlooked(1) local-in-momentum space Z(2) symmetry of a Fermi liquid does precisely this. As a result, although the Mott transition from a Fermi liquid is correctly believed to arise without breaking any continuous symmetry, a discrete symmetry is broken. This symmetry breaking serves as an organizing principle for Mott physics whether it arises from the tractable Hatsugai-Kohmoto model or the intractable Hubbard model. Through a renormalization-group analysis, we establish that both are controlled by the same fixed point. An experimental manifestation of this fixed point is the onset of particle-hole asymmetry, a widely observed(2-10) phenomenon in strongly correlated systems. Theoretically, the singly occupied region of the spectrum gives rise to a surface of zeros of the single-particle Green function, denoted as the Luttinger surface. Using K-homology, we show that the Bott topological invariant guarantees the stability of this surface to local perturbations. Our proof demonstrates that the strongly coupled fixed point only corresponds to those Luttinger surfaces with co-dimension p + 1 with odd p. We conclude that both Hubbard and Hatsugai-Kohmoto models lie in the same high-temperature universality class and are controlled by a quartic fixed point with broken Z(2) symmetry.