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arXiv 2103.03256cond-mat.str-el
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掺杂莫特绝缘体破坏费米液体的$\mathbb Z_2$对称性:强耦合不动点的稳定性

Doped Mott Insulators Break $\mathbb Z_2$ Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points

Edwin W. Huang, Gabriele La Nave, Philip W. Phillips

摘要:

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。我们发现,打破一个被忽视的局部动量空间$\mathbb Z_2$对称性的费米液体正是这样做。因此,虽然人们正确地认为费米液体的莫特跃迁不会破坏任何连续对称,但离散对称被破坏了。这种对称性破缺是莫特物理学的一个组织原则,无论它是来自于易处理的Hatsugai-Kohmoto(HK)模型还是来自于难处理的哈伯德模型。这两个都是由我们通过重整化群分析建立的同一个不动点控制的。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现象。从理论上讲,单粒子占据的光谱区域会产生单粒子格林函数的零点表面,称为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为$p+1$且$p$为奇数的Luttinger曲面.我们得出结论:Hubbard模型和HK模型都属于同一高温普适类,都受破缺的$\mathbb Z_2$对称四次不动点控制.

英文摘要:

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 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 local-in-momentum space $\mathbb Z_2$ symmetry of a Fermi liquid does precisely this. As a result, while the Mott transition from a Fermi liquid is correctly believed to obtain without the breaking of 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 (HK) model or the intractable Hubbard model. That both are controlled by the same fixed point we establish through a renormalization group analysis. An experimental manifestation of this fixed point is the onset of particle-hole asymmetry, a widely observed 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 $p$ odd. We conclude that the Hubbard and HK models both lie in the same high temperature universality class and are controlled by the broken $\mathbb Z_2$ symmetry quartic fixed point.

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