Many-body energy invariant for T -linear resistivity
Many-body energy invariant for T -linear resistivity
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T 线性电阻率的多体能量不变量
DOI：
10.1103/physrevb.105.l201108
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发表时间：
2022
影响因子：
3.7
通讯作者：
Changlani, Hitesh J.
中科院分区：
文献类型：
--
作者：
Patel, Aavishkar A.;Changlani, Hitesh J.
描述强关联量子物质的动力学是一个挑战，特别是在缺乏准粒子描述的物理情况下。然而，在这种情况下，线性响应理论中的多体Kubo公式仍然有效，该公式涉及用多体波函数计算的当前算符的矩阵元素。直接在多体Hilbert空间中工作，不涉及准粒子(或没有准粒子)，我们解决了在几个强关联的凝聚态系统中出现的非费米-液体相中的线性温度(-线性)电阻率的难题。我们基于对多体Kubo公式的贡献的分析，得到了一个简单的线性电阻率出现的判据，该公式由一个能量不变的“函数”确定，该“函数”包括电流矩阵元素和描述微正则系综中系统的直流电导率的能量本征值。利用完全对角化方法，我们在无自旋最近邻Hubbard模型和弱单粒子跃迁耦合的Sachdev-Ye-Kitaev点系统中检验了该判据。我们还研究了二维Heisenberg模型中自旋电导的函数，得到了类似的结论。我们的工作表明，在多体希尔伯特空间概念下形成的一般原理是在广泛的系统中发生-线性电阻率的核心，并精确地将-线性电阻率转化为远远超出通常与量子临界点相关的能量标度不变性的概念。
The description of the dynamics of strongly correlated quantum matter is a challenge, particularly in physical situations where a quasiparticle description is absent. In such situations, however, the many-body Kubo formula from linear response theory, involving matrix elements of the current operator computed with many-body wave functions, remains valid. Working directly in the many-body Hilbert space and not making any reference to quasiparticles (or lack thereof), we address the puzzle of linear in temperature (-linear) resistivity seen in non-Fermi-liquid phases that occur in several strongly correlated condensed matter systems. We derive a simple criterion for the occurrence of-linear resistivity based on an analysis of the contributions to the many-body Kubo formula, determined by an energy invariant “function” involving current matrix elements and energy eigenvalues that describes the dc conductivity of the system in the microcanonical ensemble. Using full diagonalization, we test this criterion for thefunction in the spinless nearest-neighbor Hubbard model and in a system of Sachdev-Ye-Kitaev dots coupled by weak single-particle hopping. We also study thefunction for the spin conductivity in the two-dimensional Heisenberg model and arrive at similar conclusions. Our work suggests that a general principle, formulated in terms of many-body Hilbert space concepts, is at the core of the occurrence of-linear resistivity in a wide range of systems, and precisely translates-linear resistivity into a notion of energy scale invariance far beyond what is typically associated with quantum critical points.