Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
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DOI：
10.1103/physrevb.101.045137
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发表时间：
2020-01-31
影响因子：
3.7
通讯作者：
Spodyneiko, Lev
中科院分区：
文献类型：
--
作者：
Kapustin, Anton;Spodyneiko, Lev
我们推导出一个类似库波公式的热霍尔电导的二维晶格系统，这是免费的含糊之处与能量磁化的定义。我们用它来定义一个相对拓扑不变量的间隙二维晶格系统在零温度。当数值因子达到一定值时，它可以用相应边缘模的手征中心电荷的差异来识别。这建立了手征中心电荷的体边界对应。我们还表明，对于任何本地对易投影哈密顿量，相对手征中心电荷消失，而自由费米子系统，它是有关的零温电霍尔电导通过Wiedemann-Franz定律。
We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. We also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.