Exceptional points and the topology of quantum many-body spectra
Exceptional points and the topology of quantum many-body spectra
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DOI：
10.1103/physrevresearch.1.033051
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发表时间：
2019-06
影响因子：
4.2
通讯作者：
D. J. Luitz;F. Piazza
中科院分区：
文献类型：
--
作者：
D. J. Luitz;F. Piazza
我们证明了在一般的遍历量子多体系统中，相互作用导致哈密顿量的任意小的非厄尔米特分量的非平凡拓扑。这是由于系统中指数大小的例外点的扩散，这些点具有作为累积(超)表面的埃尔米特极限。因此，表征厄米遍历多体系统的最近邻能级排斥被证明是更丰富的现象学的投影，其中实际上所有成指数级的多对本征值相互作用。例外点的扩散和积累也意味着将局域遍历量子多体系统从浴中分离出来的指数困难，因为健壮的拓扑签名仍然以任意接近厄米极限的例外点的形式存在。
We show that in a generic, ergodic quantum many-body system the interactions induce a non-trivial topology for an arbitrarily small non-hermitean component of the Hamiltonian. This is due to an exponential-in-system-size proliferation of exceptional points which have the hermitian limit as an accumulation (hyper-)surface. The nearest-neighbour level repulsion characterizing hermitian ergodic many-body sytems is thus shown to be a projection of a richer phenomenology where actually all the exponentially many pairs of eigenvalues interact. The proliferation and accumulation of exceptional points also implies an exponential difficulty in isolating a local ergodic quantum many-body system from a bath, as a robust topological signature remains in the form of exceptional points arbitrarily close to the hermitian limit.