Identifying the closeness of eigenstates in quantum many-body systems

Haibin Li; Yang Yang; Pei Wang; Xiaoguang Wang

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arXiv · 1512.04350

Identifying the closeness of eigenstates in quantum many-body systems

Haibin Li·Yang Yang·Pei Wang·Xiaoguang Wang

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Abstract

We propose a new quantity called modulus fidelity to measure the closeness of two quantum pure states. Especially, we use it to investigate the closeness of eigenstates of quantum many-body systems. When the system is integrable, the modulus fidelity of neighbor eigenstates displays a large fluctuation. But the modulus fidelity is close to a constant when system becomes non-integrable with fluctuation reduced drastically. Average modulus fidelity of neighbor eigenstates increases with the increase of parameters that destroy the integrability, which also indicates the integrable-chaos transition. In non-integrable case, it is found two eigenstates are closer to each other if their level spacing is small. We also show that the closeness of eigenstates in non-integrable domain is the underlying mechanism of \emph{eigenstate thermalization hypothesis} (ETH) which explains the thermalization in nonintegrable system we studied.

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Haibin Li, Yang Yang, Pei Wang, Xiaoguang Wang. 2015-12-14. Identifying the closeness of eigenstates in quantum many-body systems. https://arxiv.org/abs/1512.04350

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