Reviving the Lieb-Schultz-Mattis theorem in open quantum systems  

作　　者：Yi-Neng Zhou Xingyu Li Hui Zhai Chengshu Li Yingfei Gu 

机构地区：[1]Institute for Advanced Study,Tsinghua University,Beijing 100084,China [2]Hefei National Laboratory,Hefei 230088,China

出　　处：《National Science Review》2025年第1期29-36,共8页国家科学评论(英文版)

基　　金：supported by the Innovation Program for Quantum Science and Technology under(2021ZD0302005);the Beijing Outstanding Young Scholar Program,the XPLORER Prize,NSFC(12042505);the National Key R&D Program of China(2023YFA1406702);the China Postdoctoral Science Foundation(2022M711868);Tsinghua University Dushi Program;C.L.is also supported by the Chinese International Postdoctoral Exchange Fellowship Program and the Shuimu Tsinghua Scholar Program at Tsinghua University.

摘　　要：In closed systems,the celebrated Lieb-Schultz-Mattis(LSM)theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetries cannot have a non-degenerate gapped ground state.However,the applicability of this theorem is diminished when the system interacts with a bath and loses its energy conservation.In this letter,we propose that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to the bath renders the system short-range correlated.Specifically,we argue that the entanglement spectrum cannot have a non-degenerate minimum,isolated by a gap from other states.We further support the results with numerical examples where a spin-1/2 system is coupled to another spin-3/2 chain serving as the bath.Compared with the original LSM theorem that primarily addresses UV-IR correspondence,our findings reveal that the UV data and topological constraints also play a pivotal role in shaping the entanglement in open quantum many-body systems.

关 键 词：Lieb-Schultz-Mattis theorem open quantum system entanglement Hamiltonian 

分 类 号：X24[环境科学与工程—环境科学] X176