Eigenstate properties of the disordered Bose-Hubbard chain  

作　　者：Jie Chen Chun Chen Xiaoqun Wang 

机构地区：[1]Key Laboratory of Artificial Structures and Quantum Control(Ministry of Education),School of Physics and Astronomy,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Physics,Zhejiang University,Hangzhou 310058,China [3]Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China

出　　处：《Frontiers of physics》2024年第4期57-72,共16页物理学前沿（英文版）

基　　金：This work is supported by the Ministry of Science and Technology of China(Grant No.2016YFA0300500);the National Natural Science Foundation of China(No.11974244).

摘　　要：Many-body localization(MBL)of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half.The von Neumann entanglement entropy Svn is commonly used to detect the MBL phase transition but remains challenging to be directly measured.Based on the U(1)symmetry from the particle number conservation,Svn can be decomposed into the particle number entropy S_(n) and the configuration entropy Sc.In light of the tendency that the eigenstate's S_(c) nears zero in the localized phase,we introduce a quantity describing the deviation of S from the ideal thermalization distribution;finite-size scaling analysis illustrates that it shares the same phase transition point with Sv but displays the better critical exponents.This observation hints that the phase transition to MBL might largely be determined by S and its fluctuations Notably,the recent experiments[A.Lukin,et al.,Science 364,256(2019);J.Leonard,et al.,Nat.Phys.19,481(2023)]demonstrated that this deviation can potentially be measured through the Sn measurement.Furthermore,our investigations reveal that the thermalized states primarily occupy the low-energy section of the spectrum,as indicated by measures of localization length,gap ratio,and energy density distribution.This low-energy spectrum of the Bose model closely resembles the entire spectrum of the Fermi(or spin XXZ)model,accommodating a transition from the thermalized to the localized states.While,owing to the bosonic statistics,the high-energy spectrum of the model allows the formation of distinct clusters of bosons in the random potential background.We analyze the resulting eigenstate properties and briefly summarize the associated dynamics.To distinguish between the phase regions at the low and high energies,a probing quantity based on the structure of S_(VN) is also devised.Our work highlights the importance of symmetry combined with entanglement in the study of MBL.In this regard,for the disordered Heisenberg XXZ chain,the recent pure eigenvalue analyses in[J.S

关 键 词：entanglement entropy decomposition U(1)symmetry thermalization-to-localization transition 

分 类 号：O41[理学—理论物理]