物理学报2025，Vol.74Issue(10)：28-35,8.DOI:10.7498/aps.74.20250061
分形子模型中的彩虹伤痕态
Rainbow scar states in the fracton model
摘要
Abstract
The eigenstate thermalization hypothesis describes the nonequilibrium dynamics of an isolated quantum many-body system,during which a pure state becomes locally indistinguishable from a thermal ensemble.The discovery of quantum many-body scars(QMBS)shows a weak violation of ergodicity,characterized by coherent oscillations of local observables after a quantum quench.These states consist of the tower of regular eigenstates which are equally spaced in the energy spectrum.Although subextensive entanglement scaling is a primary feature widely used to detect QMBS numerically as entropy outliers,rainbow scars exhibit volume-law scaling,which may challenge this property.In this work,we construct the rainbow scar state in the fracton model on a two-leg ladder.The fracton model is composed of four-body ring-exchange interactions,exhibiting global time-reversal symmetry(T)=Ki(σ)y and subsystem Û(1)=Πj∈{row/col} exp(iθ/2(σ)zj)symmetry.The subsystem symmetry constrains particle mobility,hindering the establishment of thermal equilibrium and leading to a series of anomalous dynamical processes.We construct the rainbow scar state with distributed four-body GHZ states whose entanglement entropy follows the volume law.By calculating the eigenstates of the fracton model with exact diagonalization,the rainbow scar state consists of a series of degenerate high-energy excited states that are not significant outliers among other eigenstates in the spectrum.By introducing the on-site interaction to break the time-reversal symmetry,the degeneracy of rainbow scar states is lifted into an equally spaced tower of states,ensuring the revival of the initial state.However,when subsystem Û(1)symmetry is broken,the scar state is quickly thermalized,indicating that the weak thermalization may be protected by subsystem Û(1)symmetry.Additionally,we propose a scheme for preparing the rainbow scar state by modulating the strength of the four-body interaction and(σ)z operations,analyzing the influence of noise on the strength of the four-body interaction.This work provides new insights into the weak thermalization processes in fracton model and aids in understanding the nature of ETH-violation in various nonequilibrium systems.关键词
四体相互作用/分形子模型/多体伤痕态Key words
four-body ring exchange interactions/fracton model/many-body scar states引用本文复制引用
谢岩骏,戴汉宁..分形子模型中的彩虹伤痕态[J].物理学报,2025,74(10):28-35,8.基金项目
国家自然科学基金(批准号:12074367)、国家重点研发计划(批准号:2020YFA0309804,2023YFC2206200)、上海市市级科技重大专项(批准号:2019SHZDZX01)和科技创新2030—"量子通信与量子计算机"重大项目(批准号:2021ZD0302002)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No.12074367),the National Key R&D Program of China(Grant Nos.2020YFA0309804,2023YFC2206200),the Shanghai Municipal Science and Technology Major Project,China(Grant No.2019SHZDZX01),and the Innovation Program for Quantum Science and Technology,China(Grant No.2021ZD0302002). （批准号:12074367）
