2021/08/31 by Jie Ren, Chenguang Liang, Cheng‐Guang Liang +1 · 34 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Eigenvalues and eigenvectors #Geometry #Hilbert space #Linear subspace #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum state #Simple (philosophy) #Subspace topology #Symmetry (geometry) #Tensor decomposition and applications #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · open access · doi:10.1103/physrevresearch.4.013155
published in Physical Review Research 4(1) (American Physical Society) · 30 pages, 7 figures, improved presentation, updated reference
arxiv created 2021/11/29 · openalex publication_date 2022/02/25 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is required to have at least a U(1) sub-Lie-group symmetry to allow coherent periodic dynamics from certain low-entangled initial states. We enumerate several possible deforming transformations based on the sub-group symmetry requirement and recover many existing models whose scar states are not connected by symmetry. In particular, a two-dimensional scar model is proposed, which hosts a periodic dynamical trajectory on which all states are topologically ordered.