Tunable Hilbert space fragmentation and extended critical regime

Lisiecki, Mateusz (author), Bonča, Janez (author), Mierzejewski, Marcin (author), Herbrych, Jacek (author), Łydżba, Patrycja (author)

Systems exhibiting the Hilbert-space fragmentation are nonergodic, and their Hamiltonians decompose into exponentially many blocks in the computational basis. In many cases, these blocks can be labeled by eigenvalues of statistically localized integrals of motion (SLIOMs), which play a similar role in fragmented systems as local integrals of motion in integrable systems. While a nonzero perturbation eliminates all nontrivial conserved quantities from integrable models, we demonstrate for the $t$-$J_\mathrm{z}$ chain that an appropriately chosen perturbation may gradually eliminate SLIOMs (one by one) by progressively merging the fragmented subspaces. This gradual recovery of ergodicity manifests as an extended critical regime characterized by multiple peaks of the fidelity susceptibility. Each peak signals a change in the number of SLIOMs and blocks, as well as an ultra-slow relaxation of local observables.

• Language: English
• Keywords: eigenstate thermalization, strongly correlated systems, integrable systems, exact diagonalization
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2025
• Number of pages: Str. 195116-1-195116-11
• Numbering: Vol. 112, iss. 19
• PID: 20.500.12556/RUL-176181
• UDC: 538.9
• ISSN on article: 2469-9950
• DOI: 10.1103/fysk-w1vs
• COBISS.SI-ID: 258339843
• Publication date in RUL: 24.11.2025

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

Secondary language

• Language: Slovenian
• Keywords: termalizacija lastnih stanj, močno korelirani sistemi, integrabilni sistemi, točna diagonalizacija