[{"article_number":"010352","oa":1,"external_id":{"arxiv":["2504.17627"]},"OA_type":"gold","language":[{"iso":"eng"}],"publication_status":"published","citation":{"ista":"Nicolau Jimenez E, Ljubotina M, Serbyn M. 2026. Fragmentation, zero modes, and collective bound states in constrained models. PRX Quantum. 7, 010352.","apa":"Nicolau Jimenez, E., Ljubotina, M., &#38; Serbyn, M. (2026). Fragmentation, zero modes, and collective bound states in constrained models. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/sl79-1xgb\">https://doi.org/10.1103/sl79-1xgb</a>","chicago":"Nicolau Jimenez, Eulalia, Marko Ljubotina, and Maksym Serbyn. “Fragmentation, Zero Modes, and Collective Bound States in Constrained Models.” <i>PRX Quantum</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/sl79-1xgb\">https://doi.org/10.1103/sl79-1xgb</a>.","mla":"Nicolau Jimenez, Eulalia, et al. “Fragmentation, Zero Modes, and Collective Bound States in Constrained Models.” <i>PRX Quantum</i>, vol. 7, 010352, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/sl79-1xgb\">10.1103/sl79-1xgb</a>.","ieee":"E. Nicolau Jimenez, M. Ljubotina, and M. Serbyn, “Fragmentation, zero modes, and collective bound states in constrained models,” <i>PRX Quantum</i>, vol. 7. American Physical Society, 2026.","short":"E. Nicolau Jimenez, M. Ljubotina, M. Serbyn, PRX Quantum 7 (2026).","ama":"Nicolau Jimenez E, Ljubotina M, Serbyn M. Fragmentation, zero modes, and collective bound states in constrained models. <i>PRX Quantum</i>. 2026;7. doi:<a href=\"https://doi.org/10.1103/sl79-1xgb\">10.1103/sl79-1xgb</a>"},"arxiv":1,"date_created":"2026-03-28T14:57:56Z","has_accepted_license":"1","acknowledgement":"The authors acknowledge useful discussions with Berislav Buca. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). M.L. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).","publisher":"American Physical Society","type":"journal_article","volume":7,"article_processing_charge":"Yes","ec_funded":1,"intvolume":"         7","ddc":["530"],"project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020","grant_number":"850899"}],"oa_version":"Published Version","doi":"10.1103/sl79-1xgb","date_published":"2026-03-13T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","day":"13","PlanS_conform":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"title":"Fragmentation, zero modes, and collective bound states in constrained models","DOAJ_listed":"1","publication_identifier":{"eissn":["2691-3399"]},"scopus_import":"1","file_date_updated":"2026-03-30T06:08:07Z","year":"2026","OA_place":"publisher","_id":"21501","department":[{"_id":"MaSe"}],"abstract":[{"text":"Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as zero modes—stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a U(1) particle-conservation symmetry. We use the U(1) East, which lacks inversion symmetry, and the inversion-symmetric U(1) East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body\r\nHilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of collective bound states, a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the U(1) North-East, and in the pairflip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained\r\nmodels. ","lang":"eng"}],"month":"03","publication":"PRX Quantum","corr_author":"1","date_updated":"2026-03-30T06:09:28Z","article_type":"original","quality_controlled":"1","file":[{"file_size":1848724,"content_type":"application/pdf","creator":"dernst","file_id":"21505","date_created":"2026-03-30T06:08:07Z","relation":"main_file","checksum":"d155ffa9e1a8275702149165f4bf963c","success":1,"date_updated":"2026-03-30T06:08:07Z","access_level":"open_access","file_name":"2026_PRXQuantum_Nicolau.pdf"}],"author":[{"id":"04b4791c-8fd7-11ee-a7df-be2fdc569c48","full_name":"Nicolau Jimenez, Eulalia","first_name":"Eulalia","last_name":"Nicolau Jimenez"},{"id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","first_name":"Marko","full_name":"Ljubotina, Marko","last_name":"Ljubotina","orcid":"0000-0003-0038-7068"},{"id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","first_name":"Maksym","last_name":"Serbyn"}]}]