{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:08:21Z","timestamp":1790726901050,"version":"4.1.0"},"reference-count":62,"publisher":"American Physical Society (APS)","issue":"18","license":[{"start":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T00:00:00Z","timestamp":1778112000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["PHY-2310429"],"award-info":[{"award-number":["PHY-2310429"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["994308"],"award-info":[{"award-number":["994308"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>\n                    We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:mo stretchy=\"false\">\u27e8<\/a:mo>\n                        <a:mi>tr<\/a:mi>\n                        <a:mtext>\u2009<\/a:mtext>\n                        <a:msup>\n                          <a:mrow>\n                            <a:mi>X<\/a:mi>\n                          <\/a:mrow>\n                          <a:mrow>\n                            <a:mn>2<\/a:mn>\n                          <\/a:mrow>\n                        <\/a:msup>\n                        <a:mo stretchy=\"false\">\u27e9<\/a:mo>\n                      <\/a:mrow>\n                    <\/a:math>\n                    in the confining phase of the theory in the infinite\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:mi>N<\/e:mi>\n                    <\/e:math>\n                    limit. Exploiting the symmetries of these models and applying nonlinear relaxation, we impose constraints that include traces of words of length up to 14. Our results yield rigorous bounds on the large-\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mi>N<\/g:mi>\n                    <\/g:math>\n                    ground-state dynamics, along with estimates of selected low-order observables to eight significant digits.\n                  <\/jats:p>","DOI":"10.1103\/cyq8-4sd7","type":"journal-article","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T16:18:33Z","timestamp":1774973913000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["High-Precision Bootstrap of Multimatrix Quantum Mechanics"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2767-6142","authenticated-orcid":true,"given":"Henry W.","family":"Lin","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00f54p054","id-type":"ROR","asserted-by":"publisher"}],"name":"Stanford University"},{"id":[{"id":"https:\/\/ror.org\/00hx57361","id-type":"ROR","asserted-by":"publisher"}],"name":"Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1507-8700","authenticated-orcid":true,"given":"Zechuan","family":"Zheng","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/013m0ej23","id-type":"ROR","asserted-by":"publisher"}],"name":"Perimeter Institute for Theoretical Physics"},{"id":[{"id":"https:\/\/ror.org\/03a26mh11","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratoire de Physique de l\u2019Ecole Normale Sup\u00e9rieure"},{"id":[{"id":"https:\/\/ror.org\/013cjyk83","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e9 PSL"},{"id":[{"id":"https:\/\/ror.org\/02feahw73","id-type":"ROR","asserted-by":"publisher"}],"name":"CNRS"},{"id":[{"id":"https:\/\/ror.org\/02en5vm52","id-type":"ROR","asserted-by":"publisher"}],"name":"Sorbonne Universit\u00e9"},{"id":[{"id":"https:\/\/ror.org\/05f82e368","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e9 Paris Cit\u00e9"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,5,7]]},"reference":[{"key":"cyq8-4sd7Cc1R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2017.06.009","type":"journal-article"},{"key":"cyq8-4sd7Cc2R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2020)090","type":"journal-article"},{"key":"cyq8-4sd7Cc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.041601","type":"journal-article"},{"key":"cyq8-4sd7Cc4R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2022)030","type":"journal-article"},{"key":"cyq8-4sd7Cc5R1","unstructured":"Alternatively, at finite N, one may impose trace relations [6].","type":"other"},{"key":"cyq8-4sd7Cc6R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP03(2025)099","type":"journal-article"},{"key":"cyq8-4sd7Cc7R1","doi-asserted-by":"publisher","DOI":"10.4310\/ATMP.2004.v8.n4.a1","type":"journal-article"},{"key":"cyq8-4sd7Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.21.446","type":"journal-article"},{"key":"cyq8-4sd7Cc9R1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(80)90353-6","type":"journal-article"},{"key":"cyq8-4sd7Cc10R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/21\/22\/010","type":"journal-article"},{"key":"cyq8-4sd7Cc11R1","doi-asserted-by":"publisher","DOI":"10.1088\/1126-6708\/2007\/10\/097","type":"journal-article"},{"key":"cyq8-4sd7Cc12R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2010)034","type":"journal-article"},{"key":"cyq8-4sd7Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.L051501","type":"journal-article"},{"key":"cyq8-4sd7Cc14R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP01(2025)190","type":"journal-article"},{"key":"cyq8-4sd7Cc15R1","unstructured":"H. Lin and Z. Zheng, Bootstrapping BFSS, part II (to be published).","type":"other"},{"key":"cyq8-4sd7Cc16R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0217751X01003949","type":"journal-article"},{"key":"cyq8-4sd7Cc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.100.021601","type":"journal-article"},{"key":"cyq8-4sd7Cc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.191602","type":"journal-article"},{"key":"cyq8-4sd7Cc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.78.041502","type":"journal-article"},{"key":"cyq8-4sd7Cc20R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2016)167","type":"journal-article"},{"key":"cyq8-4sd7Cc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.94.094501","type":"journal-article"},{"key":"cyq8-4sd7Cc23R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2018)124","type":"journal-article"},{"key":"cyq8-4sd7Cc24R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP03(2023)071","type":"journal-article"},{"key":"cyq8-4sd7Cc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0550-3213(99)00749-X","type":"journal-article"},{"key":"cyq8-4sd7Cc26R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2013.01.001","type":"journal-article"},{"key":"cyq8-4sd7Cc27R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP08(2024)198","type":"journal-article"},{"key":"cyq8-4sd7Cc28R1","doi-asserted-by":"publisher","DOI":"10.1142\/S0217751X25400032","type":"journal-article"},{"key":"cyq8-4sd7Cc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.11.395","type":"journal-article"},{"key":"cyq8-4sd7Cc30R1","unstructured":"See Refs.\u00a0[1, 6, 13, 31, 32] for some bootstrap approaches to the Euclidean path integral approach to pure Yang-Mills theory.","type":"other"},{"key":"cyq8-4sd7Cc31R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP08(2024)154","type":"journal-article"},{"key":"cyq8-4sd7Cc32R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP12(2025)033","type":"journal-article"},{"key":"cyq8-4sd7Cc33R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/cyq8-4sd7 for additional details on the numerical implementation, the relaxation procedure, the large-D analysis, and a pedagogical example illustrating the bootstrap framework.","type":"other"},{"key":"cyq8-4sd7Cc34R1","unstructured":"This is equivalent to introducing a formal \u210f=1\/N so that [Xij,Pkl]\u221di\u210f.","type":"other"},{"key":"cyq8-4sd7Cc35R1","unstructured":"Here Oi are single letters, e.g., an XI or a PJ.","type":"other"},{"key":"cyq8-4sd7Cc36R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01625778","type":"journal-article"},{"key":"cyq8-4sd7Cc37R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-51592-3","type":"journal-article"},{"key":"cyq8-4sd7Cc38R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP04(2025)186","type":"journal-article"},{"key":"cyq8-4sd7Cc40R1","volume-title":"Group Theory: Birdtracks, Lie\u2019s, and Exceptional Groups","author":"P. Cvitanovic","year":"2020","type":"book"},{"key":"cyq8-4sd7Cc41R1","unstructured":"In principle, one can also consider other methods like the navigator function [42].","type":"other"},{"key":"cyq8-4sd7Cc42R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.11.3.072","type":"journal-article"},{"key":"cyq8-4sd7Cc43R1","unstructured":"Although, in principle, we could relax all quadratic variables, we found it best to scan over \u27e8trXIXI\u27e9 while relaxing the remaining quadratic variables.","type":"other"},{"key":"cyq8-4sd7Cc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/t8m6-zhrm","type":"journal-article"},{"key":"cyq8-4sd7Cc45R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2024)054","type":"journal-article"},{"key":"cyq8-4sd7Cc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.3.010324","type":"journal-article"},{"key":"cyq8-4sd7Cc47R1","unstructured":"Our \u03bbeff=1 becomes m=2, g=2 in the conventions of [45], after a canonical transformation.","type":"other"},{"key":"cyq8-4sd7Cc48R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(83)90180-3","type":"journal-article"},{"key":"cyq8-4sd7Cc49R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(84)90215-3","type":"journal-article"},{"key":"cyq8-4sd7Cc50R1","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(85)90077-X","type":"journal-article"},{"key":"cyq8-4sd7Cc51R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP01(2022)168","type":"journal-article"},{"key":"cyq8-4sd7Cc52R1","unstructured":"See Refs.\u00a0[53] and [14] for similar bounds in the BFSS case.","type":"other"},{"key":"cyq8-4sd7Cc53R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP06(2023)038","type":"journal-article"},{"key":"cyq8-4sd7Cc54R1","doi-asserted-by":"publisher","DOI":"10.21468\/SciPostPhys.19.3.081","type":"journal-article"},{"key":"cyq8-4sd7Cc56R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2006.10.005","type":"journal-article"},{"key":"cyq8-4sd7Cc57R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.55.5112","type":"journal-article"},{"key":"cyq8-4sd7Cc58R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.58.046004","type":"journal-article"},{"key":"cyq8-4sd7Cc61R1","volume-title":"Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design","author":"M. Nakata","year":"2010","type":"conference-proceedings"},{"key":"cyq8-4sd7Cc62R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1169-9","type":"journal-article"},{"key":"cyq8-4sd7Cc63R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0550-3213(99)00056-5","type":"journal-article"},{"key":"cyq8-4sd7Cc64R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.111.025003","type":"journal-article"},{"key":"cyq8-4sd7Cc65R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2025.139768","type":"journal-article"},{"key":"cyq8-4sd7Cc66R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP04(2018)084","type":"journal-article"},{"key":"cyq8-4sd7Cc67R1","unstructured":"R. Lanzette and Z. Zheng, Upper bound on the gap of quantum system (to be published).","type":"other"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/cyq8-4sd7","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/cyq8-4sd7\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:27:01Z","timestamp":1790724421000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/cyq8-4sd7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,7]]},"references-count":62,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2026,5]]}},"URL":"https:\/\/doi.org\/10.1103\/cyq8-4sd7","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2507.21007","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,7]]},"assertion":[{"value":"2025-12-15","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"181603"}}