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Therefore, the relativistic density matrix renormalization group algorithm (R-DMRG) only employing particle number symmetry is much more expensive than nonrelativistic DMRG. In addition, artificial breaking of Kramers degeneracy can happen in the treatment of systems with an odd number of electrons. To overcome these issues, we propose time-reversal symmetry adaptation for R-DMRG. Since the time-reversal operator is antiunitary, this cannot be simply achieved in the usual way. We introduce a time-reversal symmetry-adapted renormalized basis and present strategies to maintain the structure of basis functions during the sweep optimization. With time-reversal symmetry adaptation, only half of the renormalized operators are needed, and the computational costs of Hamiltonian-wavefunction multiplication and renormalization are reduced by half. The present construction of the time-reversal symmetry-adapted basis also directly applies to other tensor network states without loops.<\/jats:p>","DOI":"10.1063\/5.0127621","type":"journal-article","created":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T15:34:59Z","timestamp":1673451299000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm"],"prefix":"10.1063","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0683-6293","authenticated-orcid":false,"given":"Zhendong","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University , Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2023,1,26]]},"reference":[{"key":"2023081022463039000_c1","volume-title":"Introduction to Relativistic Quantum Chemistry","year":"2007"},{"key":"2023081022463039000_c2","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1080\/00268971003781571","volume":"108","year":"2010","journal-title":"Mol. 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