Pure State v-Representability of Density Matrix Embedding TheoryClick to copy article linkArticle link copied!
- Fabian M. FaulstichFabian M. FaulstichDepartment of Mathematics, University of California, Berkeley, California 94720, United StatesMore by Fabian M. Faulstich
- Raehyun KimRaehyun KimDepartment of Mathematics, University of California, Berkeley, California 94720, United StatesMore by Raehyun Kim
- Zhi-Hao CuiZhi-Hao CuiDivision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United StatesMore by Zhi-Hao Cui
- Zaiwen WenZaiwen WenBeijing International Center for Mathematical Research, BICMR, Peking University, Beijing 100871, ChinaMore by Zaiwen Wen
- Garnet Kin-Lic ChanGarnet Kin-Lic ChanDivision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United StatesMore by Garnet Kin-Lic Chan
- Lin Lin*Lin Lin*Email: [email protected]Department of Mathematics, University of California, Berkeley, California 94720, United StatesComputational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United StatesMore by Lin Lin
Abstract

Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are noninteracting pure-state v-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. To relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for the 2D Hubbard and hydrogen model systems indicate that, in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.
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