The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
Open accessAbstract
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
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Cites
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Self-citationThe density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
The Density Matrix Renormalization Group in Quantum Chemistry
Chan, G. K.-L., & Sharma, S. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103338 · Cited by 822
Self-citationAb initio quantum chemistry using the density matrix renormalization group
White, S. R., & Martin, R. L. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478295 · Cited by 558
Self-citationLegeza, Ö., Röder, J., & Hess, B. A. (2003) · Physical Review B · doi:10.1103/physrevb.67.125114 · Cited by 263
Simulating strongly correlated quantum systems with tree tensor networks
Murg, V., Verstraete, F., Legeza, Ö., & Noack, R. M. (2010) · Physical Review B · doi:10.1103/physrevb.82.205105 · Cited by 245
Murg, V., Verstraete, F., Schneider, R., Nagy, P. R., & Legeza, O. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/ct501187j · Cited by 97
Analytic response theory for the density matrix renormalization group
Dorando, J. J., Hachmann, J., & Chan, G. K.-L. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3121422 · Cited by 60
Self-citationNakatani, N., Wouters, S., Van Neck, D., & Chan, G. K.-L. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4860375 · Cited by 59
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Fdez. Galván, I., Vacher, M., Alavi, A., Angeli, C., Aquilante, F., Autschbach, J., Bao, J. J., Bokarev, S. I., Bogdanov, N. A., Carlson, R. K., et al. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00532 · Cited by 1,114
The ITensor Software Library for Tensor Network Calculations
Fishman, M., White, S., & Stoudenmire, E. M. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.4 · Cited by 1,084
Self-citationTime-evolution methods for matrix-product states
Paeckel, S., Köhler, T., Swoboda, A., Manmana, S. R., Schollwöck, U., & Hubig, C. (2019) · Annals of Physics · doi:10.1016/j.aop.2019.167998 · Cited by 768
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Freitag, L., Knecht, S., Angeli, C., & Reiher, M. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00778 · Cited by 119
Metadata
- Authors
- Chan, G. K.-L., Keselman, A., Nakatani, N., Li, Z., & White, S. R.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2016-07-05
- Volume
- 145
- Issue
- 1
- Pages
- 014102-014102
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2361647693
- Cited by
- 200
- References
- 9
- FWCI
- 9.05
- Type
- journal article
- Language
- en
- Open access
- green
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