Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
Open accessAbstract
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods for studying two-dimensional quantum lattice systems, despite a perception that it is only suitable for one dimension. Reviewing past applications of DMRG in 2D demonstrates its success in treating a wide variety of problems, although it remains underutilized in this context. We present techniques for performing cutting-edge 2D DMRG studies including methods for ensuring convergence, extrapolating finite-size data, and extracting gaps and excited states. Finally, we consider a selection of recently developed 2D tensor network methods and compare the performance of one of these to 2D DMRG.
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In one-dimensional systems, DMRG, MERA and TTN techniques scale favorably and can in principle treat very large systems.
“In the case of 1D systems, DMRG, MERA and TTN techniques scale favorably and can, in principle, treat very large systems [77-79].”
From Can one trust quantum simulators? (2012) · cites this paper as [78]
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- Authors
- Stoudenmire, E. M., & White, S. R.
- Affiliations
- University of California, Irvine (US)
- Venue
- Annual Review of Condensed Matter Physics
- Publisher
- Annual Reviews
- Published
- 2012-03-01
- Volume
- 3
- Issue
- 1
- Pages
- 111-128
- ISSN
- 1947-5454 (ISSN-L)
- 1947-5462
- OpenAlex
- W2010492822
- Cited by
- 451
- References
- 89
- Citations by year
- 2026: 34 · 2025: 38 · 2024: 45 · 2023: 40 · 2022: 39 · 2021: 49 · 2020: 41 · 2019: 27 · 2018: 23 · 2017: 23 · 2016: 22 · 2015: 19 · 2014: 22 · 2013: 14 · 2012: 14
- FWCI
- 1.28
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- Locations
- Annual Review of Condensed Matter Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- density matrix renormalization group, tensor networks, finite-size extrapolation, excited states, convergence acceleration, quantum many-body systems
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