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Spin and Charge Order in the Doped Hubbard Model: Long-Wavelength Collective Modes
Open accessAbstract
Determining the properties of the two-dimensional Hubbard model is an outstanding problem in physics. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular supercells, we characterize the magnetic and charge properties in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wavelike (delocalized) to a particlelike (localized) state, and charge ordering develops which eventually evolves into stripelike states.
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These differences have not been clear in previous studies on narrower cylinders, which are impacted by strong finite-size effects.
“These differences have not been clear in previous studies on narrower cylinders, which are impacted by strong finite-size effects ( 48,49 ).”
From Coexistence of superconductivity with partially filled stripes in the Hubbard model (2024) · cites this paper as [49]
On p. 1, the paper says earlier simulations used lattices up to about 16 × 16 and could miss collective modes longer than the simulated cell. This supports the concern about finite-size effects, but the paper describes periodic lattices, not previous studies on narrower cylinders, and does not identify the particular differences referred to in the claim. (LLM, conf=0.84)
Experimental — accuracy not yet measuredDeviations are visible from width-4 systems, which can have different pairing symmetry from ordinary d-wave.
“(Deviations are visible from width-4 systems, which can have different pairing symmetry from ordinary d -wave ( 49 ).)”
From Coexistence of superconductivity with partially filled stripes in the Hubbard model (2024) · cites this paper as [49]
The paper studies 4 × Ly systems (p. 2) and reports spin-density-wave behavior in a 4 × 64 system (p. 3). Its discussion of those systems does not address pairing symmetry or deviations from ordinary d-wave pairing; searches for those terms found no supporting passage. (LLM, conf=0.72)
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Cites
Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen(De), A., & Sen, U. (2007) · Advances in Physics · doi:10.1080/00018730701223200 · Cited by 2,104
Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms
Lin, C., Zong, F. H., & Ceperley, D. M. (2001) · Physical Review E · doi:10.1103/physreve.64.016702 · Cited by 371
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Cited by
Sorted by citations
Coexistence of superconductivity with partially filled stripes in the Hubbard model
Xu, H., Chung, C.-M., Qin, M., Schollwöck, U., White, S. R., & Zhang, S. (2024) · Science · doi:10.1126/science.adh7691 · Cited by 144
“In the pure Hubbard model, f ¼ 1 because l SDW ¼ 2 = d ( 51 , 52 ).”
BackgroundSelf-citationStripe order from the perspective of the Hubbard model
Huang, E. W., Mendl, C. B., Jiang, H.-C., Moritz, B., & Devereaux, T. P. (2018) · npj Quantum Materials · doi:10.1038/s41535-018-0097-0 · Cited by 151
Xu, H., Shi, H., Vitali, E., Qin, M., & Zhang, S. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013239 · Cited by 74
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Metadata
- Authors
- Chang, C.-C., & Zhang, S.
- Affiliations
- William & Mary (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-03-18
- Volume
- 104
- Issue
- 11
- Pages
- 116402-116402
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2008343627
- Cited by
- 94
- References
- 2
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 5 · 2023: 1 · 2022: 6 · 2021: 9 · 2020: 6 · 2019: 10 · 2018: 7 · 2017: 6 · 2016: 7 · 2015: 10 · 2014: 7 · 2013: 4 · 2012: 2
- FWCI
- 2.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- doped Hubbard model, spin density wave, charge ordering, collective excitations, antiferromagnetic ordering, incommensurate order, critical doping, hole localization, two-dimensional strongly correlated electrons, ground-state properties
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