Stripes in the two-dimensionalt-Jmodel with infinite projected entangled-pair states
Open accessAbstract
We simulate the $t$-$J$ model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, that is, a unidirectional modulation of hole-density and antiferromagnetic order with a $\ensuremath{\pi}$-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.5$ per unit length of a stripe. The superconducting order parameter is maximal around ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.75\text{--}0.8$.
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In two dimensions, DMRG and TTN work only for reasonably small systems.
“In 2D the situation is more complex - similar to exact diagonalization, DMRG and TTN work only for reasonably small systems [80-82]”
From Can one trust quantum simulators? (2012) · cites this paper as [81]
In higher-dimensional lattices, states obeying the Area law may still be amenable to classical simulation using tensor networks, density functional theories, or quantum Monte Carlo.
“In higher-dimensional lattices, states which obey the socalled 'Area law' [97], where quantum correlations are smaller than in generic states, may still be amenable to a classical simulation using state-of-the-art techniques such as tensor networks [77, 81, 82, 198, 199], Density Functional Theories [86], or Quantum Monte Carlo [75].”
From Can one trust quantum simulators? (2012) · cites this paper as [81]
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References 42 · Cited by 212
Research works printed but not linked: 4
- 1 M. Troyer and U.-J. Wiese, Phys. Rev. Lett. 94, 170201 (2005).
- 2 D. F. B. ten Haaf, H. J. M. van Bemmel, J. M. J. van Leeuwen, W. van Saarloos, and D. M. Ceperley, Phys. Rev. B 51, 13039 (1995).
- 3 M. Lugas, L. Spanu, F. Becca, and S. Sorella, Phys. Rev. B 74, 165122 (2006).
- 4 G. Vidal, Phys. Rev. Lett. 99, 220405 (2007); G. Vidal, Phys. Rev. Lett. 101, 110501 (2008); L. Cincio, J. Dziar- only little influence on the energy, and from the present data we cannot determine which state is preferred. The mean pairing amplitude (averaged over the unit cell) in Fig. 5 exhibits a maximum around ρ l = 0 . 75 ( ρ l = 0 . 8 in DMRG). For ρ l = 1 the stripes are insulating with a vanishing pairing amplitude. For ρ l = 0 . 5 the pairing amplitude for D = 8 is finite, but decreases quickly with increasing D , and is possibly insulating for larger D , too. In between these two insulating states, excess holes (or electrons) form pairs, leading to an increase of the pairing.
- Authors
- Corboz, P., White, S. R., Vidal, G., & Troyer, M.
- Affiliations
- ETH Zurich (CH)
- University of California, Irvine (US)
- The University of Queensland (AU)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-07-29
- Volume
- 84
- Issue
- 4
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2037370906
- Cited by
- 212
- References
- 42
- Citations by year
- 2026: 10 · 2025: 19 · 2024: 9 · 2023: 15 · 2022: 16 · 2021: 12 · 2020: 12 · 2019: 16 · 2018: 9 · 2017: 11 · 2016: 11 · 2015: 14 · 2014: 16 · 2013: 14 · 2012: 26
- FWCI
- 13.94
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- 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 › Advanced Condensed Matter Physics
- Keywords
- t-J model, two-dimensional antiferromagnetism, stripe phase, infinite projected entangled pair states, antiferromagnetic ordering, superconducting order parameter, variational energy, unit cell, density matrix renormalization group
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