Physical Review B
covering condensed matter and materials physics
- Highlights
- Recent
- Accepted
- Collections
- Authors
- Referees
- Search
- Press
- About
- Editorial Team
- Editors' Suggestion
Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo
Y. F. Kung, C.-C. Chen, Yao Wang, E. W. Huang, E. A. Nowadnick, B. Moritz, R. T. Scalettar, S. Johnston, and T. P. Devereaux
Phys. Rev. B 93, 155166 – Published 29 April 2016
- Article
- References
- Citing Articles (41)
PDFHTMLExport Citation
Abstract
We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.
11 More
- Received 20 January 2016
- Revised 12 April 2016
DOI:https://doi.org/10.1103/PhysRevB.93.155166
©2016 American Physical Society
Physics Subject Headings (PhySH)
- Physical Systems
High-temperature superconductors
- Techniques
Hubbard modelQuantum Monte Carlo
Condensed Matter, Materials & Applied Physics
Authors & Affiliations
Y. F. Kung1,2, C.-C. Chen3,4, Yao Wang2,5, E. W. Huang1,2, E. A. Nowadnick1,2,6, B. Moritz2,7, R. T. Scalettar8, S. Johnston9, and T. P. Devereaux2,10
- 1Department of Physics, Stanford University, Stanford, California 94305, USA
- 2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Stanford, California 94305, USA
- 3Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, USA
- 4Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA
- 5Department of Applied Physics, Stanford University, California 94305, USA
- 6School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
- 7Department of Physics and Astrophysics, University of North Dakota, Grand Forks, North Dakota 58202, USA
- 8Department of Physics, University of California - Davis, Davis, California 95616, USA
- 9Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- 10Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
Article Text (Subscription Required)
Click to Expand
References (Subscription Required)
Click to Expand
Issue
Vol. 93, Iss. 15 — 15 April 2016
Access Options
- Buy Article »
- Log in with individual APS Journal Account »
- Log in with a username/password provided by your institution »
- Get access through a U.S. public or high school library »
Article Available via CHORUS
Download Accepted Manuscript![Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo (11) Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo (11)](https://i0.wp.com/cdn.journals.aps.org/development/journals/images/author-services-placard.png)
Authorization Required
Other Options
- Buy Article »
- Find an Institution with the Article »
Images
Figure 1
A copper orbital and its surrounding oxygen or orbitals are shown. The colors indicate the phase factors (blue for positive, red for negative).
Figure 2
The average fermion sign is plotted versus filling for , and at and eV. In general, a larger system size results in a more severe sign problem.
Figure 3
The average fermion sign is plotted versus filling for different values of and at and . Reducing the interactions improves the sign problem and, in the case of , can even flip which side of diagram has the more severe problem.
Figure 4
The average fermion sign is plotted versus filling for a range of temperatures for the (a) and (b) systems, with to access lower temperatures. Decreasing the temperature significantly decreases the average sign but preserves the direction of the particle-hole asymmetry. The partially protected fillings in the system become more pronounced with decreasing temperature.
Figure 5
The average fermion sign is plotted versus filling for different values of to demonstrate the effect of decreasing the number of hopping pathways. Again, the particle-hole asymmetry is evident, as invariably enhances the average sign for hole doping more than it does for electron doping.
Figure 6
The double occupancy versus filling on the copper and oxygen orbitals is shown for different temperatures, with and eV. It exhibits no significant system size or temperature dependence.
Figure 7
Kinetic energy of the holes versus filling for different temperatures in and systems, with and 0eV. The non-interacting kinetic energy (solid black line) is shown for comparison.
Figure 8
(a) The total filling curve shows a gap opening with decreasing temperature, with eV and to access the lowest possible temperatures. The inset shows the total filling for eV, and and has the same axes. (b) The orbitally resolved fillings are shown for the same parameters as the inset in (a) and demonstrate that doped holes preferentially reside on oxygen atoms. As we are using the larger system size, the fermion sign is too small at certain chemical potentials to determine the filling; however, the solid lines indicate the trend that is consistent with results in smaller systems. A dashed line indicates the chemical potential corresponding to the undoped system.
Figure 9
The spin-spin correlation function is plotted versus filling for four different possible ordering vectors on the copper and oxygen (inset) orbitals. On copper, antiferromagnetism dominates in the undoped system, decreasing with doping. The oxygen orbitals do not show signs of any particular spin order. Parameters used here are eV, and .
Figure 10
The copper spin-spin correlation function shows that order is strengthened by increasing system size and decreasing temperature (). The inset shows the finite size scaling at doping and .
Figure 11
Nearest and next-nearest neighbor Cu-Cu spin-spin correlation function versus filling, with eV and , showing the crossover from AFM to short-ranged FM correlations for and 36.
Figure 12
Density-density correlation function versus filling on the (a) copper and (b) oxygen orbitals for different ordering vectors with and (qualitatively similar results are obtained for eV). The system shows a slight tendency to charge ordering on the electron-doped side on copper.
Figure 13
Density-density correlations between the copper and oxygen orbitals, and between the oxygen orbitals for different ordering vectors in a system (qualitatively similar results are obtained for eV).
Figure 14
The orbitally-resolved spectral functions at (a) , (b) , (c) , and (d) hole doping illustrate the doping evolution of the lower Hubbard band (LHB), Zhang-Rice triplet (ZRT) band, nonbonding (NB) band, Zhang-Rice singlet (ZRS) band, and upper Hubbard band (UHB) in the system, where eV, and eV. The insets show the density of states for each doping level, with the same frequency axis as the spectral functions.
Figure 15
The orbitally-resolved spectral functions at hole doping are shown for high-symmetry cuts in the first Brillouin zone in the system, where eV, and eV.
Figure 16
The (a) copper and (b) oxygen spectral functions are calculated in the undoped system using DQMC, ED, and CPT. Despite the different system sizes and temperatures, the peak positions show reasonable agreement. With fine momentum resolution, CPT resolves the (c)band dispersion and (d) DOS in detail. In (c), the noninteracting bands are overlaid as dashed lines on the CPT band structure. In (d), the shading in the DOS indicates orbital content (red for copper, blue for oxygen) in the filled bands. For example, the color gradient in the ZRS band indicates the increasing copper content away from .
Figure 17
The filling versus chemical potential curves are shown on an cluster in order to access low temperatures to highlight the opening of a charge transfer gap. The inset shows an extrapolation of the gap size to zero temperature.
Figure 18
Comparison of the (a) orbitally-resolved filling and (b) local moments on copper and oxygen, showing good quantitative agreement between DQMC and ED. The DQMC simulations are performed with and .