skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model

Abstract

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling t . The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one to two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. In conclusion, the DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [7];  [8];  [9];  [4]
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States); Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne (Switzerland)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Warsaw, Warsaw (Poland)
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., Stanford, CA (United States)
  5. Univ. of Alabama, Birmingham, AL (United States)
  6. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  7. Univ. of Tennessee, Knoxville, TN (United States)
  8. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of North Dakota, Grand Forks, ND (United States)
  9. Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne (Switzerland)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1410543
Alternate Identifier(s):
OSTI ID: 1406656; OSTI ID: 1418216
Grant/Contract Number:  
AC02-76SF00515; AC02-05CH11231; 1147470; 2012/04/A/ST3/00331; 2016/22/E/ST3/00560
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Kung, Y. F., Bazin, C., Wohlfeld, K., Wang, Yao, Chen, C. -C., Jia, C. J., Johnston, S., Moritz, B., Mila, F., and Devereaux, T. P. Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.195106.
Kung, Y. F., Bazin, C., Wohlfeld, K., Wang, Yao, Chen, C. -C., Jia, C. J., Johnston, S., Moritz, B., Mila, F., & Devereaux, T. P. Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model. United States. doi:10.1103/PhysRevB.96.195106.
Kung, Y. F., Bazin, C., Wohlfeld, K., Wang, Yao, Chen, C. -C., Jia, C. J., Johnston, S., Moritz, B., Mila, F., and Devereaux, T. P. Thu . "Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model". United States. doi:10.1103/PhysRevB.96.195106. https://www.osti.gov/servlets/purl/1410543.
@article{osti_1410543,
title = {Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model},
author = {Kung, Y. F. and Bazin, C. and Wohlfeld, K. and Wang, Yao and Chen, C. -C. and Jia, C. J. and Johnston, S. and Moritz, B. and Mila, F. and Devereaux, T. P.},
abstractNote = {Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling t⊥. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one to two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. In conclusion, the DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.},
doi = {10.1103/PhysRevB.96.195106},
journal = {Physical Review B},
number = 19,
volume = 96,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Quantum Monte Carlo study of the two-dimensional fermion Hubbard model
journal, August 2009


Temperature Dependence of Spin Correlation Length of Half-Filled One-Dimensional Hubbard Model
journal, May 1991

  • Tsunetsugu, Hirokazu
  • Journal of the Physical Society of Japan, Vol. 60, Issue 5
  • DOI: 10.1143/JPSJ.60.1460

Energy Separation of Single-Particle and Continuum States in an S = 1 / 2 Weakly Coupled Chains Antiferromagnet
journal, November 2000


One-dimensional Fermi liquids
journal, September 1995


Spinon confinement: Dynamics of weakly coupled Hubbard chains
journal, August 2013


Static and dynamical properties of doped Hubbard clusters
journal, May 1992


Numerical study of the two-dimensional Hubbard model
journal, July 1989


Asymmetry of collective excitations in electron- and hole-doped cuprate superconductors
journal, October 2014

  • Lee, W. S.; Lee, J. J.; Nowadnick, E. A.
  • Nature Physics, Vol. 10, Issue 11
  • DOI: 10.1038/nphys3117

Theory of magnetic short-range order in the t J model
journal, October 1998


Monte Carlo study of the S=12 and S=1 Heisenberg antiferromagnet on a spatially anisotropic square lattice
journal, September 2000


Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data
journal, May 1996


Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011

  • Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
  • Reviews of Modern Physics, Vol. 83, Issue 2
  • DOI: 10.1103/RevModPhys.83.349

High-Doping Regime in a Planar Model for Strongly Correlated Electrons
journal, September 1989


Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal
journal, January 2015


A plane of weakly coupled Heisenberg chains: theoretical arguments and numerical calculations
journal, November 1994

  • Affeck, I.; Gelfand, M. P.; Singh, R. R. P.
  • Journal of Physics A: Mathematical and General, Vol. 27, Issue 22
  • DOI: 10.1088/0305-4470/27/22/009

Persistence of magnetic excitations in La2−xSrxCuO4 from the undoped insulator to the heavily overdoped non-superconducting metal
journal, August 2013

  • Dean, M. P. M.; Dellea, G.; Springell, R. S.
  • Nature Materials, Vol. 12, Issue 11
  • DOI: 10.1038/nmat3723

Cluster perturbation theory for Hubbard models
journal, August 2002


Mott Quantum Criticality in the Anisotropic 2D Hubbard Model
journal, February 2016


Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model
journal, June 1990


Geometry dependence of the sign problem in quantum Monte Carlo simulations
journal, July 2015


Two-dimensional Hubbard model: Numerical simulation study
journal, April 1985


Spectral Weight of the Hubbard Model through Cluster Perturbation Theory
journal, January 2000


Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981


Spin polarons in the t - t ′- J model
journal, August 1995


Fractionalization, entanglement, and separation: Understanding the collective excitations in a spin-orbital chain
journal, April 2015

  • Chen, Cheng-Chien; van Veenendaal, Michel; Devereaux, Thomas P.
  • Physical Review B, Vol. 91, Issue 16
  • DOI: 10.1103/PhysRevB.91.165102

Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering
journal, February 2014

  • Jia, C. J.; Nowadnick, E. A.; Wohlfeld, K.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4314

Dimensional-Crossover-Driven Mott Transition in the Frustrated Hubbard Model
journal, September 2012


Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015

  • LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
  • Physical Review X, Vol. 5, Issue 4
  • DOI: 10.1103/PhysRevX.5.041041

Hole spectral functions in lightly doped quantum antiferromagnets
journal, November 2011


First-order Mott transition at zero temperature in two dimensions: Variational plaquette study
journal, January 2009


Doping evolution of spin and charge excitations in the Hubbard model
journal, November 2015


One-particle interchain hopping in coupled Hubbard chains
journal, October 1996


New Approach to the Theory of Superexchange Interactions
journal, July 1959


Interchain-Frustration-Induced Metallic State in Quasi-One-Dimensional Mott Insulators
journal, September 2007


Confinement and transverse conductivity in coupled Luttinger liquids
journal, December 1996


Dynamic spin susceptibility in the t J model
journal, September 2009


Doping dependence of magnetic excitations of one-dimensional cuprates as probed by resonant inelastic x-ray scattering
journal, June 2011


Absence of Hole Confinement in Transition-Metal Oxides with Orbital Degeneracy
journal, February 2008


Competition of spin and charge excitations in the one-dimensional Hubbard model
journal, December 2013


Itinerancy effects on spin correlations in one-dimensional Mott insulators
journal, January 2005


Elementary Excitations of One-Dimensional t J Model with Inverse-Square Exchange
journal, November 1994


Temperature dependence of spectral functions for the one-dimensional Hubbard model: Comparison with experiments
journal, April 2006


Dispersive spin excitations in highly overdoped cuprates revealed by resonant inelastic x-ray scattering
journal, July 2013


Correlated electrons in high-temperature superconductors
journal, July 1994


Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems
journal, October 1999


2 p F and 4 p F instabilities in a one-quarter-filled-band Hubbard model
journal, June 1983


Deconfinement Transition and Luttinger to Fermi Liquid Crossover in Quasi-One-Dimensional Systems
journal, December 2001


Intense paramagnon excitations in a large family of high-temperature superconductors
journal, July 2011

  • Le Tacon, M.; Ghiringhelli, G.; Chaloupka, J.
  • Nature Physics, Vol. 7, Issue 9
  • DOI: 10.1038/nphys2041

Spectral Properties of the One-Dimensional Hubbard Model
journal, August 1994


Resonant Inelastic X-Ray Scattering of the Holon-Antiholon Continuum in SrCuO 2
journal, April 2004


Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

  • Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
  • Reviews of Modern Physics, Vol. 68, Issue 1
  • DOI: 10.1103/RevModPhys.68.13

Distinct spinon and holon dispersions in photoemission spectral functions from one-dimensional SrCuO2
journal, May 2006

  • Kim, B. J.; Koh, H.; Rotenberg, E.
  • Nature Physics, Vol. 2, Issue 6
  • DOI: 10.1038/nphys316

Finite-energy spectral function of an anisotropic two-dimensional system of coupled Hubbard chains
journal, July 2011


Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006

  • Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
  • Reviews of Modern Physics, Vol. 78, Issue 1
  • DOI: 10.1103/RevModPhys.78.17

Implications of resonant inelastic x-ray scattering data for theoretical models of cuprates
journal, November 2013


One-Particle and Two-Particle Instability of Coupled Luttinger Liquids
journal, February 1995


Spin and charge dynamics of the one-dimensional extended Hubbard model
journal, May 2007


Coherence–incoherence and dimensional crossover in layered strongly correlated metals
journal, June 2002


Strong-coupling phases of two Hubbard chains with interchain hopping
journal, August 1992


Topological origin of the fermion sign problem
journal, March 2016


Spin polarons in the t - J model
journal, July 1991


Phases of the Infinite U Hubbard Model on Square Lattices
journal, March 2012