Ground state phase diagram of the doped Hubbard model on the four-leg cylinder
Abstract
We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site δ ≤ 12.5% using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping t'. Without t' the ground state of the system corresponds to the insulating filled stripe phase with long-range charge-density-wave (CDW) order, and short-range incommensurate spin correlations appears. However, for a small negative t' a phase characterized by coexisting algebraic d-wave superconducting (SC) and algebraic CDW correlations. In addition, it shows short-range spin- and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge and spin periodicities are consistent with half-filled stripes instead of the 4kF and 2kF wave vectors that are generic for one-dimensional chains. For a small positive t' yet another phase takes over, showing similar SC and CDW correlations. However, the fermions are now characterized by a (nearly) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE liquid formed from a weakly coupledmore »
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1638557
- Alternate Identifier(s):
- OSTI ID: 1639102
- Grant/Contract Number:
- AC02-76SF00515
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 3; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Superconductivity; strongly correlated systems; density matrix renormalization group
Citation Formats
Jiang, Yi-Fan, Zaanen, Jan, Devereaux, Thomas P., and Jiang, Hong-Chen. Ground state phase diagram of the doped Hubbard model on the four-leg cylinder. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.033073.
Jiang, Yi-Fan, Zaanen, Jan, Devereaux, Thomas P., & Jiang, Hong-Chen. Ground state phase diagram of the doped Hubbard model on the four-leg cylinder. United States. https://doi.org/10.1103/PhysRevResearch.2.033073
Jiang, Yi-Fan, Zaanen, Jan, Devereaux, Thomas P., and Jiang, Hong-Chen. Wed .
"Ground state phase diagram of the doped Hubbard model on the four-leg cylinder". United States. https://doi.org/10.1103/PhysRevResearch.2.033073.
@article{osti_1638557,
title = {Ground state phase diagram of the doped Hubbard model on the four-leg cylinder},
author = {Jiang, Yi-Fan and Zaanen, Jan and Devereaux, Thomas P. and Jiang, Hong-Chen},
abstractNote = {We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site δ ≤ 12.5% using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping t'. Without t' the ground state of the system corresponds to the insulating filled stripe phase with long-range charge-density-wave (CDW) order, and short-range incommensurate spin correlations appears. However, for a small negative t' a phase characterized by coexisting algebraic d-wave superconducting (SC) and algebraic CDW correlations. In addition, it shows short-range spin- and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge and spin periodicities are consistent with half-filled stripes instead of the 4kF and 2kF wave vectors that are generic for one-dimensional chains. For a small positive t' yet another phase takes over, showing similar SC and CDW correlations. However, the fermions are now characterized by a (nearly) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE liquid formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect of stabilizing a cuprate style magnetic resonance.},
doi = {10.1103/PhysRevResearch.2.033073},
journal = {Physical Review Research},
number = 3,
volume = 2,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 2020},
month = {Wed Jul 15 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevResearch.2.033073
https://doi.org/10.1103/PhysRevResearch.2.033073
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
symmetry and the pairing mechanism
journal, December 1996
- Bulut, N.; Scalapino, D. J.
- Physical Review B, Vol. 54, Issue 21
Stripe order from the perspective of the Hubbard model
journal, April 2018
- Huang, Edwin W.; Mendl, Christian B.; Jiang, Hong-Chen
- npj Quantum Materials, Vol. 3, Issue 1
Charged magnetic domain lines and the magnetism of high- oxides
journal, October 1989
- Zaanen, Jan; Gunnarsson, Olle
- Physical Review B, Vol. 40, Issue 10
The geometric order of stripes and Luttinger liquids
journal, October 2001
- Zaanen, J.; Osman, O. Y.; Kruis, H. V.
- Philosophical Magazine B, Vol. 81, Issue 10
Colloquium : Theory of intertwined orders in high temperature superconductors
journal, May 2015
- Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
- Reviews of Modern Physics, Vol. 87, Issue 2
Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering
journal, October 2019
- Robinson, Neil J.; Johnson, Peter D.; Rice, T. Maurice
- Reports on Progress in Physics, Vol. 82, Issue 12
Superconductivity in the doped model: Results for four-leg cylinders
journal, October 2018
- Jiang, Hong-Chen; Weng, Zheng-Yu; Kivelson, Steven A.
- Physical Review B, Vol. 98, Issue 14
Elementary excitations in one-dimensional quantum wires: Exact equivalence between the random-phase approximation and the Tomonaga-Luttinger model
journal, June 1992
- Li, Q. P.; Das Sarma, S.; Joynt, R.
- Physical Review B, Vol. 45, Issue 23
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012
- Stoudenmire, E. M.; White, Steven R.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1
Role of backflow correlations for the nonmagnetic phase of the Hubbard model
journal, July 2008
- Tocchio, Luca F.; Becca, Federico; Parola, Alberto
- Physical Review B, Vol. 78, Issue 4
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
journal, March 2017
- Ehlers, G.; White, S. R.; Noack, R. M.
- Physical Review B, Vol. 95, Issue 12
Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t ′
journal, September 2019
- Jiang, Hong-Chen; Devereaux, Thomas P.
- Science, Vol. 365, Issue 6460
Bloch state tomography using Wilson lines
journal, May 2016
- Li, T.; Duca, L.; Reitter, M.
- Science, Vol. 352, Issue 6289
From quantum matter to high-temperature superconductivity in copper oxides
journal, February 2015
- Keimer, B.; Kivelson, S. A.; Norman, M. R.
- Nature, Vol. 518, Issue 7538
Slave Boson Approach to Neutron Scattering in Superconductors
journal, April 1999
- Brinckmann, Jan; Lee, Patrick A.
- Physical Review Letters, Vol. 82, Issue 14
Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model
journal, February 1990
- Ogata, Masao; Shiba, Hiroyuki
- Physical Review B, Vol. 41, Issue 4
Incommensurate antiferromagnetism in the two-dimensional Hubbard model
journal, March 1990
- Schulz, H. J.
- Physical Review Letters, Vol. 64, Issue 12
Correlated electrons in high-temperature superconductors
journal, July 1994
- Dagotto, Elbio
- Reviews of Modern Physics, Vol. 66, Issue 3
Ground states of the doped four-leg t-J ladder
journal, June 1997
- White, Steven R.; Scalapino, D. J.
- Physical Review B, Vol. 55, Issue 22
Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method
journal, November 2018
- Darmawan, Andrew S.; Nomura, Yusuke; Yamaji, Youhei
- Physical Review B, Vol. 98, Issue 20
Competition between stripes and pairing in a model
journal, July 1999
- White, Steven R.; Scalapino, D. J.
- Physical Review B, Vol. 60, Issue 2
Numerical evidence of fluctuating stripes in the normal state of high- T c cuprate superconductors
journal, November 2017
- Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu
- Science, Vol. 358, Issue 6367
Intertwined order in a frustrated four-leg cylinder
journal, April 2017
- Dodaro, John F.; Jiang, Hong-Chen; Kivelson, Steven A.
- Physical Review B, Vol. 95, Issue 15
Effective Hamiltonian for cuprate superconductors derived from multiscale ab initio scheme with level renormalization
journal, June 2019
- Hirayama, Motoaki; Misawa, Takahiro; Ohgoe, Takahiro
- Physical Review B, Vol. 99, Issue 24
Magnetism in La2CuO4 based compounds
journal, April 1989
- Machida, Kazushige
- Physica C: Superconductivity, Vol. 158, Issue 1-2
Nature of stripes in the generalized t – J model applied to the cuprate superconductors
journal, May 2009
- Yang, Kai-Yu; Chen, Wei Qiang; Rice, T. M.
- New Journal of Physics, Vol. 11, Issue 5
Competing States in the - Model: Uniform -Wave State versus Stripe State
journal, July 2014
- Corboz, Philippe; Rice, T. M.; Troyer, Matthias
- Physical Review Letters, Vol. 113, Issue 4
Period 4 stripe in the extended two-dimensional Hubbard model
journal, November 2019
- Ponsioen, Boris; Chung, Sangwoo S.; Corboz, Philippe
- Physical Review B, Vol. 100, Issue 19
Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model
journal, May 2013
- Gull, Emanuel; Parcollet, Olivier; Millis, Andrew J.
- Physical Review Letters, Vol. 110, Issue 21
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
journal, January 2011
- Fagotti, Maurizio; Calabrese, Pasquale
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2011, Issue 01
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
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
The one-dimensional Hubbard model: a reminiscence
journal, April 2003
- Lieb, Elliott H.; Wu, F. Y.
- Physica A: Statistical Mechanics and its Applications, Vol. 321, Issue 1-2
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
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
Stripe structures in the t–t′-J model
journal, November 2012
- Scalapino, D. J.; White, S. R.
- Physica C: Superconductivity, Vol. 481
Doping the holographic Mott insulator
journal, July 2018
- Andrade, Tomas; Krikun, Alexander; Schalm, Koenraad
- Nature Physics, Vol. 14, Issue 10
Ineluctable complexity
journal, November 2012
- Fradkin, Eduardo; Kivelson, Steven A.
- Nature Physics, Vol. 8, Issue 12
Friedel oscillations and charge density waves in chains and ladders
journal, April 2002
- White, Steven R.; Affleck, Ian; Scalapino, Douglas J.
- Physical Review B, Vol. 65, Issue 16
Geometry and the hidden order of Luttinger liquids: The universality of squeezed space
journal, August 2004
- Kruis, H. V.; McCulloch, I. P.; Nussinov, Z.
- Physical Review B, Vol. 70, Issue 7
Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017
- Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe
- Science, Vol. 358, Issue 6367
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
Energetics of superconductivity in the two-dimensional Hubbard model
journal, December 2012
- Gull, E.; Millis, A. J.
- Physical Review B, Vol. 86, Issue 24
Ab initio effective Hamiltonians for cuprate superconductors
journal, October 2018
- Hirayama, Motoaki; Yamaji, Youhei; Misawa, Takahiro
- Physical Review B, Vol. 98, Issue 13