Ground-state phase diagram and superconductivity of the doped Hubbard model on six-leg square cylinders

Jiang, Yi-Fan; Devereaux, Thomas P.; Jiang, Hong-Chen

doi:10.1103/physrevb.109.085121

Ground-state phase diagram and superconductivity of the doped Hubbard model on six-leg square cylinders

Journal Article · Wed Feb 14 00:00:00 EST 2024 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.109.085121· OSTI ID:2405028

^[1]; Devereaux, Thomas P. ^[2]; ^[3]

ShanghaiTech Univ. (China); SLAC
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Stanford Univ., CA (United States)
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Here, we have studied the ground state properties of Hubbard model on long six-leg square cylinders with doped hole concentration per site 5.55%≤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 electron hopping t'. In the positive t' side, we find a robust d-wave superconducting (SC) phase characterized by coexisting quasi-long-range SC and charge density wave (CDW) correlations. Without t' the ground state forms an insulating stripe phase with long-range CDW order but short-range spin-spin and SC correlations. In stark contrast to four-leg cylinders, our results show that the lightly doped Hubbard model on six-leg cylinders remains insulating in the negative t' side where the SC correlations decay exponentially with short correlation lengths. In the larger negative t' side, the doped holes form a novel holon Wigner crystal with one doped hole per emergent unit cell and short-range spin-spin correlations.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2405028

Alternate ID(s):: OSTI ID: 2473580

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 109; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (53)

Doping Quantum Spin Liquids on the Kagome Lattice Peng, Cheng; Jiang, Yi‐Fan; Sheng, Dong‐Ning Advanced Quantum Technologies, Vol. 4, Issue 3 https://doi.org/10.1002/qute.202000126	journal	January 2021
Magnetism in La2CuO4 based compounds Machida, Kazushige Physica C: Superconductivity, Vol. 158, Issue 1-2 https://doi.org/10.1016/0921-4534(89)90316-X	journal	April 1989
Current Ideas on the Origin of Stripes Zaanen, J. Journal of Physics and Chemistry of Solids, Vol. 59, Issue 10-12 https://doi.org/10.1016/S0022-3697(98)00106-1	journal	October 1998
Stripe structures in the t–t′-J model Scalapino, D. J.; White, S. R. Physica C: Superconductivity, Vol. 481 https://doi.org/10.1016/j.physc.2012.04.004	journal	November 2012
From quantum matter to high-temperature superconductivity in copper oxides Keimer, B.; Kivelson, S. A.; Norman, M. R. Nature, Vol. 518, Issue 7538 https://doi.org/10.1038/nature14165	journal	February 2015
Stripe order from the perspective of the Hubbard model Huang, Edwin W.; Mendl, Christian B.; Jiang, Hong-Chen npj Quantum Materials, Vol. 3, Issue 1 https://doi.org/10.1038/s41535-018-0097-0	journal	April 2018
Ground-state phase diagram of the t-t ′ -J model Jiang, Shengtao; Scalapino, Douglas J.; White, Steven R. Proceedings of the National Academy of Sciences, Vol. 118, Issue 44 https://doi.org/10.1073/pnas.2109978118	journal	October 2021
The geometric order of stripes and Luttinger liquids Zaanen, J.; Osman, O. Y.; Kruis, H. V. Philosophical Magazine B, Vol. 81, Issue 10 https://doi.org/10.1080/13642810108208566	journal	October 2001
Nature of stripes in the generalized t – J model applied to the cuprate superconductors Yang, Kai-Yu; Chen, Wei Qiang; Rice, T. M. New Journal of Physics, Vol. 11, Issue 5 https://doi.org/10.1088/1367-2630/11/5/055053	journal	May 2009
Period 4 stripe in the extended two-dimensional Hubbard model Ponsioen, Boris; Chung, Sangwoo S.; Corboz, Philippe Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevB.100.195141	journal	November 2019
Plaquette versus ordinary d -wave pairing in the t ′ -Hubbard model on a width-4 cylinder Chung, Chia-Min; Qin, Mingpu; Zhang, Shiwei Physical Review B, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevB.102.041106	journal	July 2020
Critical role of the sign structure in the doped Mott insulator: Luther-Emery versus Fermi-liquid-like state in quasi-one-dimensional ladders Jiang, Hong-Chen; Chen, Shuai; Weng, Zheng-Yu Physical Review B, Vol. 102, Issue 10 https://doi.org/10.1103/PhysRevB.102.104512	journal	September 2020
Pairing properties of the t−t′−t″−J model Jiang, Shengtao; Scalapino, Douglas J.; White, Steven R. Physical Review B, Vol. 106, Issue 17 https://doi.org/10.1103/PhysRevB.106.174507	journal	November 2022
Enhanced superconductivity by near-neighbor attraction in the doped extended Hubbard model Peng, Cheng; Wang, Yao; Wen, Jiajia Physical Review B, Vol. 107, Issue 20 https://doi.org/10.1103/PhysRevB.107.L201102	journal	May 2023
Superconducting valence bond fluid in lightly doped eight-leg t−J cylinders Jiang, Hong-Chen; Kivelson, Steven A.; Lee, Dung-Hai Physical Review B, Vol. 108, Issue 5 https://doi.org/10.1103/PhysRevB.108.054505	journal	August 2023
Numerical study of the two-dimensional Hubbard model White, S. R.; Scalapino, D. J.; Sugar, R. L. Physical Review B, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevB.40.506	journal	July 1989
Charged magnetic domain lines and the magnetism of high- T c oxides Zaanen, Jan; Gunnarsson, Olle Physical Review B, Vol. 40, Issue 10 https://doi.org/10.1103/PhysRevB.40.7391	journal	October 1989
Ground states of the doped four-leg t-J ladder White, Steven R.; Scalapino, D. J. Physical Review B, Vol. 55, Issue 22 https://doi.org/10.1103/PhysRevB.55.R14701	journal	June 1997
Competition between stripes and pairing in a t − t ′ − J model White, Steven R.; Scalapino, D. J. Physical Review B, Vol. 60, Issue 2 https://doi.org/10.1103/PhysRevB.60.R753	journal	July 1999
Antiferromagnetism and d -wave superconductivity in cuprates: A cluster dynamical mean-field theory Lichtenstein, A. I.; Katsnelson, M. I. Physical Review B, Vol. 62, Issue 14 https://doi.org/10.1103/PhysRevB.62.R9283	journal	October 2000
Friedel oscillations and charge density waves in chains and ladders White, Steven R.; Affleck, Ian; Scalapino, Douglas J. Physical Review B, Vol. 65, Issue 16 https://doi.org/10.1103/PhysRevB.65.165122	journal	April 2002
Competition between d -wave superconductivity and antiferromagnetism in the two-dimensional Hubbard model Capone, M.; Kotliar, G. Physical Review B, Vol. 74, Issue 5 https://doi.org/10.1103/PhysRevB.74.054513	journal	August 2006
Role of backflow correlations for the nonmagnetic phase of the t – t ′ Hubbard model Tocchio, Luca F.; Becca, Federico; Parola, Alberto Physical Review B, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevB.78.041101	journal	July 2008
Stripes in the two-dimensional t - J model with infinite projected entangled-pair states Corboz, Philippe; White, Steven R.; Vidal, Guifré Physical Review B, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevB.84.041108	journal	July 2011
Energetics of superconductivity in the two-dimensional Hubbard model Gull, E.; Millis, A. J. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.241106	journal	December 2012
Origin of high- T c superconductivity in doped Hubbard models and their extensions: Roles of uniform charge fluctuations Misawa, Takahiro; Imada, Masatoshi Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevB.90.115137	journal	September 2014
Sign structure, electron fractionalization, and emergent gauge description of the Hubbard model Zhang, Long; Weng, Zheng-Yu Physical Review B, Vol. 90, Issue 16 https://doi.org/10.1103/PhysRevB.90.165120	journal	October 2014
Hidden Mott transition and large- U superconductivity in the two-dimensional Hubbard model Tocchio, Luca F.; Becca, Federico; Sorella, Sandro Physical Review B, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevB.94.195126	journal	November 2016
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model Ehlers, G.; White, S. R.; Noack, R. M. Physical Review B, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevB.95.125125	journal	March 2017
Intertwined order in a frustrated four-leg t − J cylinder Dodaro, John F.; Jiang, Hong-Chen; Kivelson, Steven A. Physical Review B, Vol. 95, Issue 15 https://doi.org/10.1103/PhysRevB.95.155116	journal	April 2017
Competition among various charge-inhomogeneous states and d -wave superconducting state in Hubbard models on square lattices Ido, Kota; Ohgoe, Takahiro; Imada, Masatoshi Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045138	journal	January 2018
Superconductivity in the doped t − J model: Results for four-leg cylinders Jiang, Hong-Chen; Weng, Zheng-Yu; Kivelson, Steven A. Physical Review B, Vol. 98, Issue 14 https://doi.org/10.1103/PhysRevB.98.140505	journal	October 2018
Competing States in the t - J Model: Uniform d -Wave State versus Stripe State Corboz, Philippe; Rice, T. M.; Troyer, Matthias Physical Review Letters, Vol. 113, Issue 4 https://doi.org/10.1103/PhysRevLett.113.046402	journal	July 2014
Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid Jiang, Hong-Chen; Devereaux, T.; Kivelson, S. A. Physical Review Letters, Vol. 119, Issue 6 https://doi.org/10.1103/PhysRevLett.119.067002	journal	August 2017
High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid Jiang, Hong-Chen; Kivelson, Steven A. Physical Review Letters, Vol. 127, Issue 9 https://doi.org/10.1103/PhysRevLett.127.097002	journal	August 2021
Robust d -Wave Superconductivity in the Square-Lattice t − J Model Gong, Shoushu; Zhu, W.; Sheng, D. N. Physical Review Letters, Vol. 127, Issue 9 https://doi.org/10.1103/PhysRevLett.127.097003	journal	August 2021
Superconductivity and the Quantum Hard-Core Dimer Gas Rokhsar, Daniel S.; Kivelson, Steven A. Physical Review Letters, Vol. 61, Issue 20 https://doi.org/10.1103/PhysRevLett.61.2376	journal	November 1988
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Superconductivity in the Two-Dimensional t − J Model Sorella, S.; Martins, G. B.; Becca, F. Physical Review Letters, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevLett.88.117002	journal	February 2002
Ground state phase diagram of the doped Hubbard model on the four-leg cylinder Jiang, Yi-Fan; Zaanen, Jan; Devereaux, Thomas P. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033073	journal	July 2020
Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model Qin, Mingpu; Chung, Chia-Min; Shi, Hao Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031016	journal	July 2020
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041041	journal	December 2015
Correlated electrons in high-temperature superconductors Dagotto, Elbio Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.763	journal	July 1994
The density-matrix renormalization group Schollwöck, U. Reviews of Modern Physics, Vol. 77, Issue 1 https://doi.org/10.1103/RevModPhys.77.259	journal	April 2005
A common thread: The pairing interaction for unconventional superconductors Scalapino, D. J. Reviews of Modern Physics, Vol. 84, Issue 4 https://doi.org/10.1103/RevModPhys.84.1383	journal	October 2012
Numerical evidence of fluctuating stripes in the normal state of high- T _c cuprate superconductors Huang, Edwin W.; Mendl, Christian B.; Liu, Shenxiu Science, Vol. 358, Issue 6367 https://doi.org/10.1126/science.aak9546	journal	November 2017
Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t ′ Jiang, Hong-Chen; Devereaux, Thomas P. Science, Vol. 365, Issue 6460 https://doi.org/10.1126/science.aal5304	journal	September 2019
Stripe order in the underdoped region of the two-dimensional Hubbard model Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe Science, Vol. 358, Issue 6367 https://doi.org/10.1126/science.aam7127	journal	November 2017
Soliton Lattice Modulation of Incommensurate Spin Density Wave in Two Dimensional Hubbard Model -A Mean Field Study- Kato, Masaru; Machida, Kazushige; Nakanishi, Hiizu Journal of the Physical Society of Japan, Vol. 59, Issue 3 https://doi.org/10.1143/JPSJ.59.1047	journal	March 1990
The Hubbard Model Arovas, Daniel P.; Berg, Erez; Kivelson, Steven A. Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031620-102024	journal	November 2021
The Hubbard Model: A Computational Perspective Qin, Mingpu; Schäfer, Thomas; Andergassen, Sabine Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-090921-033948	journal	November 2021
The non-Abelian density matrix renormalization group algorithm McCulloch, I. P.; Gulácsi, M. Europhysics Letters (EPL), Vol. 57, Issue 6 https://doi.org/10.1209/epl/i2002-00393-0	journal	March 2002
Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model Tocchio, Luca Fausto; Montorsi, Arianna; Becca, Federico SciPost Physics, Vol. 7, Issue 2 https://doi.org/10.21468/SciPostPhys.7.2.021	journal	January 2019

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