Intertwined order in a frustrated four-leg t-J cylinder

Dodaro, John F.; Jiang, Hong -Chen; Kivelson, Steven A.

doi:10.1103/PhysRevB.95.155116

Intertwined order in a frustrated four-leg $t - J$ cylinder

Journal Article · Wed Apr 12 00:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.95.155116· OSTI ID:1368573

Dodaro, John F. ^[1]; Jiang, Hong -Chen ^[2]; Kivelson, Steven A. ^[1]

Stanford Univ., Stanford, CA (United States)
SLAC National Accelerator Lab. and Stanford Univ., Menlo Park, CA (United States)

Here, we report a density-matrix renormalization group study of the t–J model with nearest (t₁ and J₁) and next-nearest (t₂ and J₂) interactions on a four-leg cylinder with concentration δ=1/8 of doped holes. We observe an astonishingly complex interplay between uniform d-wave superconductivity (SC) and strong spin and charge-density wave ordering tendencies (SDW and CDW). Depending on parameters, the CDWs can be commensurate with period 4 or 8. By comparing the charge ordering vectors with 2k_F, we rule out Fermi surface nesting-induced density wave order in our model. Magnetic frustration (i.e., J₂/J₁~1/2) significantly quenches SDW correlations with little effect on the CDW. Typically, the SC order is strongly modulated at the CDW ordering vector and exhibits d-wave symmetry around the cylinder. There is no evidence of a near-degenerate tendency to pair-density wave (PDW) ordering, charge 4e SC, or orbital current order.

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Lab., 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) (SC-22)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1368573

Alternate ID(s):: OSTI ID: 1351675

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 15 Vol. 95; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (59)

Two soluble models of an antiferromagnetic chain Lieb, Elliott; Schultz, Theodore; Mattis, Daniel Annals of Physics, Vol. 16, Issue 3 https://doi.org/10.1016/0003-4916(61)90115-4	journal	December 1961
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
Frustrated electronic phase separation and high-temperature superconductors Emery, V. J.; Kivelson, S. A. Physica C: Superconductivity, Vol. 209, Issue 4 https://doi.org/10.1016/0921-4534(93)90581-A	journal	May 1993
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
Stripes and superconductivity in cuprates Tranquada, John M. Physica B: Condensed Matter, Vol. 407, Issue 11 https://doi.org/10.1016/j.physb.2012.01.026	journal	June 2012
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
Evidence for stripe correlations of spins and holes in copper oxide superconductors Tranquada, J. M.; Sternlieb, B. J.; Axe, J. D. Nature, Vol. 375, Issue 6532 https://doi.org/10.1038/375561a0	journal	June 1995
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
Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x Hamidian, M. H.; Edkins, S. D.; Joo, Sang Hyun Nature, Vol. 532, Issue 7599 https://doi.org/10.1038/nature17411	journal	April 2016
Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 Chang, J.; Blackburn, E.; Holmes, A. T. Nature Physics, Vol. 8, Issue 12 https://doi.org/10.1038/nphys2456	journal	October 2012
Quantum dimer model for the pseudogap metal Punk, Matthias; Allais, Andrea; Sachdev, Subir Proceedings of the National Academy of Sciences, Vol. 112, Issue 31 https://doi.org/10.1073/pnas.1512206112	journal	July 2015
Local antiferromagnetic correlations and d _{x ² -y ²} pairing Scalapino, D. J.; Trugman, S. A. Philosophical Magazine B, Vol. 74, Issue 5 https://doi.org/10.1080/01418639608240361	journal	November 1996
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
Topology of the resonating valence-bond state: Solitons and high- T c superconductivity Kivelson, Steven A.; Rokhsar, Daniel S.; Sethna, James P. Physical Review B, Vol. 35, Issue 16 https://doi.org/10.1103/PhysRevB.35.8865	journal	June 1987
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
Exact diagonalization of finite frustrated spin-(1/2 Heisenberg models Figueirido, F.; Karlhede, A.; Kivelson, S. Physical Review B, Vol. 41, Issue 7 https://doi.org/10.1103/PhysRevB.41.4619	journal	March 1990
Density-matrix algorithms for quantum renormalization groups White, Steven R. Physical Review B, Vol. 48, Issue 14 https://doi.org/10.1103/PhysRevB.48.10345	journal	October 1993
Properties of lightly doped t - J two-leg ladders Troyer, Matthias; Tsunetsugu, Hirokazu; Rice, T. M. Physical Review B, Vol. 53, Issue 1 https://doi.org/10.1103/PhysRevB.53.251	journal	January 1996
Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals Varma, C. M. Physical Review B, Vol. 55, Issue 21 https://doi.org/10.1103/PhysRevB.55.14554	journal	June 1997
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
Landau theory of stripe phases in cuprates and nickelates Zachar, Oron; Kivelson, S. A.; Emery, V. J. Physical Review B, Vol. 57, Issue 3 https://doi.org/10.1103/PhysRevB.57.1422	journal	January 1998
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
Hidden order in the cuprates Chakravarty, Sudip; Laughlin, R. B.; Morr, Dirk K. Physical Review B, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevB.63.094503	journal	January 2001
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
Periodic density-of-states modulations in superconducting Bi 2 Sr 2 CaCu 2 O 8 + δ Howald, C.; Eisaki, H.; Kaneko, N. Physical Review B, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevB.67.014533	journal	January 2003
Charge-density-wave instabilities driven by multiple umklapp scattering Schmitteckert, Peter; Werner, Ralph Physical Review B, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevB.69.195115	journal	May 2004
Bipairing and the stripe phase in four-leg Hubbard ladders Chang, Ming-Shyang; Affleck, Ian Physical Review B, Vol. 76, Issue 5 https://doi.org/10.1103/PhysRevB.76.054521	journal	August 2007
Fermi surface nesting and the origin of charge density waves in metals Johannes, M. D.; Mazin, I. I. Physical Review B, Vol. 77, Issue 16 https://doi.org/10.1103/PhysRevB.77.165135	journal	April 2008
Theory of the striped superconductor Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A. Physical Review B, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevB.79.064515	journal	February 2009
Pair-density-wave superconducting order in two-leg ladders Jaefari, Akbar; Fradkin, Eduardo Physical Review B, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevB.85.035104	journal	January 2012
Spin liquid ground state of the spin- 1 2 square J 1 - J 2 Heisenberg model Jiang, Hong-Chen; Yao, Hong; Balents, Leon Physical Review B, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevB.86.024424	journal	July 2012
Comparison of charge modulations in La 1.875 Ba 0.125 CuO 4 and YBa 2 Cu 3 O 6.6 Thampy, V.; Blanco-Canosa, S.; García-Fernández, M. Physical Review B, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevB.88.024505	journal	July 2013
Charge-density-wave order with momentum ( 2 Q , 0 ) and ( 0 , 2 Q ) within the spin-fermion model: Continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates Wang, Yuxuan; Chubukov, Andrey Physical Review B, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevB.90.035149	journal	July 2014
Resonant x-ray scattering study of charge-density wave correlations in YBa 2 Cu 3 O 6 + x Blanco-Canosa, S.; Frano, A.; Schierle, E. Physical Review B, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevB.90.054513	journal	August 2014
Competing charge, spin, and superconducting orders in underdoped YBa 2 Cu 3 O y Hücker, M.; Christensen, N. B.; Holmes, A. T. Physical Review B, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevB.90.054514	journal	August 2014
Renormalization group analysis of a fermionic hot-spot model Whitsitt, Seth; Sachdev, Subir Physical Review B, Vol. 90, Issue 10 https://doi.org/10.1103/PhysRevB.90.104505	journal	September 2014
Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors Pépin, C.; de Carvalho, V. S.; Kloss, T. Physical Review B, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevB.90.195207	journal	November 2014
Tensor-product state approach to spin- 1 2 square J 1 − J 2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank Physical Review B, Vol. 94, Issue 7 https://doi.org/10.1103/PhysRevB.94.075143	journal	August 2016
Electronic quasiparticles in the quantum dimer model: Density matrix renormalization group results Lee, Junhyun; Sachdev, Subir; White, Steven R. Physical Review B, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevB.94.115112	journal	September 2016
Direct observation of charge order in underdoped and optimally doped Bi 2 ( Sr , La ) 2 CuO 6 + δ by resonant inelastic x-ray scattering Peng, Y. Y.; Salluzzo, M.; Sun, X. Physical Review B, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevB.94.184511	journal	November 2016
Pair-Density-Wave Correlations in the Kondo-Heisenberg Model Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A. Physical Review Letters, Vol. 105, Issue 14 https://doi.org/10.1103/PhysRevLett.105.146403	journal	September 2010
Momentum-Dependent Charge Correlations in YBa 2 Cu 3 O 6 + δ Superconductors Probed by Resonant X-Ray Scattering: Evidence for Three Competing Phases Blanco-Canosa, S.; Frano, A.; Loew, T. Physical Review Letters, Vol. 110, Issue 18 https://doi.org/10.1103/PhysRevLett.110.187001	journal	May 2013
Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- 1 2 J 1 − J 2 Square Heisenberg Model Gong, Shou-Shu; Zhu, Wei; Sheng, D. N. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.027201	journal	July 2014
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
Incommensurate antiferromagnetism in the two-dimensional Hubbard model Schulz, H. J. Physical Review Letters, Vol. 64, Issue 12 https://doi.org/10.1103/PhysRevLett.64.1445	journal	March 1990
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
Study of an Ising model with competing long- and short-range interactions Löw, U.; Emery, V. J.; Fabricius, K. Physical Review Letters, Vol. 72, Issue 12 https://doi.org/10.1103/PhysRevLett.72.1918	journal	March 1994
Dimensional Crossover in Quantum Antiferromagnets Chakravarty, Sudip Physical Review Letters, Vol. 77, Issue 21 https://doi.org/10.1103/PhysRevLett.77.4446	journal	November 1996
Correlation Lengths in Quantum Spin Ladders Syljuåsen, Olav F.; Chakravarty, Sudip; Greven, Martin Physical Review Letters, Vol. 78, Issue 21 https://doi.org/10.1103/PhysRevLett.78.4115	journal	May 1997
Nonperturbative Approach to Luttinger's Theorem in One Dimension Yamanaka, Masanori; Oshikawa, Masaki; Affleck, Ian Physical Review Letters, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevLett.79.1110	journal	August 1997
Density Matrix Renormalization Group Study of the Striped Phase in the 2D t − J Model White, Steven R.; Scalapino, D. J. Physical Review Letters, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevLett.80.1272	journal	February 1998
Fractionalized Fermi Liquids Senthil, T.; Sachdev, Subir; Vojta, Matthias Physical Review Letters, Vol. 90, Issue 21 https://doi.org/10.1103/PhysRevLett.90.216403	journal	May 2003
Colloquium : Theory of intertwined orders in high temperature superconductors Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M. Reviews of Modern Physics, Vol. 87, Issue 2 https://doi.org/10.1103/RevModPhys.87.457	journal	May 2015
Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x Ghiringhelli, G.; Le Tacon, M.; Minola, M. Science, Vol. 337, Issue 6096 https://doi.org/10.1126/science.1223532	journal	July 2012
Charge Order Driven by Fermi-Arc Instability in Bi2Sr2-xLaxCuO6+ Comin, R.; Frano, A.; Yee, M. M. Science, Vol. 343, Issue 6169 https://doi.org/10.1126/science.1242996	journal	December 2013
Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates da Silva Neto, E. H.; Aynajian, P.; Frano, A. Science, Vol. 343, Issue 6169 https://doi.org/10.1126/science.1243479	journal	December 2013
The Resonating Valence Bond State in La2CuO4 and Superconductivity Anderson, P. W. Science, Vol. 235, Issue 4793 https://doi.org/10.1126/science.235.4793.1196	journal	March 1987
Magnetic Neutron Scattering in Hole-Doped Cuprate Superconductors J. Birgeneau, Robert; Stock, Chris; M. Tranquada, John Journal of the Physical Society of Japan, Vol. 75, Issue 11 https://doi.org/10.1143/JPSJ.75.111003	journal	November 2006
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group Stoudenmire, E. M.; White, Steven R. Annual Review of Condensed Matter Physics, Vol. 3, Issue 1 https://doi.org/10.1146/annurev-conmatphys-020911-125018	journal	March 2012

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