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

Title: Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results]

Abstract

Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

Authors:
ORCiD logo [1];  [2];  [1]; ORCiD logo [3]; ORCiD logo [3];  [1];  [4]
  1. Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Univ. of Tennessee, Knoxville, TN (United States); Univ. de Sherbrooke, Sherbrooke, QC (Canada)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Univ. of Tennessee, Knoxville, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1440816
Alternate Identifier(s):
OSTI ID: 1439731
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Nocera, Alberto, Wang, Yan, Patel, Niravkumar D., Alvarez, Gonzalo, Maier, Thomas A., Dagotto, Elbio R., and Johnston, Steven S. Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results]. United States: N. p., 2018. Web. doi:10.1103/physrevb.97.195156.
Nocera, Alberto, Wang, Yan, Patel, Niravkumar D., Alvarez, Gonzalo, Maier, Thomas A., Dagotto, Elbio R., & Johnston, Steven S. Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results]. United States. https://doi.org/10.1103/physrevb.97.195156
Nocera, Alberto, Wang, Yan, Patel, Niravkumar D., Alvarez, Gonzalo, Maier, Thomas A., Dagotto, Elbio R., and Johnston, Steven S. Thu . "Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results]". United States. https://doi.org/10.1103/physrevb.97.195156. https://www.osti.gov/servlets/purl/1440816.
@article{osti_1440816,
title = {Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results [Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and RPA+FLEX results]},
author = {Nocera, Alberto and Wang, Yan and Patel, Niravkumar D. and Alvarez, Gonzalo and Maier, Thomas A. and Dagotto, Elbio R. and Johnston, Steven S.},
abstractNote = {Here, we study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.},
doi = {10.1103/physrevb.97.195156},
url = {https://www.osti.gov/biblio/1440816}, journal = {Physical Review B},
issn = {2469-9950},
number = 19,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

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

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

FIG.1 FIG.1: (a) Superconducting gap function (in units of $$t$$) computed with RPA+FLEX as a function of space and leg index ($$α$$ corresponds to lower leg, while $$β$$ to upper leg). Here, $$U$$/$$t$$ = 6.0, electron filling $$n$$ = 0.96. The inset in (a) is a pictorial representation of the pairingmore » gap at first few sites of the two-leg ladder, with one of the electron fixed at site-0 of the lower leg. The upward triangle means a positive gap and the downward triangle means a negative gap and the size of the triangle is proportional to the gap magnitude. (b) Rung-rung, rung-leg, and rung-diagonal pair singlet correlation functions computed with DMRG as a function of the distance from the center of the ladder. Here, $$U$$/$$t$$ = 6.0, $$n$$ = 0.875. (c) Maximal anomalous self-energy (in units of $$t$$) in the first Brillouin zone computed in RPA+FLEX as a function of electron filling and different values of $$U$$, as indicated. (d) Pairing strength computed with DMRG as a function of electron filling, for different values of $$U$$, as indicated. The pairing strength is computed from the rung-rung pair singlet correlation functions as $$\bar{D}$$ = $$Σ^{j=12}_{j=6}$$ $$P$$($$j$$)/$$P$$(1), where $$P$$($$j$$) = $$\langle$$$$Δ^{†}_{r}$$($$c$$)$$Δ$ $$r$$($$c$$ + $$j$$)$$\rangle$$. The persistent background at $$U$$/$$t$$ = 2 over a wide range of doping originates in short distance correlations even in the non-interacting limit.« less

Save / Share:

Works referenced in this record:

Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model
journal, April 2007


Role of vertex corrections in the matrix formulation of the random phase approximation for the multiorbital Hubbard model
journal, December 2016


Persistence of High-Frequency Spin Fluctuations in Overdoped Superconducting La 2 x Sr x CuO 4 ( x = 0.22 )
journal, August 2007


Dispersive collective charge modes in an incommensurately modulated cuprate Mott insulator
journal, September 2007


Magnetic properties of the overdoped superconductor La 2 x Sr x Cu O 4 with and without Zn impurities
journal, August 2005


Comparison of Monte Carlo and diagrammatic calculations for the two-dimensional Hubbard model
journal, February 1993


Anisotropic scattering rates and antiferromagnetic precursor effects in the t-t'-U Hubbard model
journal, December 2000


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


Plasmons and interband transitions of Ca 11 Sr 3 Cu 24 O 41 investigated by electron energy-loss spectroscopy
journal, December 2010


Density-matrix algorithms for quantum renormalization groups
journal, October 1993


Resonant inelastic x-ray scattering studies of elementary excitations
journal, June 2011


Non-Perturbative Many-Body Approach to the Hubbard Model and Single-Particle Pseudogap
journal, November 1997


Density matrix formulation for quantum renormalization groups
journal, November 1992


Role of transverse hopping in a two-coupled-chains model
journal, December 1993


Renormalization of the elementary excitations in hole- and electron-doped cuprates due to spin fluctuations
journal, April 2003


Observation of a Spin Gap in Sr Cu 2 O 3 Comprising Spin-½ Quasi-1D Two-Leg Ladders
journal, December 1994


Magnetic properties of the two-dimensional Hubbard model
journal, January 1991


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


Self-consistent d x 2 - y 2 pairing in a two-dimensional Hubbard model
journal, March 1994


Excitation spectrum of Heisenberg spin ladders
journal, February 1993


Friedel oscillations and charge density waves in chains and ladders
journal, April 2002


Theory for the Excitation Spectrum of High- T c Superconductors: Quasiparticle Dispersion and Shadows of the Fermi Surface
journal, December 1995


Signatures of pairing in the magnetic excitation spectrum of strongly correlated two-leg ladders
journal, November 2017


NMR Study of Carrier Doping Effects on Spin Gaps in the Spin Ladder Sr 1 4 x A x Cu 24 O 41 ( A = C a , Y, and La)
journal, March 1997


Weak-coupling phase diagram of the two-chain Hubbard model
journal, May 1996


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


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


Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior
journal, November 2016


Self-consistent calculations of superconductivity in a nearly antiferromagnetic Fermi liquid
journal, October 1994


Superconductivity in ladders and coupled planes
journal, March 1992


The case for dx2 − y2 pairing in the cuprate superconductors
journal, January 1995


Dynamical correlation functions using the density matrix renormalization group
journal, July 1999


Strong-coupling theory of superconductivity in a degenerate Hubbard model
journal, March 2004


Weak-coupling analysis of the neutron-scattering spectral weight
journal, February 1993


Superconductivity in the Ladder Material Sr 0.4 Ca 13.6 Cu 24 O 41.84
journal, September 1996


Complexity in Strongly Correlated Electronic Systems
journal, July 2005


Correlations in a Two-Chain Hubbard Model
journal, August 1994


One- and Two-Triplon Spectra of a Cuprate Ladder
journal, January 2007


Resonant X-Ray Scattering Studies of Charge Order in Cuprates
journal, March 2016


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


Pair correlations in doped Hubbard ladders
journal, November 2015


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


Electronic Properties of the Trellis-Lattice Hubbard Model: Pseudogap and Superconductivity
journal, June 1998


Variations of T c for changes in the spin-fluctuation spectral weight
journal, October 1994


Antiferromagnetic spin fluctuation and superconductivity
journal, July 2003


Theory for superconducting properties of the cuprates: doping dependence of the electronic excitations and shadow states
journal, April 1996


The Challenge of Unconventional Superconductivity
journal, April 2011


Phase diagram of hole doped two-leg Cu O ladders
journal, October 2007


Orbital current patterns in doped two-leg Cu-O Hubbard ladders
journal, August 2008


Spin Waves and Electronic Interactions in La 2 CuO 4
journal, June 2001


A common thread: The pairing interaction for unconventional superconductors
journal, October 2012


Origin of Weak Pseudogap Behaviors in Na 0.35 CoO 2 : Absence of Small Hole Pockets
journal, August 2005


Orbital coupling and superconductivity in the iron pnictides
journal, June 2009


Weak-coupling model of spin fluctuations in the superconducting state of the layered cuprates
journal, February 1992


    Works referencing / citing this record:

    Fingerprints of an orbital-selective Mott phase in the block magnetic state of BaFe2Se3 ladders
    journal, June 2019


    Pseudogap in the c -axis (along the ladder) optical conductivity of t   −   J ladders and its quasiparticle interpretation
    journal, February 2019


    Low-energy antiferromagnetic spin fluctuations limit the coherent superconducting gap in cuprates
    journal, December 2018


      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.