DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Magnetic properties of alternating Hubbard ladders

Abstract

We explore the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The density matrix renormalization group (DMRG) method is used to obtain the groundstate properties, e.g., excitation gaps, charge and spin densities as well as their correlation functions at half filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long-range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2];  [3]
  1. University of Tunis El-Manar (Tunisia)
  2. Leibniz University, Hannover (Germany)
  3. Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1851970
Grant/Contract Number:  
SC0014671
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 103; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Ferrimagnetism; Magnetic order; Magnetism; Strongly correlated systems; Density matrix renormalization group; Hubbard model

Citation Formats

Essalah, Kaouther, Benali, Ali, Abdelwahab, Anas, Jeckelmann, Eric, and Scalettar, Richard T. Magnetic properties of alternating Hubbard ladders. United States: N. p., 2021. Web. doi:10.1103/physrevb.103.165127.
Essalah, Kaouther, Benali, Ali, Abdelwahab, Anas, Jeckelmann, Eric, & Scalettar, Richard T. Magnetic properties of alternating Hubbard ladders. United States. https://doi.org/10.1103/physrevb.103.165127
Essalah, Kaouther, Benali, Ali, Abdelwahab, Anas, Jeckelmann, Eric, and Scalettar, Richard T. Thu . "Magnetic properties of alternating Hubbard ladders". United States. https://doi.org/10.1103/physrevb.103.165127. https://www.osti.gov/servlets/purl/1851970.
@article{osti_1851970,
title = {Magnetic properties of alternating Hubbard ladders},
author = {Essalah, Kaouther and Benali, Ali and Abdelwahab, Anas and Jeckelmann, Eric and Scalettar, Richard T.},
abstractNote = {We explore the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The density matrix renormalization group (DMRG) method is used to obtain the groundstate properties, e.g., excitation gaps, charge and spin densities as well as their correlation functions at half filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long-range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.},
doi = {10.1103/physrevb.103.165127},
journal = {Physical Review. B},
number = 16,
volume = 103,
place = {United States},
year = {Thu Apr 22 00:00:00 EDT 2021},
month = {Thu Apr 22 00:00:00 EDT 2021}
}

Works referenced in this record:

Resonating Valence Bond Theory of Coupled Heisenberg Chains
journal, August 1994


Monte Carlo Study of Correlations in Quantum Spin Ladders
journal, August 1996


High-field magnetization of a quasi-one-dimensional S=1 antiferromagnet Ni( C 2 H 8 N 2 ) 2 NO 2 ( ClO 4 : Observation of the Haldane gap
journal, September 1989


Superconductivity in ladders and coupled planes
journal, March 1992


Spin- and charge-density waves in the Hartree–Fock ground state of the two-dimensional Hubbard model
journal, November 2011


Many-body physics with ultracold gases
journal, July 2008

  • Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
  • Reviews of Modern Physics, Vol. 80, Issue 3
  • DOI: 10.1103/RevModPhys.80.885

Dynamics in the S = 1 One-Dimensional Antiferromagnet AgV P 2 S 6 via 31 P and 51 V NMR
journal, March 1996


The Doped Two-Chain Hubbard Model
journal, April 1995


Phase diagram of the Hubbard model: A variational wave-function approach
journal, June 1989


Superconductivity in a quasi-one-dimensional spin liquid
journal, May 1994


Density-matrix renormalization-group method in momentum space
journal, April 1996


Low-lying excited states and low-temperature properties of an alternating spin-1–spin-1/2 chain: A density-matrix renormalization-group study
journal, April 1997


The density-matrix renormalization group
journal, April 2005


Strong correlation effects in the fullerene C 20 studied using a one-band Hubbard model
journal, July 2007


Experimental realization and characterization of an electronic Lieb lattice
journal, April 2017

  • Slot, Marlou R.; Gardenier, Thomas S.; Jacobse, Peter H.
  • Nature Physics, Vol. 13, Issue 7
  • DOI: 10.1038/nphys4105

The Anderson-Mott transition
journal, April 1994


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


Frustrated spin ladder with alternating spin-1 and spin- 1 2 rungs
journal, January 2010


Electronic Correlation Effects and Superconductivity in Doped Fullerenes
journal, November 1991


Inelastic-neutron-scattering study of the spin dynamics in the Haldane-gap system Ni( C 2 H 8 N 2 ) 2 NO 2 ClO 4
journal, October 1994


Ground-state and spectral properties of an asymmetric Hubbard ladder
journal, April 2015


Thermodynamic properties of Heisenberg ferrimagnetic spin chains: Ferromagnetic-antiferromagnetic crossover
journal, June 1998


Alternating-spin ladders in a magnetic field: Formation of magnetization plateaux
journal, November 2000


Spin-wave series for quantum one-dimensional ferrimagnets
journal, June 1998


Ferrimagnetic long-range order of the Hubbard model
journal, February 1994


Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
journal, February 1996


Ultracold quantum gases in optical lattices
journal, October 2005


Experimental Evidence of a Haldane Gap in an S = 2 Quasi-Linear-Chain Antiferromagnet
journal, August 1996


Two theorems on the Hubbard model
journal, March 1989


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


A density matrix renormalization group approach to interacting quantum systems on Cayley trees
journal, October 1997


Atomic spin-chain realization of a model for quantum criticality
journal, April 2016

  • Toskovic, R.; van den Berg, R.; Spinelli, A.
  • Nature Physics, Vol. 12, Issue 7
  • DOI: 10.1038/nphys3722

Alternating-spin ladders
journal, January 1998


Elementary excitations of Heisenberg ferrimagnetic spin chains
journal, June 1998


Three-Leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties
journal, December 1997

  • Kawano, Kenro; Takahashi, Minoru
  • Journal of the Physical Society of Japan, Vol. 66, Issue 12
  • DOI: 10.1143/JPSJ.66.4001

Ferromagnetism in one-dimensional monatomic metal chains
journal, March 2002

  • Gambardella, P.; Dallmeyer, A.; Maiti, K.
  • Nature, Vol. 416, Issue 6878
  • DOI: 10.1038/416301a

Highly parallel scanning tunneling microscope based hydrogen depassivation lithography
journal, November 2018

  • Randall, John N.; Owen, James H. G.; Lake, Joseph
  • Journal of Vacuum Science & Technology B, Vol. 36, Issue 6
  • DOI: 10.1116/1.5047939

Optical lattices
journal, June 2008

  • Greiner, Markus; Fölling, Simon
  • Nature, Vol. 453, Issue 7196
  • DOI: 10.1038/453736a

Comparison of different ladder models
journal, October 1998


Absence of pair binding in the U=? Hubbard model
journal, December 1991

  • Chakravarty, S.; Chayes, L.; Kivelson, S. A.
  • Letters in Mathematical Physics, Vol. 23, Issue 4
  • DOI: 10.1007/bf00398823

Stripes in a three-chain Hubbard ladder: A comparison of density-matrix renormalization group and constrained-path Monte Carlo results
journal, February 2000


Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials
journal, February 1996