Journal of the Korean Physical Society

, Volume 74, Issue 7, pp 674–678 | Cite as

Strong Odd Bond - Weak Even Bond Picture in the Half-Filled One-Dimensional Hubbard Model

  • Myung-Hoon ChungEmail author


We study the strong odd bond - weak even bond picture by measuring the bond energy and the half-chain entanglement entropy in the one-dimensional Hubbard model. By using the infinite density matrix renormalization group with matrix product operator, we obtain the ground state of the matrix product state. As a function of the bond dimension, the bond energy and the half-chain entanglement entropy support the strong odd bond - weak even bond picture. From the expectation values of the occupation number, we numerically observe that the odd - even effect appears only for the half-filling case with a finite bond dimension. Our results confirm that the matrix product operator method is successful in exploring itinerant fermionic systems.


Entanglement entropy Infinite density matrix renormalization group Matrix product operator 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. NRF-2017 R1D1A1A0201845 to M.H.C.). The author would like to thank S. Capponi, J. Y. Chen and D. Poilblanc for helpful discussions.


  1. [1]
    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2011).CrossRefzbMATHGoogle Scholar
  2. [2]
    J. Eisert, M. Cramer and M. B. Plenio, Rev. Mod. Phys. 82, 277 (2010).ADSCrossRefGoogle Scholar
  3. [3]
    S. Östlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995).ADSCrossRefGoogle Scholar
  4. [4]
    U. Schollwöck, Ann. Phys. 326, 96 (2011).ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    D. Pérez-García, F. Verstraete, M. M. Wolf and J. I. Cirac, Quant. Inf. Comp. 8, 0650 (2008).Google Scholar
  6. [6]
    G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).ADSCrossRefGoogle Scholar
  7. [7]
    I. P. McCulloch, arXiv:0804.2509.Google Scholar
  8. [8]
    F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper and V. E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press, Cambridge, 2005).CrossRefzbMATHGoogle Scholar
  9. [9]
    M.C. Cha and M.H. Chung, PhysicaB 536, 701 (2018).ADSCrossRefGoogle Scholar
  10. [10]
    M. Schreiber et al., Science 21, 842 (2015).ADSCrossRefGoogle Scholar
  11. [11]
    N. Laflorencie, E. S. Sorensen, M. S. Chang and I. Affleck, Phys. Rev. Lett. 96, 100603 (2006).ADSCrossRefGoogle Scholar
  12. [12]
    C. Yang, A. N. Kocharian and Y. L. Chiang, J. Phys.: Condens. Matter 12, 7433 (2000).ADSGoogle Scholar
  13. [13]
    D. F. Mross and T. Senthil, Phys. Rev. B 84, 041102 (2011).ADSCrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2019

Authors and Affiliations

  1. 1.College of Science and TechnologyHongik UniversitySejongKorea

Personalised recommendations