Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain

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  • Additional Information
    • Publication Date:
      2020
    • Collection:
      Condensed Matter
    • Abstract:
      We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.
    • Accession Number:
      edsarx.2005.10980
  • Citations
    • ABNT:
      KIM, J. et al. Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain. [s. l.], 2020. Disponível em: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580. Acesso em: 4 jul. 2020.
    • AMA:
      Kim J, Kim M, Kawashima N, Han JH, Lee H-Y. Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain. 2020. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580. Accessed July 4, 2020.
    • AMA11:
      Kim J, Kim M, Kawashima N, Han JH, Lee H-Y. Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain. Published online 2020. Accessed July 4, 2020. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580
    • APA:
      Kim, J., Kim, M., Kawashima, N., Han, J. H., & Lee, H.-Y. (2020). Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain.
    • Chicago/Turabian: Author-Date:
      Kim, Jintae, Minsoo Kim, Naoki Kawashima, Jung Hoon Han, and Hyun-Yong Lee. 2020. “Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain.” http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580.
    • Harvard:
      Kim, J. et al. (2020) ‘Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain’. Available at: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580 (Accessed: 4 July 2020).
    • Harvard: Australian:
      Kim, J, Kim, M, Kawashima, N, Han, JH & Lee, H-Y 2020, ‘Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain’, viewed 4 July 2020, .
    • MLA:
      Kim, Jintae, et al. Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain. 2020. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580.
    • Chicago/Turabian: Humanities:
      Kim, Jintae, Minsoo Kim, Naoki Kawashima, Jung Hoon Han, and Hyun-Yong Lee. “Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain,” 2020. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580.
    • Vancouver/ICMJE:
      Kim J, Kim M, Kawashima N, Han JH, Lee H-Y. Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain. 2020 [cited 2020 Jul 4]; Available from: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.2005.10980&custid=s6224580