SciPost Physics

SciPost Phys. 6, 019 (2019) · published 6 February 2019

• doi: 10.21468/SciPostPhys.6.2.019
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin-$\frac{1}{2}$ ferromagnetic ($J_1$) Heisenberg chain with next-nearest-neighbor antiferromagnetic ($J_2$) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at $J_2/|J_1|>1/4$ and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.

• Ortiz et al., Magnetic frustration and fractionalization in oligo(indenoindenes)
  Phys. Rev. B 107, L100416 (2023) [Crossref]
• Wardyn et al., Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic J1−J1′−J2 chain
  Phys. Rev. B 108, 205111 (2023) [Crossref]
• Rausch et al., Quantum spin spiral ground state of the ferrimagnetic sawtooth chain
  SciPost Phys. 14, 052 (2023) [Crossref]
• Ueda et al., Roles of easy-plane and easy-axis XXZ anisotropy and bond alternation in a frustrated ferromagnetic spin- 12 chain
  Phys. Rev. B 101, 224439 (2020) [Crossref]
• Furukawa et al., Effects of Dzyaloshinskii–Moriya Interactions in Volborthite: Magnetic Orders and Thermal Hall Effect
  J. Phys. Soc. Jpn. 89, 034711 (2020) [Crossref]
• Matsuda et al., Highly dispersive magnons with spin-gap-like features in the frustrated ferromagneticS=12chain compoundCa2Y2Cu5O10detected by inelastic neutron scattering
  Phys. Rev. B 100, 104415 (2019) [Crossref]
• Reja et al., Critical spin-12tetramer compoundCuInVO5: Exploring the vicinity of two multimerized singlet states
  Phys. Rev. B 99, 134420 (2019) [Crossref]
• Fumani et al., Quantum phases of the 1D anisotropic spin-1/2 frustrated ferromagnetic model: view point of quantum correlations
  Phys. Scr. 95, 055806 (2020) [Crossref]
• Ueda et al., Emergent spin-1 Haldane gap and ferroelectricity in a frustrated spin- 12 ladder
  Phys. Rev. B 101, 140408 (2020) [Crossref]
• Rausch et al., Topological phases arising from attractive interaction and pair hopping in the extended Hubbard model
  New J. Phys. 22, 073051 (2020) [Crossref]
• Veríssimo et al., Ground-state phase diagram and universality of sequential topological valence-bond-solid quantum transitions in a mixed tetramer chain
  J. Phys.: Condens. Matter 36, 165802 (2024) [Crossref]
• Yamaguchi et al., Variety of order-by-disorder phases in the asymmetric J1−J2 zigzag ladder: From the delta chain to the J1−J2 chain
  Phys. Rev. B 101, 104407 (2020) [Crossref]
• Kaneko et al., Ground-State Properties of the t–J Model for the CuO Double-Chain Structure
  J. Phys. Soc. Jpn. 93, 084703 (2024) [Crossref]
• Yamaguchi et al., Anomalous fractional quantization in the kagomelike Heisenberg ladder: Emergence of the effective spin-1 chain
  Phys. Rev. B 103, 184410 (2021) [Crossref]
• Saha et al., Hybrid exact diagonalization and density matrix renormalization group approach to the thermodynamics of one-dimensional quantum models
  Phys. Rev. B 99, 195144 (2019) [Crossref]
• Saito et al., Phase diagram of the quantum spin- 12 Heisenberg- Γ model on a frustrated zigzag chain
  Phys. Rev. B 110, 024409 (2024) [Crossref]