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Bulletin of the American Physical Society

Phase diagram and chirality of the spin-1/2 J1-J2 Heisenberg model on the kagome lattice

Shou-Shu Gong, Dong-Ning Sheng

Published Mar 20, 2013• 0 citations
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We assess the ground-state phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the Kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For ${J}_{2}=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $\ensuremath{\pi}$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017).]. Here we show that its accuracy improves in the presence of a small antiferromagnetic superexchange ${J}_{2}$, leading to a finite region where the gapless spin liquid is stable; then, for ${J}_{2}/{J}_{1}=0.11(1)$, a first-order transition to a magnetic phase with pitch vector $\mathbf{q}=(0,0)$ is detected by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of $|{J}_{2}|/{J}_{1}$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on 36 sites where exact diagonalization is possible. Then, on increasing the ratio $|{J}_{2}|/{J}_{1}$, a magnetically ordered state with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic ${J}_{2}$ regime, evidence is shown in favor of a first-order transition at ${J}_{2}/{J}_{1}=\ensuremath{-}0.065(5)$.

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We study the quantum phase diagram of the spin-1/21/21/2 Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions J1,J2{J}_{1},{J}_{2}J1​,J2​, and J3{J}_{3}J3​ by means of density matrix renormalization group. For small J2{J}_{2}J2​ and J3{J}_{3}J3​, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing J2{J}_{2}J2​ and J3{J}_{3}J3​, we find in addition a q=(0,0)q=(0,0)q=(0,0) N\'eel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the q=(0,0)q=(0,0)q=(0,0) phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.
We assess the ground-state phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the Kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For J2=0{J}_{2}=0J2​=0, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $\ensuremath{\pi}$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017).]. Here we show that its accuracy improves in the presence of a small antiferromagnetic superexchange J2{J}_{2}J2​, leading to a finite region where the gapless spin liquid is stable; then, for J2/J1=0.11(1){J}_{2}/{J}_{1}=0.11(1)J2​/J1​=0.11(1), a first-order transition to a magnetic phase with pitch vector q=(0,0)\mathbf{q}=(0,0)q=(0,0) is detected by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of ∣J2∣/J1|{J}_{2}|/{J}_{1}∣J2​∣/J1​, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on 36 sites where exact diagonalization is possible. Then, on increasing the ratio ∣J2∣/J1|{J}_{2}|/{J}_{1}∣J2​∣/J1​, a magnetically ordered state with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic J2{J}_{2}J2​ regime, evidence is shown in favor of a first-order transition at ${J}_{2}/{J}_{1}=\ensuremath{-}0.065(5)$.