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Gapless spin liquid state of the spin-$\frac12$ honeycomb antiferromagnetic $\Gamma$ model

Qiang Luo, Jize Zhao, Hae‐Young Kee, Xiaoqun Wang

Published Oct 3, 2019• 0 citations
OpenAlex

Abstract

To understand the ground state of the spin-$1/2$ honeycomb $\Gamma$ antiferromagnet (HC$\Gamma$A), we propose a choreographed model which includes a bond-modulated Heisenberg interaction~($J$) aside from the $\Gamma$ term. By varying $\vartheta = \mathrm{atan}(\Gamma/J)$ in $[0, \pi]$, we demonstrate that the classical ground state changes from a zigzag order to a stripy order, through an extensive intermediate region. Using the linear spin-wave theory we find that the sublattice magnetization of the zigzag order is dramatically suppressed when close to HC$\Gamma$A. The intermediate region is fragile against quantum fluctuations and gives way to a gapless quantum spin liquid~(QSL) phase in a wide interval of $0.50 \lesssim \vartheta/\pi \leq 0.66(1)$ at the quantum level. Based on a series of compelling evidences including the vanishing magnetic and nematic orders, and also a perceptible correlation of the hexagonal plaquette operator, we conclude that the ground state of HC$\Gamma$A is a gapless QSL phase with a plaquette correlation.

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Gapless spin liquid state of the spin-12\frac1221​ honeycomb antiferromagnetic Γ\GammaΓ model
To understand the ground state of the spin-1/21/21/2 honeycomb Γ\GammaΓ antiferromagnet (HCΓ\GammaΓA), we propose a choreographed model which includes a bond-modulated Heisenberg interaction~(JJJ) aside from the Γ\GammaΓ term. By varying ϑ=atan(Γ/J)\vartheta = \mathrm{atan}(\Gamma/J)ϑ=atan(Γ/J) in [0,π][0, \pi][0,π], we demonstrate that the classical ground state changes from a zigzag order to a stripy order, through an extensive intermediate region. Using the linear spin-wave theory we find that the sublattice magnetization of the zigzag order is dramatically suppressed when close to HCΓ\GammaΓA. The intermediate region is fragile against quantum fluctuations and gives way to a gapless quantum spin liquid~(QSL) phase in a wide interval of 0.50≲ϑ/π≤0.66(1)0.50 \lesssim \vartheta/\pi \leq 0.66(1)0.50≲ϑ/π≤0.66(1) at the quantum level. Based on a series of compelling evidences including the vanishing magnetic and nematic orders, and also a perceptible correlation of the hexagonal plaquette operator, we conclude that the ground state of HCΓ\GammaΓA is a gapless QSL phase with a plaquette correlation.
Abstract A family of spin–orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal Γ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb Γ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the Γ region with a staggered Heisenberg interaction which favours the zigzag ordering. Despite such favour, we find a wide disordered region inclusive of the Γ limit in the phase diagram. Further, this phase exhibits a vanishing energy gap, a collapse of excitation spectrum, and a logarithmic entanglement entropy scaling on long cylinders, indicating a gapless QSL. Other quantities such as plaquette-plaquette correlation are also discussed.
We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J1>0{J}_{1}>0J1​>0 and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.
We investigate the ground-state and finite-temperature properties of the bond-random s=1/2s=1/2s=1/2 Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, J1J_1J1​ and J2J_2J2​, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (J2/J1J_2/J_1J2​/J1​) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba3_33​CuSb2_22​O9_99​ and 6HB-Ba3_33​NiSb2_22​O9_99​ exhibiting the gapless QSL-like behaviors are discussed.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor J1{J}_{1}J1​ and second-neighbor J2{J}_{2}J2​ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. N\'eel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio J2/J1{J}_{2}/{J}_{1}J2​/J1​, we find strong evidence for a continuous transition to a nonmagnetic phase at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For $0.23\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.36$, a gapless Z2{Z}_{2}Z2​ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the N\'eel order melts, this ordered state becomes clearly favored only for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.3$. Finally, for $0.36\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the N\'eel antiferromagnet from the plaquette valence-bond solid.
Recent experimental evidence for a field-induced quantum spin liquid (QSL) in ααα-RuCl3_33​ calls for an understanding for the ground state of honeycomb Kitaev model under a magnetic field. In this work we address the nature of an enigmatic gapless paramagnetic phase in the antiferromagnetic Kitave model, under an intermediate magnetic field perpendicular to the plane. Combining theoretical and numerical efforts, we identify this gapless phase as a U(1)U(1)U(1) QSL with spinon Fermi surfaces. We also reveal the nature of continuous quantum phase transitions involving this U(1)U(1)U(1) QSL, and obtain a phase diagram of the Kitaev model as a function of bond anisotropy and perpendicular magnetic field.
We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.