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Register a new userEmergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
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We investigate the ground state nature of the transverse field Ising model on the $J_1-J_2$ square lattice at the highly frustrated point $J_2/J_1=0.5$. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem. However, the string-type anharmonic fluctuations of COA are able to lift the degeneracy toward a string-valence bond solid (VBS) state, which is obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent non-magnetic string-VBS phase is gapped and breaks lattice rotational symmetry with only two-fold degeneracy, which bears a continuous quantum phase transition at $Gamma/J_1 cong 0.50$ to the quantum paramagnet phase of high fields. The critical behavior is characterized by $ u cong 1.0$ and $gamma cong 0.33$ exponents.
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We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {it plaquette crystal}, connected with the neighboring Neel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Neel and columnar phases. Our results suggest that the quantum phase transition between Neel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
We investigate the magnetic properties of LiYbO$_2$, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb$^{3+}$ ions in LiYbO$_2$ enters a long-range incommensurate, helical state with an ordering wave vector ${bf{k}} = (0.384, pm 0.384, 0)$ that locks-in to a commensurate ${bf{k}} = (1/3, pm 1/3, 0)$ phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO$_2$ can be understood in the framework of a Heisenberg $J_1-J_2$ Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of $J_2/|J_1|$. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.
We study the plaquette valence-bond solid phase of the spin-1/2 J_1-J_2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J_1-J_2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34 < J_2/J_1 < 0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J_2 = 0.34 J_1 and J_2 = 0.59 J_1. Interestingly, for J_2 < 0.48 J_1, the excitation gap corresponds to a singlet-triplet excitation at the $Gamma$ point while, for J_2 > 0.48 J_1, it is related to a singlet-singlet excitation at the X = (pi/2,0) point of the tetramerized Brillouin zone.
We report magnetic and thermodynamic properties of a $4d^1$ (Mo$^{5+}$) magnetic insulator MoOPO$_4$ single crystal, which realizes a $J_1$-$J_2$ Heisenberg spin-$1/2$ model on a stacked square lattice. The specific-heat measurements show a magnetic transition at 16 K which is also confirmed by magnetic susceptibility, ESR, and neutron diffraction measurements. Magnetic entropy deduced from the specific heat corresponds to a two-level degree of freedom per Mo$^{5+}$ ion, and the effective moment from the susceptibility corresponds to the spin-only value. Using {it ab initio} quantum chemistry calculations we demonstrate that the Mo$^{5+}$ ion hosts a purely spin-$1/2$ magnetic moment, indicating negligible effects of spin-orbit interaction. The quenched orbital moments originate from the large displacement of Mo ions inside the MoO$_6$ octahedra along the apical direction. The ground state is shown by neutron diffraction to support a collinear Neel-type magnetic order, and a spin-flop transition is observed around an applied magnetic field of 3.5 T. The magnetic phase diagram is reproduced by a mean-field calculation assuming a small easy-axis anisotropy in the exchange interactions. Our results suggest $4d$ molybdates as an alternative playground to search for model quantum magnets.
We investigate the role of a transverse field on the Ising square antiferromagnet with first-($J_1$) and second-($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1$-$J_2$ Ising antiferromagnet.
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