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Physica A Statistical Mechanics and its Applications

Longitudinal-field fidelity susceptibility analysis of the 𝐽1-𝐽2 transverse-field Ising model around 𝐽2βˆ•π½1 β‰ˆ 0.5

Yoshihiro Nishiyama

Published Jan 7, 2026β€’ 0 citations
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We study the effect of quantum fluctuations by means of a transverse magnetic field ($\Gamma$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for $J_2>J_1$ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el ($J_2 J_1$) phases, respectively. At the homogeneous coupling ($J_1=J_2$) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, $\Gamma/J_1\lesssim 0.4$, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point ($J_2=0.5 J_1$) of the antiferromagnetic $J_1-J_2$ Ising square lattice.

β€’May 6, 2014β€’0 citations
We exploit the quantum cluster variational method (QCVM) to study the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other mean field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between g=J2/J1g={J}_{2}/{J}_{1}g=J2​/J1​, the temperature and the longitudinal and transverse external fields. Our results show that quantum fluctuations may change the order of the transition and induce a gap between the ferromagnetic and the stripe phases. Moreover, when both longitudinal and transverse fields are present, thermal fluctuations and quantum effects contribute to the appearance of a nematic phase.
The ground-state properties of the S=1/2S=1/2S=1/2 transverse-field Ising model on the checkerboard lattice are studied using linear spin-wave theory. We consider the general case of different couplings between nearest neighbors (J1{J}_{1}J1​) and next-to-nearest neighbors (J2{J}_{2}J2​). In zero field, the system displays a large degeneracy of the ground state, which is exponential in the system size (for J1=J2{J}_{1}={J}_{2}J1​=J2​) or in the system's linear dimensions (for J2>J1{J}_{2}>{J}_{1}J2​>J1​). Quantum fluctuations induced by a transverse field are found to be unable to lift this degeneracy in favor of a classically ordered state at the harmonic level. This remarkable fact suggests that a quantum-disordered ground state can be instead promoted when nonlinear fluctuations are accounted for, in agreement with existing results for the isotropic case J1=J2{J}_{1}={J}_{2}J1​=J2​. Moreover, spin-wave theory shows sizable regions of instability, which are further candidates for quantum-disordered behavior.
We study the effect of quantum fluctuations by means of a transverse magnetic field (Ξ“\GammaΞ“) on the antiferromagnetic J1βˆ’J2J_1-J_2J1β€‹βˆ’J2​ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for J2>J1J_2>J_1J2​>J1​ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el (J2J1J_2 J_1J2​J1​) phases, respectively. At the homogeneous coupling (J1=J2J_1=J_2J1​=J2​) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, Ξ“/J1≲0.4\Gamma/J_1\lesssim 0.4Ξ“/J1​≲0.4, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point (J2=0.5J1J_2=0.5 J_1J2​=0.5J1​) of the antiferromagnetic J1βˆ’J2J_1-J_2J1β€‹βˆ’J2​ Ising square lattice.