Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

TL;DR

This paper investigates the phase diagram of the J1-J2 transverse field Ising model on a checkerboard lattice using a plaquette operator approach, revealing quantum fluctuation effects, phase boundaries, and the nature of phase transitions.

Contribution

It introduces a plaquette operator formalism to analyze quantum fluctuations and phase transitions in the J1-J2 Ising model on a checkerboard lattice, providing new insights into the phase diagram.

Findings

Identification of a plaquette ordered solid (RPS) state due to quantum fluctuations.

Determination of critical points and phase boundaries for Néel and collinear phases.

Observation of the transition types between different phases, including possible deconfined quantum phase transitions.

Abstract

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 the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes 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 solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for $J_2>J_1$. The bosonic excitation gap vanishes at the critical points to the N\'{e}el ($J_2 < J_1$) and collinear ($J_2 > J_1$) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling ($J_2=J_1$) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, $\Gamma/J_1\lesssim 0.3$, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the N\'{e}el phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.