Quantum tricriticality in antiferromagnetic Ising model with transverse field: A quantum Monte Carlo study

Abstract

Quantum tricriticality of a J1-J2 antiferromagnetic Ising model on a square lattice is studied using the mean-field (MF) theory, scaling theory, and the unbiased world-line quantum MonteCarlo (QMC) method based on the Feynman path integral formula. The critical exponents of the quantum tricritical point (QTCP) and the qualitative phase diagram are obtained from the MF analysis. By performing the unbiased QMC calculations, we provide the numerical evidence for the existence of the QTCP and numerically determine the location of the QTCP in the case of J1 = J2. From the systematic finite-size scaling analysis, we conclude that the QTCP is located at HQTCP/J1 = 3.260(2) and ΓQTCP/J1 = 4.10(5). We also show that the critical exponents of the QTCP are identical to those of the MF theory because the QTCP in this model is in the upper critical dimension. The QMC simulations reveal that unconventional proximity effects of the ferromagnetic susceptibility appear close to the antiferromagnetic QTCP, and the proximity effects survive for the conventional quantum critical point. We suggest that the momentum dependence of the dynamical and static spin structure factors is useful for identifying the QTCP in experiments.

Fermion-induced quantum critical point in the Landau-Devonshire model

“…It was shown that FOPT and continuous phase transition have been observed in a spin model with both nearest-neighbor and next-nearest neighbor interactions [71]. The effective theory for this model is just the Landau-Devonshire theory [71]. We can consider a similar model in graphene, whose elementary excitation is the Dirac fermion with N f = 2 and the spin freedom is naturally coupled to the Dirac fermion.…”

Quantum Ising model on the frustrated square lattice

“…From the theoretical point of view, the transverse Ising model on the square lattice is the simplest model to exhibit both classical and quantum phase transitions. For instance, when first-neighbor (J 1 ) antiferromagnetic (AF) interactions are considered, increasing a transverse magnetic field can change the ground-state of this model from a Néel AF long-range order to a polarized paramagnetic (PM) state at a quantum critical point [4]. By considering also second-neighbor antiferromagnetic interactions (J 2 ), the model becomes the so called J 1 -J 2 Ising model, in which frustration can be introduced by tuning g ≡ J 2 /J 1 .…”

“…Despite several studies have addressed the magnetic behavior of the classical J 1 -J 2 Ising model, only few efforts have been made to understand the effect of transverse fields in this model [4,7,17]. Recently, a cluster operator approach was used to describe the highly frustrated limit (g = 0.5) of the quantum J 1 -J 2 Ising model at zero temperature [17].…”

Chiral Tricritical Point: A New Universality Class in Dirac Systems

“…We further study tricritical points of Heisenberg transitions in Dirac semimetals [19,21,[34][35][36][37] by extending the Ising fields to Heisenberg spins. The relevance of these universality classes to real materials like graphene or graphene-like systems will also be discussed.Lattice model and phase diagram.-It is known that the (2+1)-dimensional Ising model under both transversal and longitudinal Zeeman fields can realize a tricritical point at the phase boundary between first-and secondorder transitions [7]. The Hamiltonian on the honeycomb lattice is given bywhere σ denotes the Ising spins defined at each site, and and refer to nearest neighbors (NN) and nextnearest neighbors (NNN), respectively.…”