Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields

Abstract

Motivated by the recent experiments with Rydberg atoms in an optical tweezer array, we accurately map out the ground-state phase diagram of the antiferromagnetic Ising model on a square lattice with longitudinal and transverse magnetic fields using the quantum Monte Carlo method. For a small but nonzero transverse field, the transition longitudinal field is found to stay nearly constant. By scrutinizing the phase diagram, we have uncovered a narrow region where the system exhibits reentrant transitions between the disordered and antiferromagnetic phases when the transverse field increases. Our phase diagram provides a useful benchmark for quantum simulation with the Rydberg-atom system.

Dynamics of correlation spreading in low-dimensional transverse-field Ising models

“…Both ferromagnetic and antiferromagnetic models are equivalent under appropriate unitary transformations for bipartite lattices. The ground state is ordered (disordered) for Γ < Γ c (Γ > Γ c ), where Γ c is the transition point given as Γ c /J = 1/2 [40] in 1D and Γ c /J ≈ 1.522 [17,41,42] in 2D. Hereafter we take J as the unit of energy.…”

“…As long as we consider a quench to a strong transverse field so that the transverse magnetization is large enough ( S x i ≈ 1/2), this approach should be a good approximation. We specifically study the parameter region Γ ∈ (Γ classical c , ∞), where the classical transition point obtained by the mean-field approximation [17,105,106] is Γ classical c = JD with D being the spatial dimension. We review the derivation of the longitudinal correlation functions [59] and then calculate the transverse correlation functions.…”

“…Field dependence of the group velocity along the horizontal axis estimated from the dispersion relation obtained by the LSWA and the series expansion up to fourth order [107][108][109] in 2D. The group velocity is represented by the solid (dotted) lines above (below) the critical transverse field Γc/J ≈ 1.522 [17,41,42]. Both velocities increase with decreasing the transverse field.…”

“…Such experiments have also stimulated theoretical research on fundamental quantum many-body systems. For instance, the ground-state phase diagrams of the transverse-field Ising model and those of its strong Ising interaction limit, the PXP model, have been intensively examined using the quantum Monte Carlo method [16][17][18][19].…”

Reentrant phenomenon in the decorated ising model

“…When bulk materials and thin films degrade to nanoisland structures, periodic boundary conditions are absent, and more atoms are exposed on the surface, leading to the emergence of interesting phase transition behaviors, such as multiple critical points and multiple phases [1][2][3][4][5][6][7]. Many modern technologies utilize these complex phase transition behaviors, such as magnetic storage and high-temperature superconducting materials.…”