Transição de fase quântica no modelo J1 − J '1 − J2 antiferromagnético

Abstract

Over the last 20 years or so much theoretical effort has been expended on the two-dimensional quantum spin-1/2 Heisenberg model with competing nearestneighbor (nn) and next-nearest-neighbor(nnn) antiferromagnetic exchange interactions on square lattice (the ideal J1 − J2 model). The ideal J1 − J2 model consists of a quantum spin-1/2 Heisenberg Hamiltonian with nn interaction J1 running along the side of the diagonal the square lattice and nnn interactions J2 running the diagonal the square lattice. The two interactions (J1 and J2) are equivalent along of all direction. The ground-state phase diagram reveals two ordered phases antiferromagnetc-AF and collinear-CAF for = J2 J1< 1c and > 2c, respectively, and an intermediate quantum paramagnetic (spin-liquid) phase without magnetic long-range order in the region 1c < < 2c. In this work, we will consider the inequivalence nn couplings J1 and J01 = J1 in the two orthogonal spatial lattice dimensions with all the two orthogonal spatial dimensions with all the nnn bonds across the diagonals to have the same strength J2(J1 −J01 −J1 model). This spatial anisotropy tends to narrow the critical region and to destroy it completedy at a certain value of the interchain parameter . The Hamiltonian is solved by effective field theory (EFT) in cluster with two spins. We propose a functional for the free energy to obtain the phase diagram in the ( , ) plane. We found a result that there exists a quantum triple point (QTP) with coordinate at ( t 0.50, t 0.52) below which there is a first-order phase transition between the AF and CAF phases, while above this QTP are these two ordered phases separated by the intermediate magnetically disordered phase. The transition between the AF and intermediate phase is of second-order, while between the intermediate and CAF phases is of first-order.