We use entanglement entropy and finite-size scaling methods to investigate the ground-state properties of a spin-1/2 Ising chain with two-spin (J(2)) and four-spin (J(4)) interactions in a transverse magnetic field (B). We concentrate our study on the unexplored critical region B=1 and obtain the phase diagram of the model in the (J(4)-J(2)) plane. The phases found include ferromagnetic (F), antiferromagnetic (AF), as well as more complex phases involving spin configurations with multiple periodicity. The system presents both first- and second-order transitions separated by tricritical points. We find an unusual phase boundary on the semi-infinite segment (J(4)<-1,J(2)=0) separating the F and AF phases.
The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction
J4 is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field
B versus
J4 plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of
B, a ferromagnetic (FM) ordered phase for small
J4, and a dimerized-rung (DR) phase for large negative values of
J4. All phases are separated by quantum phase transition lines meeting at a multicritical point. The critical lines have been obtained by exploring the entanglement entropy. The results show that along the critical lines the central charge is
c=1/2, while at the multicritical point one has
c=1. The scaling dimension of the energy operator is ${X}_{\ensuremath{\epsilon}}=1$, in agreement with the universality class of the critical behavior of the quantum Ising chain. An effective field theory for the multicritical point is also discussed. The FM and the DR order parameters have also been computed and we found a region where the FM and the DR phases coexist.
We study the ground-state properties of a spin-1/2 model on a chain containing four-spin Ising-like interactions in the presence of both transverse and longitudinal magnetic fields. We use entanglement entropy and finite-size scaling methods to obtain the phase diagrams of the model. Our numerical calculations reveal a rich variety of phases and the existence of multicritical points in the system. We identify phases with both ferromagnetic and antiferromagnetic orderings. We also find periodically modulated orderings formed by a cluster of like spins followed by another cluster of opposite like spins. The quantum phases in the model are found to be separated by either first- or second-order transition lines.