Coexistence of spontaneous dimerization and magnetic order in a transverse-field Ising ladder with four-spin interactions.

Abstract

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 = 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.