The ground-state phase diagram of the one-dimensional $\mathrm{XXZ}$ model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.The ground-state phase diagram of the one-dimensional $\mathrm{XXZ}$ model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.

arXiv:cond-mat/0112145Physical review. B, Condensed matterApr 18, 200285 citations

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников +1 more

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.

arXiv:cond-mat/0204590Journal of Experimental and Theoretical PhysicsSep 1, 200285 citations

The ground state of the xy model in a transverse magnetic field

Oscar Bolina, J. Rodrigo Parreira

Canadian Journal of PhysicsJan 1, 19980 citations

On ground states of the one-dimensional ferromagnetic XXZ model

Taku Matsui

Letters in Mathematical PhysicsAug 1, 199628 citations

The ground-state phase diagram of the one-dimensional

\mathrm{XXZ}

model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.