One-dimensional anisotropic Heisenberg model in the transverse magnetic field

Abstract

One dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces the gap in the spectrum of the model with easy-plain anisotropy. Using conformal invariance the field dependence of the gap at small fields is found. The ground state phase diagram is obtained. It contains four phases with different types of the long range order (LRO) and a disordered one. These phases are separated by critical lines, where the gap and the long range order vanish. Using scaling estimations and a mean-field approach as well as numerical calculations in the vicinity of all critical lines we found the critical exponents of the gap and the LRO. It is shown that transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model. 75.10.Jm -Quantized spin models

Dynamical correlations of the spin-12Heisenberg XXZ chain in a staggered field

“…In critical systems with exchange anisotropy such as the spin-1/2 Heisenberg XXZ chain a second mechanism for inducing a gap by application of a uniform magnetic field exists. While application of a field perpendicular to the easy plane leaves the system critical, applying a field in the easy plane leads to the formation of a spectral gap [23][24][25][26]31,32 .…”

Gapless line for the anisotropic Heisenbergspin−12chain in a magnetic field and the quantum axial next-nearest-neighbor Ising chain

“…The operators in Eqs. (6) are related to each other through the operator product expansion; the RG equations for their coefficients will therefore be coupled to each other [9]. In our model, this can be derived as follows.…”

“…In phase B, m y is non-zero, and the Z 2 symmetry is broken. The scaling of m y with the perturbation δa can be found as follows [6]. At a = h = 0, the leading term in the long-distance equal-time correlation function of S y is given by…”

“…Recently, the XXZ chain in a transverse magnetic field [6] and the quantum ANNNI model [7] have been studied using bosonization. In this paper, we will study the anisotropic XY Z model in a magnetic field pointing along the x-axis.…”

Entanglement in quantum-critical spin systems

“…1 shows the ground-state phase diagram of the one-dimensional XYX model in the ∆ y − h plane. The quantum Monte Carlo data confirm that the transition belongs to the universality class of the 1D transverse-field Ising model (or of the 2D Ising model) 9 , and are in very good agreement with predictions from a mean-field treatment of the Hamiltonian 9 . On the right panel of Fig.…”