We use the bond mean field theory, which is based on the Jordan–Wigner fermionization, to investigate the quantum critical behavior of a system composed of two-coupled Heisenberg Spin-[Formula: see text] two-leg ladders in the presence of an applied magnetic field. By examining the dependence of the ground state on the magnetic field for different coupling constants, we investigate the field-induced quantum criticality. The magnetization exhibits distinct plateaus: a zero magnetization plateau for fields below a threshold value of the field [Formula: see text] and a saturation plateau for fields exceeding a second critical value [Formula: see text]. The spin bond parameters are calculated and found to show a critical behavior at [Formula: see text].
Field-induced quantum (zero temperature) criticality described using parameters that are not associated with a symmetry-breaking long-range order is found in the spin-
21 antiferromagnetic three-leg Heisenberg ladder. These parameters represent the spin bond order, which is a consequence of the probability for spins on adjacent sites to be bound in a singletlike arrangement. They underwent two phase transitions, one at the lower critical field
hc1 and the other at the upper critical field
hc2. The field dependence of these bond parameters and of the magnetization is calculated for several values of the rung coupling in all regimes. This yields the coupling field phase diagram. It is found that the rung coupling must exceed a threshold value for the plateau, at one third of the saturation magnetization, to appear. The results obtained here within the bond mean-field theory compare well with existing numerical data.
The antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals is studied using the Jordan-Wigner transformation and bond-mean-field theory. The inclusion of all three couplings introduces frustration to the system and depending on their relative strengths the ladder can adopt one of three possible magnetically disordered gapped states. The phase diagram found in this mean-field approach is in very good agreement with the one calculated by Weihong et al. [Phys. Rev. B 57, 11439 (1998)] using the Lanczos exact diagonalization method. By analyzing the ground-state energy, we study quantum criticality when the coupling parameters are varied at zero temperature. We study the effect of temperature on the phase boundaries and find that the system shows thermally induced criticality for some values of the rung and diagonal coupling constants. All the phase transitions encountered in this system occur between disordered phases and are all caused by frustration.
The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan–Wigner transformation in dimensions higher than one and the bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities in this system. The present work could constitute a prototype for those systems showing multiple, perhaps sometimes competing, quantum criticalities. We calculate several physical quantities such as magnetization and spin susceptibility as functions of field and temperature.PACS Nos.: 75.10.Jm 73.43.Nq 75.10.Pq 75.10.Dg
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-
1/2 ladder, and a two-legged spin-
1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an
XXZ spin-
1/2 chain in a magnetic field; the second-order terms give corrections to the
XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field
h. In this model,
J represents the traditional antiferromagnetic Heisenberg exchange and
Q is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for
q>qmin, where we have calculated
qmin=92 exactly. For
q>qmin, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for
q>qmin. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain
(J1>0,J2<0), but only if
J2 is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at
T>0. While the expected ``zero-scale-factor'' universality is clearly seen for
q=0 and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for
q closer to
qmin we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at
qmin. In the low-energy theory, one can expect the quartic nonlinearity to vanish at
qmin and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature
T∗(q) between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.