In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single
XXZ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of
N weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number
N of cylindrically coupled chains numerically. For
N=3 we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.
We study numerically the formation of magnetization plateaux with the Lanczos method in two-leg ladders with mixed spins of magnitudes
(S1,S2)=(1,1/2) located at alternating positions along the ladder and with dimerization $\ensuremath{\gamma}.$ For interchain coupling ${J}^{\ensuremath{'}}>0$ and $\ensuremath{\gamma}=0,$ we find normalized plateaux at
m=1/3 starting at zero field and
m=1 (saturation), while when $\ensuremath{\gamma}\ensuremath{\ne}0$ is columnar, another extra plateau at
m=2/3 shows up. For ${J}^{\ensuremath{'}}<0,$ when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find no plateau while for $\ensuremath{\gamma}>{\ensuremath{\gamma}}_{c}{(J}^{\ensuremath{'}})$ we find four plateaux at
m=0,1/3,2/3,1. We also apply several approximate analytical methods (spin-wave theory, low-energy effective Hamiltonians, and bosonization) to understand these findings and to conjecture the behavior of ferrimagnetic ladders with a larger number of legs.
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].
We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the
4kF density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio
J∕t: we found strong anomalies at low
J∕t only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and
1∕2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a
4kF charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.