By using the coupled cluster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the alternating chain is a gapped dimerized state when the parameter α exceeds a critical point α c . The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field when α > α c . In addition to the m = 0 plateau state, the results of density matrix renormalization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if α > 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.
By using the coupled cluster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the alternating chain is a gapped dimerized state when the parameter α exceeds a critical point α c . The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field when α > α c . In addition to the m = 0 plateau state, the results of density matrix renormalization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if α > 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.
By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J′ quantum Heisenberg chains with spin S=1/2, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when J is antiferromagnetic and J′ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when J is ferromagnetic and J′ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.
In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.
By using the coupled cluster method, the numerical exact diagonalization method, and the numerical density matrix renormalization group method, we investigated the properties of the one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions. In the classical limit, the ground state is in the collinear Neel state if a<1/2, while for a>1/2, there is an noncollinear canted state. For the quantum case, we found that, although the classical Neel state is absent, the canted state exists if the frustration parameter a exceeds a critical point ac1. The precise critical point ac1 can be determined by using the coupled cluster method and the numerical exact diagonalization method separately. The results of the coupled cluster method and the exact diagonalization method both disclose that the type of phase transition occurring at ac1 changes from a classical second-order transition to a quantum first-order transition due to quantum fluctuation. Although there is another critical point ac2 in a finite system at which the ground state evolves from the canted state to the collinear Neel plus ferromagnetic state, that state is absent because ac2 tends to infinity in the thermodynamic limit.