Ground-state properties of ferrimagnetic XXZ chains with alternating spins S A and S B with nearest-neighbor exchange interaction are discussed based upon the results for finite-size systems obtained mainly by the exact diagonalization method and partly by the density matrix renormalization group method. For -1<Δ<1, where Δ is the parameter of anisotropy of the interactions, the ground state is unique or doubly degenerate and gapless. When Δ=1, the ground state of 2 N sites is the state with total spin N | S A - S B |, and has nonvanishing Néel long-range order parameter. For Δ>1, the ground state is doubly degenerate Néel long-range ordered state with a finite energy gap.
The ground-state phase diagram of
S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-
D, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-
21 antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with
2N spins is ferrimagnetic with the total spin
SG=N∕2 for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin
S=SG+1 sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin
S=SG+1 is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.
The ground-state phase diagram of frustrated S=1 XXZ spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied using the infinite-system density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ_l = S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for Δ< 0.95, where Δis an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.
We use the density matrix renormalization group (DMRG) method to study the ground and low-lying excited states of three kinds of uniform and dimerized alternating spin chain. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of these systems. We consider a 2N-site system with spins and alternating from site to site and interacting via a Heisenberg antiferromagnetic exchange. The three systems studied correspond to being equal to and ; all of them have very similar properties. The ground state is found to be ferrimagnetic with total spin . We find that there is a gapless excitation to a state with spin , and a gapped excitation to a state with spin . The DMRG analysis shows that the chain is susceptible to a conditional spin - Peierls instability. Furthermore, our studies of the magnetization, magnetic susceptibility and specific heat show strong magnetic field dependences. The product shows a minimum as a function of temperature T at low magnetic fields; the minimum vanishes at high magnetic fields. This low-field behaviour is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature, and the height of the maximum increases sharply at high magnetic fields. Although all three systems show qualitatively similar behaviour, there are some notable quantitative differences between the systems in which the site spin difference, , is large and small respectively.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins
S1>S2, using
1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
We report spin wave and density-matrix renormalization-group (DMRG) studies of the ground and low-lying excited states of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of the system. The ground state of a 2N spin system with spin-1 and spin- alternating from site to site and interacting via an antiferromagnetic exchange is found to be ferrimagnetic with total spin
sG=N/2 from both DMRG and spin wave analysis. Both the studies also show that there is a gapless excitation to a state with spin
sG-1 and a gapped excitation to a state with spin
sG+1. Surprisingly, the correlation length in the ground state is found to be very small from both the studies for this gapless system. For this very reason, we show that the ground state can be described by a variational ansatz of the product type. DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls' instability. The DMRG studies of magnetization, magnetic susceptibility (\ensuremath{\chi}), and specific heat show strong magnetic-field dependence. The product \ensuremath{\chi}T shows a minimum as a function of temperature (T) at low-magnetic fields and the minimum vanishes at high-magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature and the height of the maximum increases sharply at high-magnetic fields. It is hoped that these studies will motivate experimental studies at high-magnetic fields.