= 1 andS=3/2dimers is studied in detail as a function of two considered exchange interactions ascribed to similar and dissimilar spin pairs. At zero magnetic field, the ferrimagnetic mixed spin-(1, 1, 3/2, 3/2) Heisenberg tetramer chain displays, depending on a mutual interplay between two considered exchange interactions, three distinct gapped valence-bond-solid phases separated by gap-closing quantum critical points. Using density-matrix renormalization group calculations we construct the full ground-state phase diagram as a function of the interaction ratio and magnetic field, which exhibits besides three gapped valence-bond-solid phases special Kosterlitz-Thouless and topological quantum critical points. A tangential finite-size scaling analysis is employed to obtain precise estimates of the zero-field valence-bond-solid transitions and unveil their common logarithmic correction to a power-law scaling of the correlation length.
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 have investigated Haldane's conjecture for the S = 2 antiferromagnetic quantum spin chain with nearest-neighbour exchange J . Using a density matrix renormalization group algorithm for chains up to L = 350 spins, we show that the ground state has hidden topological order: the physics of the S = 2 chain can be captured by a valence bond solid description. We also observe effective free spin-1 states at the ends of an open S = 2 chain. We find in the thermodynamic limit a gap Δ = 0.085(5) J and a spin correlation length ξ = 49(1) lattice spacings in the isotropic case. We give the phase diagram in the presence of single-ion and exchange anisotropy, showing how the Haldane phase is squeezed out when the spin S increases.
The successive phase transitions of the Heisenberg spin chain with bond alternation, H = ∑ i =1 L -1 [1-(-1) i δ] S i · S i +1 , for the spin S =3/2 case under the open boundary condition are investigated by the density-matrix renormalization-group method proposed by White. Besides the Heisenberg point, we find that another gapless point exists at δ c = 0.42 ±0.02. This result qualitatively supports the field-theoretical prediction by Affleck and Haldane. However, our estimation of δ c deviates from the field-theoretical prediction, δ c = 2/3. We also find a fourfold degeneracy of the ground state in the region 0 <δ< δ c in the thermodynamic limit. Our results show that the degeneracy is described by the edge excitations, which is essentially similar to the one in the S =1 case. We calculate the string correlation function and find that its behavior is consistent with the valence-bond-solid (VBS) picture.
We revisit the phase diagram of the dimerized XXZ spin-
21 chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic
XY couplings which have a uniform value and
ZZ couplings which have a dimerized form, with strengths
Ja and
Jb on alternate bonds. We find a rich phase diagram in the region of positive
Ja, Jb. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM
0 and IPM
π, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM
0 and IPM
π are separated by a gapless phase transition line given by
0≤Ja=Jb≤1 which is described by a conformal field theory with central charge
c=1. There are two gapless phase transition lines separating IPM
0 from IN and IPM
π from IN; these are described by conformal field theories with
c=21 corresponding to quantum Ising transitions. The
c=1 line bifurcates into the two
c=21 lines at the point
Ja=Jb=1; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM
0 is a topologically trivial phase while IPM
π is a time-reversal symmetry-protected topological phase (SPT) with spin-
21 states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.
We study quantum mixed-spin chains consisting of two integer spins
S1 and two half integer spins
S2 arrayed as ${S}^{1}\ensuremath{-}{S}^{1}\ensuremath{-}{S}^{2}\ensuremath{-}{S}^{2}$ in a unit cell with antiferromagnetic nearest-neighbor couplings
J1 (J2) between the spins of equal (different) magnitudes. By varying the ratio of two competing couplings, $\ensuremath{\alpha}{=J}_{2}{/J}_{1},$ the systems undergo successive quantum phase transitions between different valence-bond-solid (VBS) states accompanied by the vanishing of the energy gap. By a quantum Monte Carlo simulation with an improved loop cluster algorithm, we find one critical point ${\ensuremath{\alpha}}_{c}=0.762(1)$ in a $1\ensuremath{-}1\ensuremath{-}\frac{1}{2}\ensuremath{-}\frac{1}{2}$ chain and two critical points ${\ensuremath{\alpha}}_{c1}=0.479(1)$ and ${\ensuremath{\alpha}}_{c2}=1.318(1)$ in a $1\ensuremath{-}1\ensuremath{-}\frac{3}{2}\ensuremath{-}\frac{3}{2}$ chain, respectively. The calculated expectation values of the Lieb-Shultz-Mattis twist operator show the characteristic features of the single VBS transition in the $1\ensuremath{-}1\ensuremath{-}\frac{1}{2}\ensuremath{-}\frac{1}{2}$ chain and two successive VBS transitions in the $1\ensuremath{-}1\ensuremath{-}\frac{3}{2}\ensuremath{-}\frac{3}{2}$ chain at these critical points.