= 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.
= 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 interplay between competing interactions in low-dimensional quantum many-body systems gives rise to a wide variety of quantum phases and critical phenomena. Motivated by this scenario, we investigate the quantum phase diagram of the mixed-spin 1 2 , 1 antiferromagnetic Heisenberg chain with modulated single-ion anisotropy by means of the density matrix renormalization group (DMRG) method. The resulting phase diagram comprises four distinct quantum phases: three gapped phases, namely the 1 / 3 magnetization plateau, the trivial nonmagnetic (TnM) phase, and the topological valence-bond-solid (TVBS) phase, together with a gapless Luttinger liquid (LL) phase. The different phases are characterized through the analysis of magnetization, spin correlation functions, nonlocal order parameters, and entanglement-based observables. The TVBS phase is identified by the presence of exponentially localized edge states, finite values of the nonlocal string order parameter and twist operator, and the characteristic degeneracy pattern of the entanglement spectrum. The boundaries of the LL phase are determined from the transverse spin correlation function and the corresponding Luttinger parameter, revealing two Kosterlitz–Thouless transition lines characterized by the critical value K c = 2.0 , in agreement with finite-size scaling analyses of the spin gap. In addition, we identify a Gaussian critical line associated with the topological quantum phase transition separating the TVBS and TnM phases. By employing the tangential finite-size scaling approach, we accurately determine this critical line by extracting the correlation-length critical exponent ν and the conformal field theory central charge c . Our results demonstrate that the competition between exchange interactions and modulated single-ion anisotropy gives rise to a rich interplay between topology, quantum criticality, and magnetic ordering, highlighting the fundamental role of these interactions in determining the ground-state properties of low-dimensional quantum spin systems.
We investigate the phase diagram of a quantum mixed-spin (1/2,1/2,1,1) Heisenberg tetramer chain featuring bond-alternating antiferromagnetic nearest-neighbor exchange interactions and single-ion anisotropy. This model exhibits a rich phase structure comprising three gapped phases: the antiferromagnetic, topological valence-bond-solid (TVBS), and the trivial nonmagnetic phases (TnM). We identify a multicritical Wess-Zumino-Witten SU(2)1 point where two Ising critical lines merge, forming a higher-symmetry point that realizes conformal embedding on the lattice. Beyond this multicritical point, a Gaussian critical line emerges, determining the boundary between the TVBS and the TnM phases. Utilizing the tangential finite-size scaling method, we demonstrate the precision with which critical points and correlation length critical exponents can be extracted along this Gaussian line. Our results reveal rich critical phenomena induced by the interplay of bond-alternating exchange and anisotropic single-ion interactions in quantum many-body systems.
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.
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.
Density-matrix renormalization group calculations are used to determine the ground-state phase diagram of the mixed spin-(1/2, 5/2, 1/2) Heisenberg chain whose backbone consists of regularly alternating s=1/2 and S=5/2 spins, the latter of which are coupled to additional s=1/2 spins providing lateral branching. The proposed magnetic structure aims to describe the main characteristics of the heterotrimetallic coordination polymer $[{\mathrm{Cu}}^{\mathrm{II}}{\mathrm{Mn}}^{\mathrm{II}}({\mathrm{L}}^{1})][{\mathrm{Fe}}^{\mathrm{III}}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{ClO}}_{4}\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{H}}_{2}\mathrm{O}$. The full ground-state phase diagram in the parameter space exchange anisotropy versus magnetic field unveils special critical points, at which the intermediate magnetization plateaus emergent at 3/7 and 5/7 of the saturation magnetization vanish. A detailed description of the zero-temperature magnetization process and pair entanglement entropy is accomplished with the aim to distinguish the main coupling regimes. A scaling analysis is performed to accurately locate Kosterlitz-Thouless and Gaussian critical points. In particular, we introduce a new finite-size scaling protocol to properly extract the critical parameters from the size dependence of the magnetic-field range corresponding to the magnetization plateau in the close vicinity of the Gaussian point at which two gapped phases meet.
We study the frustrated and dimerized ferromagnetic-antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{'}}\text{\ensuremath{-}}{J}_{2}$ chain using the density-matrix renormalization group method. Based on numerical calculations of the second derivative of energy, spin gap, spin-spin correlations, string order parameter (SOP), and entanglement spectrum (ES), we obtain the ground-state phase diagram for a wide range of ${J}_{1}^{\ensuremath{'}}/{J}_{1}$ and J2/∣J1∣ values. This phase diagram reveals a ferromagnetic phase and two distinct valence bond solid (VBS) phases. The first VBS phase, referred to as D3-VBS, is typified by the formation of valence bonds between third-neighbor spin-1/2's, persisting as a continuation from the ${J}_{1}^{\ensuremath{'}}/{J}_{1}=1$ limit. Alternatively, the second VBS phase, referred to as mixed-VBS, exhibits a coexistence of both second- and third-neighbor valence bonds, interpreted as a continuation from the ${J}_{1}^{\ensuremath{'}}/{J}_{1}=0$ case. Remarkably, both VBS states are identified as being of Haldane type, marked by a finite SOP and twofold ES degeneracy. Unexpectedly, our analysis uncovers a significant enhancement of the valence bond stability at the boundary of the two VBS phases. This study provides an empirical demonstration of a nontrivial quantum phase transition between different topological VBS states in spin-1/2 chains. Moreover, we find that the ground state of the relevant quasi-one-dimensional material LiCuSbO4 is classified as the D3-VBS state. Collectively, these results mark a substantial stride forward in our comprehension of quantum phase transitions and topological states.