Abstract The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated. It is shown that the phase boundaries of the three phases in the model can be determined precisely, in line with the precision of its ground-state energy. Numerical calculations using the regularized time-evolving block decimation (rTEBD) algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits. Moreover, we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure, which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.
Abstract The ground-state phase diagram and nonlocal order parameters of an infinite spin tetrahedron chain with inhomogeneous exchange couplings are investigated. It is shown that the phase boundaries of the three phases in the model can be determined precisely, in line with the precision of its ground-state energy. Numerical calculations using the regularized time-evolving block decimation (rTEBD) algorithm yield the locations of the two quantum critical points with an accuracy about 10 digits. Moreover, we explain how to calculate the parity-associated string order for the output wave function obtained through the rTEBD procedure, which not only reveals the presence of long-range correlations but also identifies the symmetry-protected topological order within the intermediate phase of the model.
Quantum entanglement and non-local string order are investigated in the one-dimensional spin-1 bond-alternating Heisenberg model for quantum phase transitions. Employing the infinite matrix product state representation, ground state wavefunctions are numerically obtained by using the infinite time evolving block decimation approach in the infinite lattice system. From a bipartite entanglement measure, i.e., von Neumann entropy, a quantum phase transition point corresponding to the singular point of the von Neumann entropy between the Haldane phase and the dimerised phase is found to be δc=0.26. In addition, based on the infinite matrix product state algorithm, the non-local string order is calculated. The result shows that the non-local string order is able to characterize the topological phase transitions.
We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, in contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical exponent $\ensuremath{\beta}$ from the long-range string orders is obtained as $\ensuremath{\beta}=1/12$ and the central charge at the critical point is obtained as $c\ensuremath{\simeq}1$, which shows that the topological phase transition belongs to the Gaussian universality class. In addition, it is shown that, for the topological quantum phase transition, the phase boundary can be captured by the singular behavior of the von Neumann entropy and the pinch point of the fidelity per site.
ABSTRACT The ground‐state phase transition for the spin‐1/2 Heisenberg chain with ‐direction dimerized anisotropy is investigated by exploiting the infinite time‐evolving block decimation algorithm. Phase boundaries are identified by examining the von Neumann entropy, entanglement spectrum, and several of fidelity indicators. The phase diagram features the existence of a tri‐critical point, which signifies the complete convergence of the transition boundaries separating the Odd‐Haldane, Even‐Haldane, and Néel phases. Specifically, the high‐precision fit of the Tomonaga–Luttinger liquid parameter provides evidence for a Tomonaga–Luttinger liquid phase line which splits the Odd‐Haldane and Even‐Haldane phases. Along this critical line, it is found that the critical exponent exhibits a variation with the bond dimerization strength, which is according to a power‐law scaling. This provides a crucial theoretical framework for analyzing critical behaviors associated with topological phase transitions in quantum many‐body systems. From the odd and even string order parameters and the non‐local Néel order parameter, the Haldane phases and the Néel phase are characterized. Furthermore, the central charge and critical exponent are identified by performing a scaling analysis of finite correlation length and order parameters, indicating that the phase transition between the Haldane phases and Néel phase belongs to the classical Ising universality class, as well as a Gaussian phase transition between two types of Haldane phases.
We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.
In this study we investigate the ground-state phase diagram of the quantum spin-1/2 anisotropic XZ chain using the infinite time-evolving block decimation algorithm. The model exhibits four distinct phases: FM_{x}, FM_{z}, AFM_{z}, and PM. In terms of the transverse magnetic field h and anisotropy parameter J, our analysis focuses on the lines h=0 and 0.5 with J≥0, where different types of quantum phase transitions (QPTs) occur. We compute the bifurcation behavior of the ground-state fidelity per lattice site. On the line h=0, continuous behavior at the bifurcation point identifies a continuous QPT between the ordered FM_{x} and FM_{z} phases at the critical point J_{c1}, with bifurcations on both sides reflecting Z_{2} symmetry breaking in both phases. On the line h=0.5, a continuous bifurcation indicates a QPT between the ordered FM_{x} and disordered PM phases at J_{c2}, with bifurcation occurring only on one side, corresponding to Z_{2} symmetry breaking in a single phase. We further compute the ground-state fidelity susceptibility per lattice site. When the ground state is obtained from random initial states, the fidelity susceptibility exhibits oscillatory behavior in the symmetry-broken phase, providing a clear signature of ground-state degeneracy. These fidelity-based measures serve as effective tools for identifying critical points and characterizing the nature of symmetry breaking. To complement these results, we evaluate the two-spin Wigner-Yanase skew information and local quantum uncertainty (LQU) as indicators of quantum correlations. While both detect QPTs, we find that not all nonanalytic features in the LQU correspond to genuine phase transitions. A critical behavior analysis is carried out at J_{c1} and J_{c2} to extract the critical exponents η^{I}, η^{C}, η^{x}, and η^{z}, associated with mutual information I(r), classical correlation C(r), and spin-spin correlations 〈σ_{i}^{x}σ_{j}^{x}〉, 〈σ_{i}^{z}σ_{j}^{z}〉. Our results demonstrate that η^{I}=η^{C} and η^{x/z}=η^{α}/2 for α=I,C, consistent with known universal scaling relations. We also extract the order parameter exponent β, correlation length exponent ν, dynamic exponent z, and the central charge c. A transition at J_{c1} between the FM_{x} and FM_{z} phases is identified as a Gaussian transition with central charge c=1, involving the breaking of two Z_{2} symmetries and lying beyond the conventional Landau-Ginzburg-Wilson symmetry-breaking paradigm. The transition at J_{c2} between the FM_{x} and PM phases belongs to the quantum Ising universality class, characterized by c=1/2 and breaking of a single Z_{2} symmetry.
Ground-State Phase Diagram of the Spin-21-21-1-1 Chain
We investigate the ground-state phase diagram of the quantum mixed spin chain in which two S=21 and two S =1 spins are arranged alternatively and isotropic exchange interactions between nearest-neighboring pairs of spins are assumed. Guided by our previous results [J. Phys. Soc. Jpn. 67 (1998) 1000] for a few limiting cases of the exchange interactions, we carry out a density-matrix renormalization-group calculation to determine the ground-state phase diagram in detail. From the gapless points of the singlet-triplet energy gap, five boundary lines are determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We also present a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we classify the VBS pictures and interpret the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We investigate the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we confirm the validity of the characterization.