We propose a one-dimensional quantum Heienberg spin-2 chain, which exhibits two topologically distinct valence bond solid states in two different solvable limits. We then construct the phase diagram and study the quantum phase transition between these two states using infinite time evolving block decimation algorithms. From the scaling relation between the entanglement entropy and the correlation length, we determine that the central charge for the underlying critical conformal field theory is around two.
We propose a one-dimensional quantum Heienberg spin-2 chain, which exhibits two topologically distinct valence bond solid states in two different solvable limits. We then construct the phase diagram and study the quantum phase transition between these two states using infinite time evolving block decimation algorithms. From the scaling relation between the entanglement entropy and the correlation length, we determine that the central charge for the underlying critical conformal field theory is around two.
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.
Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the infinite time evolving block decimation method. Directly computing two distinct types of finite string correlations for very large lattice distances, in contrast to an extrapolated extreme value for finite size chains, reveals two topologically ordered phases. As the bond alternation varies, a topological quantum phase transition with continuously variable critical exponents along the phase boundary occurs between the two Haldane phases for a Dzyaloshinskii-Moriya interaction stronger than the Ising interaction while a topological quantum crossover between them happens through an intermediate antiferromagentic phase demonstrated with the quantum fidelity for a Dzyaloshinskii-Moriya interaction weaker than the Ising interaction. The critical exponents of the order parameters and the central charges from the entanglement entropy quantify the universality classes of the phase transition points. Anisotropic Heisenberg types of spin chains with bond alternations are finally discussed to share the same criticality.
The characterization of the quantum phase transition in a lowdimensional system has attracted a considerable amount of attention in quantum manybody systems. As one of the fundamental models in quantum magnetism, spin-1 models have richer phase diagrams and show more complex physical phenomena. In the spin-1 antiferromagnetic XXZ model, the Haldane phase and the Nel phase are the gapped topologic phases which cannot be characterized by the local order parameters. To characterize the nature in such phases, one has to calculate the non-local long range order parameters. Normally, the non-local order parameter in the topological phase is obtained from the extrapolation of finite-sized system in numerical study. However, it is difficult to extract the critical exponents with such an extrapolated non-local order parameter due to the numerical accuracy. In a recently developed tensor network representation, i.e., the infinite matrix product state (iMPS) algorithm, it was shown that the non-local order can be directly calculated from a very large lattice distance in an infinite-sized system rather than an extrapolated order parameter in a finite-sized system. Therefore, it is worthwhile using this convenient technique to study the non-local orders in the topological phases and characterize the quantum criticalities in the topological quantum phase transitions. In this paper, by utilizing the infinite matrix product state algorithm based on the tensor network representation and infinite time evolving block decimation method, the quantum entanglement, fidelity, and critical exponents of the topological phase transition are investigated in the one-dimensional infinite spin-1 bond-alternating XXZ Heisenberg model. It is found that there is always a local dimerization order existing in the whole parameter range when the bond-alternative strength parameter changes from 0 to 1. Also, due to the effect of the bond-alternating, there appears a quantum phase transition from the long-rang ordering topological Nel phase to the local ordering dimerization phase. The von Neumann entropy, fidelity per lattice site, and order parameters all give the same phase transition point at c = 0.638. To identify the type of quantum phase transition, the central charge c 0.5 is extracted from the ground state von Neumann entropy and the finite correlation length, which indicates that the phase transition belongs to the two-dimensional Ising universality class. Furthermore, it is found that the Nel order and the susceptibility of Nel order have power-law relations to |-c|. From the numerical fitting of the Nel order and its susceptibility, we obtain the characteristic critical exponents ' = 0.236 and ' = 0.838. It indicates that such critical exponents from our method characterize the nature of the quantum phase transition. Our critical exponents from the iMPS method can provide guidance for studying the properties of the phase transition in quantum spin systems.
By the infinite time-evolving block decimation method, the ground state properties of the S=1 Heisenberg–Ising alternating chain have been investigated in the thermodynamic limit. A ground-state phase diagram, which includes three different phases, i.e., an antiferromagnetic strip phase, a dimer phase, and an antiferromagnetic phase, is obtained. A modified definition of the string order is adopted to describe the dimer phase, and it is found to have nonzero antiferromagnetic topological string order. The quantum phase transitions (QPTs) in such a model can be well described by the singularities of bipartite entanglement and fidelity bifurcations, and two second-order QPTs points are determined to be at JI≃±0.66983. The central charges at both QPTs points are determined to be ∼1/2. Therefore, both QPTs belong to the Ising universality class with central charges c=c‾=1/2.
We study quantum phase transitions between competing orders in one-dimensional spin systems. We focus on systems that can be mapped to a dual-field double sine-Gordon model as a bosonized effective field theory. This model contains two pinning potential terms of dual fields that stabilize competing orders and allows different types of quantum phase transition to happen between two ordered phases. At the transition point, elementary excitations change from the topological soliton of one of the dual fields to that of the other, thus it can be characterized as a topological transition. We compute the dynamical susceptibilities and the entanglement entropy, which gives us access to the central charge, of the system using a numerical technique of infinite time-evolving block decimation and characterize the universality class of the transition as well as the nature of the order in each phase. The possible realizations of such transitions in experimental systems both for condensed matter and cold atomic gases are also discussed.
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.