We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
In this paper, we study quantum phase transitions in both the one- and two-dimensional XXZ models with either spin S = 1/2 or S = 1 by a local entanglement E v . We show that the behaviour of E v is dictated by the low-lying spin excitation spectra of these systems. Therefore, the anomalies of E v imply their critical points. This recalls the well-known fact in optics: the three-dimensional image of one subject can be recovered from a small piece of holograph, which records the interference pattern of the reflected light beams from it. Similarly, we find that the local entanglement, which is rooted in the quantum superposition principle, provides us with a deep insight into the long-range spin correlations in these quantum spin systems.
We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic
J1−J2 Heisenberg model, the one-dimensional XXZ
J1−J2 model, and the two-dimensional
J1−J2 Heisenberg model on a
4×4 square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding
αc(∞)=0.24116, in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding
αc(∞)=0.2681. For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at
αc(4×4)=0.40781 and
0.6208, while the ground-state SRE identifies the second at
0.6230. Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.
We investigate entanglement properties of infinite one- and two-dimensional spin-1/2 quantum Ising and XXZ models. Tensor network methods (TI MPS with single-site update and TEBD for MPS, TERG and CTMRG with “simple update” for PEPS) are used to model the ground states of the studied models. Different entanglement measures, such as the one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are compared with respect to their ability to exhibit “structures” in the phase diagram of the models (e.g., phase transitions). We study the connection between symmetries and the entanglement of ground states and analyze short- and long-range entanglement through the entanglement monogamy.
Through the Jordan—Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called “spin waves”, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.
Entanglement of the ground states in the S = 1/2 XXZ chain, dimerized Heisenberg spin chain, two-leg spin ladders as well as S = 1 anisotropic Haldane chain is analysed using the entanglement entropy between a selected sublattice of spins and the rest of the system. In particular, we reveal that quantum phase transition points/boundaries may be identified based on the analysis on the local extreme of this sublattice entanglement entropy, which is illustrated to be superior over the concurrence scenario and may enable us to explore quantum phase transitions in many other systems including higher dimensional ones.