For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of the density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-type correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase have been revealed.
For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of the density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-type correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase have been revealed.
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.
Entanglement and violation of Bell inequalities are aspects of quantum nonlocality that have been often confused in the past. It is now known that this equivalence is only true for pure states. Even though almost all the studies of quantum correlations at quantum phase transitions deal only with entanglement, we here argue that Bell inequalities can also reveal a general quantum phase transition. This is also shown for a particular case of two spin-21 particles in an infinite one-dimensional chain described by the XXZ model. In this case, the Bell inequality is able to signal not only the first-order phase transition, but also the infinite-order Kosterlitz-Thouless quantum phase transition, which cannot be revealed either by the energy of the system nor by the bipartite entanglement. We also show that although the nearest-neighbor spins are entangled, they, unexpectedly, never violate the Bell inequality. This indicates that the type of entanglement which is relevant for quantum phase transition is not trivial, i.e., it cannot be revealed by the Bell inequality.
We design a Bell inequality that is violated by correlations obtained from the ground states of an XXZ spin-1 chain with on-site anisotropies at the region of phase transition. In order to detect such correlations in spin-1 systems we exploit the formalism of the generalized Bell inequality via the use of multipartite and high-order correlations. We observe a sharp violation in the vicinity of the quantum phase transition between the so-called large-D and AFM phase. Interestingly, the violation of our Bell inequality is manifested by the change in the XXZ spin-1 chain ground state to a Greenberger-Horne-Zeilinger-like state in the critical region. Our results provide a characterization of quantum phase transition via the violation of Bell-type constraint by correlations in the XXZ spin-1 chain with multibody correlations and high-order measurements.
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-12 one-dimensional spin-chain models, viz., the Ising and anisotropic XY models in a transverse field, and the XXZ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system’s single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in detecting and characterizing first-, second- and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method’s ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function’s utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be readily analyzed.
We investigate thermal and non-thermal quantum correlations in the one-dimensional spin-1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory-such as generalized concurrence, negativity, and various measures of quantum, classical, and total correlations in bipartite states-we demonstrate that these measures effectively identify quantum phase transitions (QPTs) at critical points. Our negativity analysis reveals nearly identical results at zero or very low temperatures. Importantly, we find that partial concurrence, defined with the reduced density matrix [Formula: see text], detects more quantum critical points than total concurrence. Additionally, we argue that spin chains with an odd number of spins are more effective than those with an even number in identifying QPTs.
Abstract Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge c=1/2 c = 1 / 2 , which terminates at a critical end-point where c=7/10 c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find β=1/8 β = 1 / 8 (1/24), ν=1 ν = 1 (5/9), and η=1/4 η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.