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Physica Scripta

Generalized concurrence and quantum phase transition in spin-1 Heisenberg model

Hassan Bahmani, G. Najarbashi, Ali Tavana

Published Dec 11, 2019• 8 citations
Publisher

Abstract

Abstract In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.

DOI
10.1088/1402-4896/ab606e

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Abstract In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.
The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear–biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin and particle susceptibilities define the conditions for a high/low-density quantum entanglement and various ordered phases with different spin (particle) concentrations.
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 Using the quantum renormalization group approach, we have investigated the entanglement and critical behavior of an anisotropic XXZ Heisenberg spin chain. The resolution of the quantum renormalization equations yields stable and unstable fixed points, corresponding respectively to the phases and critical point of the system. It is shown that a quantum phase transition exists at a critical anisotropy parameter , separating the Néel phase from the spin-fluid phase. Then, the concurrence between two blocks of sites and the quantum coherence have been calculated and presented for various renormalization group iterations. In the thermodynamic limit, i.e. , for higher renormalization steps, the concurrence and coherence exhibit two different saturated values in the two regions separated by Δ c . The first derivative of concurrence diverges at the critical point as the size of the chain increases, showing nonanalytic behavior. Moreover, the scaling behavior has been examined near the critical point with some universal exponential scaling laws.
The quantum phase transition in the spin-12\frac{1}{2}21​ XX Heisenberg chain model with three-spin interaction is studied. Using the Jordan-Wigner transformation, several thermodynamic, as well as thermal and spin transport quantities of the system are calculated exactly. It is shown that the three-spin interaction influences the calculated quantities and leads to characteristic features of the quantum phase transition. The effects of a finite magnetic field on the magnetic moment and magnetic susceptibility are also discussed.
Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.