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Physics Letters A

Indicators of quantum phase transitions in the one-dimensional J1-J2 Heisenberg model: Global quantum discord and multipartite nonlocality analysis

Hongying Liu, Jia Bao, Haoran Yan, Bin Guo

Published Oct 3, 2024• 2 citations
Publisher
DOI
10.1016/j.physleta.2024.129955

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We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 111-D Heisenberg frustrated J1J_1J1​-J2J_2J2​ spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α=J2/J1≈0.241\alpha=J_2/J_1\approx0.241α=J2​/J1​≈0.241, where a quantum phase transition from spin-fluid phase to dimer phase has been previously reported. We numerically observe this phenomena for spin-chain with 888 sites to 161616 sites, and the value of α\alphaα at which the change in entanglement is observed asymptotically tends to a value αc≈0.24116\alpha_c\approx0.24116αc​≈0.24116. We have calculated the finite-size scaling exponents for spin chains with even and odd spins. It may be noted that bipartite as well as multipartite entanglement measures applied on the ground state of the system, fail to detect any quantum phase transition from the gapless to the gapped phase in the 111-D Heisenberg frustrated J1J_1J1​-J2J_2J2​ spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 222-D Heisenberg J1J_1J1​-J2J_2J2​ model and Shastry-Sutherland model and detect quantum phase transitions.
We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behavior of the entanglement entropy characterizing the unfrustrated Heisenberg chain above ${J}_{2}\ensuremath{\approx}0.25$. This feature can be used as an indicator of the dimer phase transition occurring in this model. Additionally, we also consider entanglement at the MG point J2=0.5J1{J}_{2}=0.5{J}_{1}J2​=0.5J1​.
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−J2J_1-J_2J1​−J2​ Heisenberg model, the one-dimensional XXZ J1−J2J_1-J_2J1​−J2​ model, and the two-dimensional J1−J2J_1-J_2J1​−J2​ Heisenberg model on a 4×44\times44×4 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(∞)=0.24116α_c(\infty)=0.24116αc​(∞)=0.24116, in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding αc(∞)=0.2681α_c(\infty)=0.2681αc​(∞)=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)=0.40781α_c(4\times4)=0.40781αc​(4×4)=0.40781 and 0.62080.62080.6208, while the ground-state SRE identifies the second at 0.62300.62300.6230. 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.