Abstract We investigate the efficacy of shared purity, a measure of quantum correlation that is independent of the separability-entanglement paradigm, as a quantum phase transition indicator in comparison with concurrence, a bipartite entanglement measure. The order parameters are investigated for thermal states and pseudo-thermal states, of the systems considered. In the case of the one-dimensional J 1 − J 2 Heisenberg quantum spin model and the one-dimensional transverse-field quantum Ising model, shared purity turns out to be as effective as concurrence in indicating quantum phase transitions. In the two-dimensional J 1 − J 2 Heisenberg quantum spin model, shared purity indicates the two quantum phase transitions present in the model, while concurrence detects only one of them. Moreover, we find diverging finite-size scaling exponents for the order parameters near the transitions in odd- and even-sized systems governed by the one-dimensional J 1 − J 2 model, as had previously been reported for quantum spins on odd- and even-legged ladders. It is plausible that the divergence is related to a Möbius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient.
Abstract We compute concurrence, a measure of bipartite entanglement, of the first excited state of the 1-D Heisenberg frustrated J 1 - J 2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength α = J 2 / J 1 ≈ 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 8 sites to 16 sites, and the value of α at which the change in entanglement is observed, asymptotically tends to a value α c ≈ 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 1-D Heisenberg frustrated J 1 - J 2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like 2-D Heisenberg J 1 - J 2 model and Shastry-Sutherland model and find similar indications of quantum phase transitions.
We compute concurrence, a measure of bipartite entanglement, of the first excited state of the
1-D Heisenberg frustrated
J1-
J2 spin-chain and observe a sudden change in the entanglement of the eigen state near the coupling strength
α=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
8 sites to
16 sites, and the value of
α at which the change in entanglement is observed asymptotically tends to a value
αc≈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
1-D Heisenberg frustrated
J1-
J2 spin-chain. Furthermore, we measure bipartite entanglement of first excited states for other spin models like
2-D Heisenberg
J1-
J2 model and Shastry-Sutherland model and detect quantum phase transitions.
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 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 We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the J 1 − J 2 Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic J 1 − J 2 chain has a richer phase diagram which is also clearly visible by using the same order parameter.
We derive an analytic correspondence between multipartite concentratable entanglement (CE) and quantum phase transitions in one-dimensional quantum spin systems. We prove that CE shares the same analyticity structure as generalized order parameters, identifies the same quantum phases, and, for Gaussian ground states, is completely determined by the same single-particle correlation matrix. Numerical validation on the transverse-field Ising and generalized cluster-Ising models confirms these analytical predictions for both symmetry-breaking and symmetry-protected topological quantum phase transitions. Since CE can be measured directly using a constant-depth parallelized SWAP-test circuit, our results establish CE as an experimentally accessible, model-independent probe of quantum phase transitions without requiring model-specific order parameters.