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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2202.03339 |
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| _version_ | 1866910341012652032 |
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| author | Biswas, George Biswas, Anindya Sen, Ujjwal |
| author_facet | Biswas, George Biswas, Anindya Sen, Ujjwal |
| contents | 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, pseudo-thermal states and more, 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 M{ö}bius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03339 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions Biswas, George Biswas, Anindya Sen, Ujjwal Quantum Physics 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, pseudo-thermal states and more, 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 M{ö}bius strip-like boundary condition required for odd-sized systems, while for even-sized systems, the usual periodic boundary condition is sufficient. |
| title | Shared purity and concurrence of a mixture of ground and low-lying excited states as indicators of quantum phase transitions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2202.03339 |