We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.

Journal of the Korean Physical SocietySep 1, 20173 citations

Numerical Studies of Entanglement Properties in One- and Two-Dimensional Quantum Ising and XXZ Models

Physikalisch-Technische Bundesanstalt (Bundesallee 100, 38116 Braunchweig, Germany), Briiissuurs Braiorr-Orrs, Michael Weyrauch +2 more

We investigate entanglement properties of infinite one- and two-dimensional spin-1/2 quantum Ising and XXZ models. Tensor network methods (TI MPS with single-site update and TEBD for MPS, TERG and CTMRG with “simple update” for PEPS) are used to model the ground states of the studied models. Different entanglement measures, such as the one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are compared with respect to their ability to exhibit “structures” in the phase diagram of the models (e.g., phase transitions). We study the connection between symmetries and the entanglement of ground states and analyze short- and long-range entanglement through the entanglement monogamy.We investigate entanglement properties of infinite one- and two-dimensional spin-1/2 quantum Ising and XXZ models. Tensor network methods (TI MPS with single-site update and TEBD for MPS, TERG and CTMRG with “simple update” for PEPS) are used to model the ground states of the studied models. Different entanglement measures, such as the one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are compared with respect to their ability to exhibit “structures” in the phase diagram of the models (e.g., phase transitions). We study the connection between symmetries and the entanglement of ground states and analyze short- and long-range entanglement through the entanglement monogamy.

arXiv:1504.00220Ukrainian Journal of PhysicsJul 1, 20166 citations

Model for entangled states with spin-spin interaction (12 pages)

G. Jordan Maclay, Yakir Aharonov, J. Anandan

Physical Review AJan 1, 20040 citations

Entanglement of pure two-mode Gaussian states (7 pages)

R. W. Rendell, A. K. Rajagopal

Physical Review AJan 1, 20051 citation

Ground-state entanglement in the XXZ model

Shi-Jian Gu, Guang-Shan Tian, Hai-Qing Lin

In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$ -dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground-state concurrence reaches maximum at the isotropic point. For dimensionality $d\ensuremath{\geqslant}2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground-state concurrence reaches maximum at the isotropic point. For dimensionality $d\ensuremath{\geqslant}2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.

arXiv:quant-ph/0408101Physical Review AMay 17, 200599 citations

In this paper, we investigate spin entanglement in the

XXZ

model defined on a

d

-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground-state concurrence reaches maximum at the isotropic point. For dimensionality $d\ensuremath{\geqslant}2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.