We search for translationally invariant states of qubits on a ring that maximize the nearest-neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A 63, 052302 (2001)]. We first map the problem to the search for the ground state of a spin-1/2 Heisenberg $XXZ$ model. Using the exact Bethe ansatz solution in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively, spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest-neighbor entanglement necessarily contain pairs of neighboring spins ``down.''We search for translationally invariant states of qubits on a ring that maximize the nearest-neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A 63, 052302 (2001)]. We first map the problem to the search for the ground state of a spin-1/2 Heisenberg $XXZ$ model. Using the exact Bethe ansatz solution in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively, spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest-neighbor entanglement necessarily contain pairs of neighboring spins ``down.''

arXiv:quant-ph/0512214Physical Review AMay 31, 20066 citations

Bethe ansatz solvable interacting particle systems on Z

Eunghyun Lee

Jan 1, 20110 citations

Exact solution of an integrable quantum spin chain with competing interactions*

Jian Wang, Yi Qiao, Junpeng Cao +1 more

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.

Chinese Physics BApr 22, 20211 citation

Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz

Tomohiro SASAMOTO

Jul 1, 20160 citations

Thermodynamical bethe ansatz and condensed matter

Minoru Takahashi

arXiv:cond-mat/9708087Springer eBooksApr 7, 200831 citations

XXZ

model. Using the exact Bethe ansatz solution in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively, spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest-neighbor entanglement necessarily contain pairs of neighboring spins ``down.''