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Register a new userOn the second-neighbor correlator in 1D XXX quantum antiferromagnetic spin chain
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We have calculated the energy per site for the ground state of antiferromagnetic quantum spin chain with variable range exchange $h(j-k)propto sinh^2 a sinh^{-2}a(j-k)$ in the framework of the asymptotic Bethe ansatz. By expanding it in powers of $e^{-2a}$, we have confirmed the value of the second-neighbor correlator for the model with nearest-neighbor exchange obtained earlier in the atomic limit of the Hubbard chain.
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We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationally- and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation only the first few integrals of motion can be promoted to the quasi-conserved charges, whereas higher-order integrals of motion do not survive.
The ground state and thermodynamics of a generalized spin-1/2 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration-iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second-neighbor interaction between nodal spins gives rise to a greater diversity of low-temperature magnetization curves, which may include an intermediate plateau at two-third of the saturation magnetization related to the classical ferrimagnetic (up-up-up-down-up-up-...) ground state with translationally broken symmetry besides an intermediate one-third magnetization plateau reflecting the translationally invariant quantum ferrimagnetic (monomer-dimer) spin arrangement.
By relating the ground state of Temperley-Lieb hamiltonians to partition functions of 2D statistical mechanics systems on a half plane, and using a boundary Coulomb gas formalism, we obtain in closed form the valence bond entanglement entropy as well as the valence bond probability distribution in these ground states. We find in particular that for the XXX spin chain, the number N_c of valence bonds connecting a subsystem of size L to the outside goes, in the thermodynamic limit, as <N_c> = (4/pi^2) ln L, disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.
We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2pi k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.
Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and single-ion anisotropies in an external field are studied. Our findings confirm and refine recent results by Sengupta and Batista, Physical Review Letters 99, 217205 (2007) (2007), on the same model applying Monte Carlo techniques. In particular, we present evidence for two types of biconical (or supersolid) and for two types of spin-flop (or superfluid) structures. Basic features of the quantum phase diagram may be interpreted qualitatively in the framework of classical spin models.
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