Limiting states of the planar Heisenberg dynamics with a transverse magnetic field

Е. В. Гусев

Alvaro Caramico D’Auria, L. De Cesare, Maria Teresa Mercaldo +1 more

Alf Sjölander

Michalis Skotiniotis, Pavel Sekatski, Wolfgang Dür

We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with nearest-neighbour interactions and in the presence of a global, transverse, magnetic field. We analytically solve the problem and show that the precision with which one can estimate the magnetic field (interaction strength) given one knows the interaction strength (magnetic field) scales at the Heisenberg limit, and can be achieved by a linear superposition of the vacuum and N free fermion states. In addition, we show that Greenberger–Horne–Zeilinger-type states exhibit Heisenberg scaling in precision throughout the entire regime of parameters. Moreover, we numerically observe that the optimal precision using a product input state scales at the standard quantum limit.

Jean-Sébastien Caux, Fabian H. L. Eßler, U. Löw

We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev et al. [JETP 95, 538 (2002)]. We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to neutron scattering experiments on the one-dimensional Heisenberg chain compound ${\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.$

Е. В. Гусев