Exciton entanglement in coupled quantum dots in a microcavity

Berry phases, quantum phase transitions and Chern numbers

“…In fact, all computations rely on the introduction of an additional parameter through a unitary transformation of the Hamiltonian. Then the Berry phase for a special class of loops in this extended parameter space is computed, leading to the results reported in references [1,2,3,4,5]. In this work, using the model proposed in [5], we intend to go a step further in the sense that, for each value of the external field (λ), we identify a space (isomorphic to the two-sphere) and a corresponding line bundle L λ over it, for which a topological invariant c 1 (λ) can be computed.…”

“…Recently, a close connection between Berry phases (BP) associated to quantum many-body systems and Quantum Phase Transitions (QPT) has emerged, attracting much attention [1,2,3,4,5]. From an experimental point of view such a connection is very interesting, due to the robustness of BP against continuous changes in the system's parameters.…”

“…Following Yuan et al [5], we start by considering a system consisting of a spin chain coupled to a central spin, with Hamiltonian H = H I + H C + H E , where…”

“…The parameter γ accounts for the anisotropy in the spin chain. Assuming that the spin chain is in its ground state, the following effective mean-field Hamiltonian for the central spin can be obtained [5]:…”

“…Following references [1,2,3,4,5], we change the Hamiltonian by means of a unitary transformation U (ϕ) = exp (−iϕσ z /2) to…”