We study the dynamics of two kinds of entanglement, and there interplay. On one hand, the intrinsic entanglement within a central system composed by three two level atoms, and measured by multipartite concurrence, on the other, the entanglement betwe
en the central system and a cavity, acting as an environment, and measured with purity. Using dipole-dipole and Ising interactions between atoms we propose two Hamiltonians, a homogeneous and a quasi-homogeneous one. We find an upper bound for concurrence as a function of purity, associated to the evolution of the $W$ state. A lower bound is also observed for the homogeneous case. In both situations, we show the existence of critical values of the interaction, for which the dynamics of entanglement seem complex.
We introduce a scheme for efficiently describing pure states of strongly correlated fermions in higher dimensions using unitary circuits featuring a causal cone. A local way of computing local expectation values is presented. We formulate a dynamical
reordering scheme, corresponding to time-adaptive Jordan-Wigner transformation, that avoids nonlocal string operators. Primitives of such a reordering scheme are highlighted. Fermionic unitary circuits can be contracted with the same complexity as in the spin case. The scheme gives rise to a variational description of fermionic models not suffering from a sign problem. We present numerical examples on $9times 9$ and $6times 6$ fermionic lattice model to show the functioning of the approach.
It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonian
s is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.
