Scaling of Entanglement in Finite Arrays of Exchange-Coupled Quantum Dots

Abstract

We present a finite-size scaling analysis of the entanglement in a two-dimensional arrays of quantum dots modeled by the Hubbard Hamiltonian on a triangular lattice. Using multistage block renormalization group approach, we have found that there is an abrupt jump of the entanglement when a first-order quantum phase transition occurs. At the critical point, the entanglement is constant, independent of the block size.

Entanglement, Electron Correlation, and Density Matrices

“…Recently, it has been speculated that the most entangled systems could be found at the critical point [82] when the system undergoes a quantum phase transition, i. e. a qualitative change of some physical properties takes place as an order parameter in the Hamiltonian is tuned [83]. QPT results from quantum fluctuations at the absolute zero of temperature and is a pure quantum effect featured by long-range correlations.…”

“…The Hohenberg-Kohn theorem can be used to redefine entanglement measures in terms of new physical quantities: expectation values of observables, {a l }instead of external control parameters, {λ l }. Consider an arbitrary entanglement measure M for the ground state of Hamiltonian (82). For a bipartite entanglement, one can prove a central lemma, which very generally connects M and energy derivatives.…”

Fermionic Concurrence in the Extended Hubbard Model

“…Recently, many efforts have been devoted to the entanglement in strongly correlated systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], in the hope that its nontrivial behavior in these systems may shed new lights on the understanding of physical phenomena of condensed matter physics. A typical case is the relation of entanglement to quantum phase transition [6,7,8,9,10,11,12].…”

“…Nevertheless, it is still very difficult to provide a reliable measure for the pairwise entanglement of systems with the number of local states larger than 2. To the best of our knowledge, none of previous work investigated the pairwise entanglement for systems consisting of electrons with spin, such as the Hubbard model, although there were a few works studied the local entanglement of fermionic models [14,15,16].…”

A novel scheme for entanglement engineering in a fermionic system

“…In condensed matter physics, correspondingly, much of the theoretical investigations are focused upon spin or itilerant fermionic systems, such as the transverse Ising model [15], Heisenberg model [16] and Hubbard model [17]. A marvelous progress in this direction is the discovery of the close relationship between the entanglement and the quantum phase transition (QPT) [15,18,19]. It has been found that there is an abrupt change of the entanglement over the quantum critical point.…”