We define a negative entanglement measure for separable states which shows how much entanglement one should compensate the unentangled state, at the least, to change it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure (NEM) have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the one-dimensional (1D) Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.We define a negative entanglement measure for separable states which shows how much entanglement one should compensate the unentangled state, at the least, to change it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure (NEM) have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the one-dimensional (1D) Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.

arXiv:1001.5148Physical Review ADec 13, 20103 citations

Quantum entanglement in non-Hermitian Hubbard model

L.S. Lima

Physica E Low-dimensional Systems and NanostructuresNov 18, 20238 citations

Superconductivity Induced by Negative Centers

Grzegorz Litak A, Thereza Paiva, R. T. Scalettar +2 more

We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative $U$ Hubbard model where the interaction $U_i$ , defined on the two dimensional lattice, can be $-|U|$ and 0 with probability $c$ and $1-c$ depending on the lattice site $i$ . Using the determinant quantum Monte Carlo approach, we find the critical concentration $c_0$ of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative $U$ Hubbard model where the interaction $U_i$, defined on the two dimensional lattice, can be $-|U|$ and 0 with probability $c$ and $1-c$ depending on the lattice site $i$. Using the determinant quantum Monte Carlo approach, we find the critical concentration $c_0$ of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.

arXiv:cond-mat/0206128Jun 8, 20020 citations

t/U

changes from zero to negative on approaching the critical point of quantum phase transition.

We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative

U

Hubbard model where the interaction

U_i

, defined on the two dimensional lattice, can be

-|U|

and 0 with probability

c

and

1-c

depending on the lattice site

i

. Using the determinant quantum Monte Carlo approach, we find the critical concentration

c_0

of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.