Abstract We investigate the entanglement in Hubbard models of hardcore bosons in 1 D , with an additional hardcore interaction on nearest-neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor 1/2 due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.
We analyze the developing of bipartite and multipartite entanglement through the Mott insulator-superfluid quantum phase transition. Starting from a Mott insulator state, where a filling factor ν = N/M = 1 per lattice site is considered, we derive an expression for a completely connected graph configuration of bosons and show how bipartite and multipartite entanglement evolve through the phase transition predicted in previous works. We show how, in the transition, bipartite entanglement is distributed through the system respecting monogamous relations.
In this paper, we study the entanglement properties of a spin-1 model, the exact ground state of which is given by a matrix product (MP) state. The model exhibits a critical point transition at a parameter value
a=0. The longitudinal and transverse correlation lengths are known to diverge as $a\ensuremath{\rightarrow}0$. We use three different entanglement measures
S(i) (the one-site von Neumann entropy),
S(i,j) (the two-body entanglement), and
G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter
a is varied. The entanglement length, associated with
S(i,j), is found to diverge in the vicinity of the quantum critical point
a=0. The first derivative of the entanglement measure
E [=S(i),S(i,j)] with respect to the parameter
a also diverges. The first derivative of
G(2,n) with respect to
a does not diverge as $a\ensuremath{\rightarrow}0$ but attains a maximum value at
a=0. At the quantum critical point itself all three entanglement measures become zero. We further show that multipartite correlations are involved in the quantum phase transitions at
a=0.
The study of entanglement properties of quantum critical many-particle systems has become a subject of intense interest. While the basic features of entanglement scaling for critical spin-1/2 systems (coupled qubits) are by now fairly well understood, entanglement properties of critical fermions (or bosons) are less well studied. In an effort to contribute to this problem, we have analyzed the single-site entanglement of a generic spin-1/2 lattice fermion system and found that (under certain provisos) this measure can be used as a reliable marker to identify and partly characterize a quantum critical point. We illustrate our findings by exact analytical results for the single-site entanglement at the magnetic and Mott-Hubbard transitions of the 1D Hubbard model and at the Mott-Hubbard transitions of the 1D Hubbard model with long-range hopping.
We derive exact expressions for the local entanglement entropy
E in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field
h or chemical potential $\ensuremath{\mu}$. The leading divergences of $\ensuremath{\partial}\mathcal{E}/\ensuremath{\partial}h$ and $\ensuremath{\partial}\mathcal{E}/\ensuremath{\partial}\ensuremath{\mu}$ are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.
A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to L=256 L = 256 sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.