@article {Santos2012, title = {Entanglement spectra of q-deformed higher spin VBS states}, journal = {J. Phys. A: Math. Theor.}, volume = {45}, number = {17}, year = {2012}, note = {cited By 3}, pages = {175303}, abstract = {
We calculate the reduced density matrix of a block of integer spin-S{\textquoteright}s in a q-deformed valence-bond-solid (VBS) state. This matrix is diagonalized exactly for an infinitely long block in an infinitely long chain. We construct an effective Hamiltonian with the same spectrum as the logarithm of the density matrix. We also derive analytic expressions for the von Neumann and R{\'e}nyi entanglement entropies. For blocks of finite length, we calculate the eigenvalues of the reduced density matrix by perturbation theory and numerical diagonalization. These results enable us to describe the effects of finite-size corrections on the entanglement spectrum and entropy in this generalized VBS model.
}, doi = {10.1088/1751-8113/45/17/175303}, author = {Raul A Santos and Francis N. C. Paraan and Vladimir E Korepin and Andreas Kl{\"u}mper} } @article {Santos2012, title = {Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states}, journal = {Europhys. Lett.}, volume = {98}, number = {3}, year = {2012}, note = {cited By 4}, pages = {37005}, abstract = {
We exactly calculate the reduced density matrix of matrix product states (MPS). Our compact result enables one to perform analytic studies of entanglement in MPS. In particular, we consider the MPS ground states of two anisotropic spin chains. One is a q-deformed Affleck-Kennedy-Lieb-Tasaki (AKLT) model and the other is a general spin-1 quantum antiferromagnet with nearest-neighbor interactions. Our analysis shows how anisotropy affects entanglement on different continuous parameter manifolds. We also construct an effective boundary spin model that describes a block of spins in the ground state of the q-deformed AKLT Hamiltonian. The temperature of this effective model is given in terms of the deformation parameter q.
}, doi = {10.1209/0295-5075/98/37005}, author = {Raul A Santos and Francis N. C. Paraan and Vladimir E Korepin and Andreas Kl{\"u}mper} } @article {Santos2012, title = {Quantum phase transition in a multicomponent anyonic Lieb-Liniger model}, journal = {Phys. Rev. B}, volume = {86}, number = {4}, year = {2012}, note = {cited By 2}, pages = {045123}, abstract = {
We study a one-dimensional multicomponent anyon model that reduces to a multicomponent Lieb-Liniger gas of impenetrable bosons (Tonks-Girardeau gas) for vanishing statistics parameter. At fixed component densities, the coordinate Bethe ansatz gives a family of quantum phase transitions at special values of the statistics parameter. We show that the ground-state energy changes extensively between different phases. Special regimes are studied and a general classification for the transition points is given. An interpretation in terms of statistics of composite particles is proposed.
}, doi = {10.1103/PhysRevB.86.045123}, author = {Raul A Santos and Francis N. C. Paraan and Vladimir E Korepin} } @article {Paraan2011, title = {Entanglement in bipartite pure states of an interacting boson gas obtained by local projective measurements}, journal = {Phys. Rev. A}, volume = {84}, number = {3}, year = {2011}, note = {cited By 1}, pages = {032330}, abstract = {

We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable-boson limiting value. We also present evidence indicating that the largest amount of entanglement can be extracted from the most probable projected state having half the number of bosons in a given partition. Our study points to a fundamental difference between the nature of the entanglement in free-bosonic and free-fermionic systems, with the entanglement in the former being zero after projection, while that in the latter (corresponding to the impenetrable-boson limit) being nonzero.

}, doi = {10.1103/PhysRevA.84.032330}, author = {Francis N. C. Paraan and Javier Molina-Vilaplana and Vladimir E Korepin and Sougato Bose} } @article {Paraan2010, title = {Perturbative correction to the ground-state properties of one-dimensional strongly interacting bosons in a harmonic trap}, journal = {Phys. Rev. A}, volume = {82}, number = {6}, year = {2010}, note = {cited By 2}, pages = {065603}, abstract = {
We calculate the first-order perturbation correction to the ground-state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With c denoting the interaction strength, we find that, for a large number of particles N, the 1/c correction to the ground-state energy increases as N^5/2, in contrast to the unperturbed Tonks-Girardeau value that is proportional to N^2. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground-state energy and reproduces the zero temperature thermodynamics obtained by a local-density approximation.
}, doi = {10.1103/PhysRevA.82.065603}, author = {Francis N. C. Paraan and Vladimir E Korepin} }