@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} }