In this talk we present an exact approach to calculating the entanglement entropy in spin chains that are described by conformal theory at quantum criticality. The method was initially used to study entanglement in free fermions and the XY model, but it turns out that Kitaev chains with long-ranged power law interactions also fall in the same solvable class. We evaluate the Schmidt gap in the entanglement spectrum and use it to map out the phase diagram of the model. Conformal features about the quantum critical line reveal how the universal scaling relations are affected by the power law exponent of the interactions.
}, author = {Francis N. C. Paraan and Cleofe Dennielle P. Ayang-ang} } @inproceedings {536, title = {Quantum phase transitions and Schmidt gap closing in a Kitaev chain with long-ranged interactions}, booktitle = {AQIS Conference 2019 Abstract Booklet - Poster Day 1}, year = {2019}, month = {19{\textendash}23 Aug 2019}, pages = {174-175}, address = {Korea Institute for Advanced Study, Seoul}, abstract = {The quantum phase diagram of a generalized Kitaev chain that exhibits long-ranged hopping and pairing is mapped out by looking for sharp changes in the Schmidt gap of a ground state bipartition.Finite-size scaling analysis reveals that the Schmidt gap exhibits universal scaling behavior about the quantum critical lines. The critical exponents found shows that the model displays different properties at the long- and short-range limits of the interaction.}, url = {http://aqis-conf.org/2019/program/}, author = {Cleofe Dennielle P. Ayang-ang and Francis N. C. Paraan} } @inproceedings {450, title = {Entanglement spectrum and entropy scaling in a Kitaev chain with variable-range interaction}, booktitle = {Proceedings of the 36th Samahang Pisika ng Pilipinas Physics Conference}, year = {2018}, month = {6{\textendash}9 June 2018}, pages = {SPP-2018-PC-35}, address = {Puerto Princesa City, Philippines}, abstract = {The entanglement spectrum was calculated for a contiguous block of spins in a Kitaev chain with a power law decay of interactions. Changes in the degeneracies of the four largest eigenvalues of the spectrum identify the quantum critical line separating the paramagnetic and anti-ferromagnetic phases of the model. Effective central charges along the critical lines are calculated by analyzing the finite-size scaling of the entanglement entropy with block length. For power law exponents that correspond to short-ranged interactions the effective central charge is that of free-fermionic models. For longer ranged interactions the obtained central charge deviates from this value.}, url = {https://paperview.spp-online.org/proceedings/article/view/SPP-2018-PC-35}, author = {Cleofe Dennielle P. Ayang-ang and Francis N. C. Paraan} } @inproceedings {ayang-ang, title = {Schmidt gaps in a long-range Kitaev chain}, booktitle = {Proceedings of the 35th Samahang Pisika ng Pilipinas Physics Conference}, year = {2017}, month = {7{\textendash}10 June 2017}, pages = {SPP-2017-1C-04}, address = {Cebu City, Philippines}, abstract = {The Schmidt gap for a block of spins in an infinite long-range Kitaev chain is calculated as a function of interaction range and the relative strengths of the chemical potential and hopping terms. We find that for long-ranged interactions where area law violations to the entanglement entropy occur, the Schmidt gap does not appear to close rapidly with chain length. For short-ranged interactions however, the Schmidt gap vanishes in a parameter region corresponding to an antiferromagnetic phase with gapless edge modes. These results demonstrate that the Schmidt gap can be used to distinguish quantum phases in the long-range Kitaev model.}, url = {http://paperview.spp-online.org/proceedings/article/view/107}, author = {Cleofe Dennielle P. Ayang-ang and Francis N. C. Paraan} } @inproceedings {322, title = {Molecular dynamics of rapid melting in a copper-silver alloy}, booktitle = {Proceedings of the 34th Samahang Pisika ng Pilipinas Physics Congress}, year = {2016}, month = {18{\textendash}21 Aug 2016}, pages = {SPP-2016-PA-22}, address = {University of the Philippines Visayas, Iloilo City}, abstract = {A copper-silver alloy (64\% Cu / 36\% Ag atomic ratio) is simulated by molecular dynamics. The alloy is subjected to rapid linear heating protocols from room temperature to 2100 K at several ramp rates of the order ~K/ps. Numerical evidence for a first-order melting transition at 1.19 x 10^3 K is observed. This elevated value is suggested to be the result of high pressures in the microscopic sample.}, author = {Cleofe Dennielle P. Ayang-ang and John Joseph S Solo and Zed Harold E. Fernandez and Francis N. C. Paraan} }