arXiv subjects

L. Justino

Publications and source records attributed to L. Justino.

2 recordsLinked to original sources

arXiv2014

Effects of spontaneous symmetry break in the origin of non-analytic behavior of entanglement at quantum phase transitions

We present an example where Spontaneous Symmetry Breaking may effect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of the non-analyticity. In particular, in the XXZ model, we study the non analyticities in the concurrence between two spins, which was claimed to be accidental, since it had its origin in the optimization involved in the concurrence definition. We show that when one takes in account the effect of the Spontaneous Symmetry Breaking, even tough the values of the entanglement measure does not change, the origin the the non-analytical behavior changes: it is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the Spontaneous Symmetry Breaking not noticed before. However the non-analytical behavior still suggests a second order quantum phase transition and not the first order that occurs and we explain why. We also show that the value of entanglement between one site and the rest of the chain does change when taking into account the Spontaneous Symmetry Breaking.

quant-ph↗

arXiv2012

Bell inequalities and entanglement at quantum phase transition in the XXZ Model

Entanglement and violation of Bell inequalities are aspects of quantum nonlocality that have been often confused in the past. It is now known that this equivalence is only true for pure states. Even though almost all the studies of quantum correlations at quantum phase transitions deal only with entanglement, we here argue that Bell inequalities can also reveal a general quantum phase transition. This is also shown for a particular case of two spin-1/2 particles in an infinite one-dimensional chain described by the XXZ model. In this case, the Bell inequality is able to signal not only the first-order phase transition, but also the infinite-order Kosterlitz-Thouless quantum phase transition, which cannot be revealed either by the energy of the system nor by the bipartite entanglement. We also show that although the nearest-neighbor spins are entangled, they, unexpectedly, never violate the Bell inequality. This indicates that the type of entanglement which is relevant for quantum phase transition is not trivial, i.e., it cannot be revealed by the Bell inequality.

quant-ph↗