Abstract
We present an example where spontaneous symmetry breaking may affect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of its 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 into account the effect of the spontaneous symmetry breaking, even though the values of the entanglement measure does not change, the origin of the non-analytical behavior changes. The non-analytical behavior 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 observed before. We also show that the value of entanglement between one site and the rest of the chain changes after taking into account the spontaneous symmetry breaking.
Highlights
It is generally accepted that entanglement may help in finding and characterizing Quantum Phase Transitions (QPT), since it may inherit the non-analytic behavior of the ground state energy [1, 2]
Another possibility is to look at the entanglement between two particles in the system; tracing out the rest. This measure is maximum at the critical point and can signal the quantum phase transition, this is not always true. All these entanglement measures can be written in terms of the reduced density matrices and in terms of correlation functions which contain information about non-analytic behavior of the ground state energy at the critical point [1, 2]
There are non-analytical behaviors in the entanglement measurements which do not correspond to QPT, Origin of Non-analytic Behavior of Entanglement at Criticality as first showed by Yang [4], for example
Summary
It is generally accepted that entanglement may help in finding and characterizing Quantum Phase Transitions (QPT), since it may inherit the non-analytic behavior of the ground state energy [1, 2] (see [3] for a review on entanglement and QPT). This measure is maximum at the critical point and can signal the quantum phase transition, this is not always true All these entanglement measures can be written in terms of the reduced density matrices and in terms of correlation functions which contain information about non-analytic behavior of the ground state energy at the critical point [1, 2]. Even though the characterization of entanglement gives more information about the nature of the ground state and its correlation it may be easier to use the usual correlation functions and thermodynamic quantities to study the quantum phase transition Besides such caveats, the study of the entanglement at QPT is in general more intricate than of thermodynamical quantities, because of the spontaneous symmetry breaking (SSB).
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