engleski

The Frustration of being Odd: Universal Area Law violation in local systems

At the core of every frustrated system one can identify the existence of frustrated rings that is usually interpreted in terms of single particle physics. We challenge this point of view, by showing that the ring's entanglement entropy cannot be accounted for through a single excitation. Moreover, we are lead to question whether different boundary conditions can determine a different phase. In particular, we consider spin chains made by an odd number of sites with short-range antiferromagnetic interactions and periodic boundary conditions. While for distances of the order of the correlation length the phenomenology is similar to that of the non-frustrated case, we find that correlation functions involving a number of sites scaling like the system size follow different rules. The von Neumann entanglement entropy violates the area law, while not diverging with the system size, resulting into a new behavior, never observed before, which we determine to follow a universal law. In certain regions of parameters, the frustrated boundary conditions induce exact degeneracies for the ground states (even at finite sizes) and we can define an order parameter that characterizes a phase due to boundary conditions. While we are sure of these striking results, we would like to have a discussion on their interpretation.

Entanglement ; Frustration ; Area Law Violation

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