Effects of geometric frustration in Kitaev chains

We study the topological phase transitions of a Kitaev chain frustrated by the addition of a single long-range hopping. In order to study the topological properties of the resulting legged-ring geometry (Kitaev tie model), we generalize the transfer matrix approach through which the emergence of Majorana edge modes is analyzed. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the hopping and the chemical potential. Robustness to disorder of non-trivial phases is also proven. Moreover, geometric frustration effects persist when translational invariance is restored by considering a multiple-tie system. These findings shed light on an entire class of experimentally realizable topological systems with long-range couplings.

10. Frustration

Without assuming prior legal knowledge, books in the Directions series introduce and guide readers through key points of law and legal debate. Questions, diagrams and exercises help readers to engage fully with each subject and check their understanding as they progress. This chapter examines the frustration of a contract. Fundamental changes in the facts assumed by the parties, ‘frustrating events’ such as natural disasters and less catastrophic events may fundamentally change the parties’ obligations and frustrate the contract. Frustration of a contract brings the parties’ obligations to an end; a less substantial, non-frustrating event will have no effect and the parties must continue to perform their obligations even if they have become more onerous. The discussions cover the allocation of risk, examples of frustration, limits on frustration, effects of frustration and the Law Reform (Frustrated Contracts) Act 1943.

10. Frustration

Without assuming prior legal knowledge, books in the Directions series introduce and guide readers through key points of law and legal debate. Questions, diagrams and exercises help readers to engage fully with each subject and check their understanding as they progress. This chapter examines the frustration of a contract. Fundamental changes in the facts assumed by the parties, ‘frustrating events’ such as natural disasters and less catastrophic events, may fundamentally change the parties’ obligations and frustrate the contract. Frustration of a contract brings the parties’ obligations to an end; a less substantial, non-frustrating event will have no effect and the parties must continue to perform their obligations even if they have become more onerous. The discussions cover the allocation of risk, examples of frustration, limits on frustration, effects of frustration and the Law Reform (Frustrated Contracts) Act 1943.