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In this talk we discuss the method of Majorana reflection positivity and its applications in the study of strongly correlated systems. The first application concerns the ground state degeneracy of interacting spinless fermions. Based on Majorana reflection positivity, we prove rigourously that the ground state of this model is either unique or doubly degenerate if the lattice size N is even, and is always doubly degenerate if N is odd. This proof holds in all dimensions with arbitrary lattice structures. The second application is about the sign problem in quantum Monte Carlo simulations. We examine this problem with a new perspective based on the Majorana reflection positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for nearly all the interacting lattice fermion models that are previously known to be free of the sign problem. It also allows us to identify a number of new sign-problem-free interacting fermion models.

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Zhong-Chao Wei, Chinese Academy of Sciences, Beijing
SR 0.03 (new building)
Contact: Alexander Alldridge