Zhong-Chao Wei

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