Split Orthogonal Group: A Guiding Principle for SignProblemFree Fermionic Simulations
Abstract
We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for signfree simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuoustime quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.
 Publication:

Physical Review Letters
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevLett.115.250601
 arXiv:
 arXiv:1506.05349
 Bibcode:
 2015PhRvL.115y0601W
 Keywords:

 05.10.Ln;
 02.20.Tw;
 02.70.Ss;
 71.10.Fd;
 Monte Carlo methods;
 Infinitedimensional Lie groups;
 Quantum Monte Carlo methods;
 Lattice fermion models;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 See http://mathoverflow.net/questions/204460/howtoprovethisdeterminantispositive and https://terrytao.wordpress.com/2015/05/03/thestandardbranchofthematrixlogarithm/ for discussions on mathematical aspect of the paper