# Solving condensed matter ground state problems by semidefinite relaxations

Thomas Barthel (LMU)

09.11.2012 at 10:15

I will present a new generic approach to the condensed matter ground state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground state problem in a certain manner, one obtains semidefinite programs (SDP). These can be solved efficiently, yielding lower bounds to the ground state energy and approximations to the few-particle Green’s functions. As the method is applicable for all particle statistics, it represents in particular a novel route for the study of strongly correlated fermionic and frustrated spin systems in D>1 spatial dimensions. It is demonstrated for the XXZ model and the Hubbard model of spinless fermions. The results are compared against exact solutions, Quantum Monte Carlo, and Anderson bounds, showing the competitiveness of the SDP method. Reference: T. Barthel and R. Hübener, Phys. Rev. Lett. 108, 200404 (2012)

A348 - Theresienstr. 37