Approaching condensed matter ground states from below

Details Approaching condensed matter ground states from below Approaching condensed matter ground states from below

2011-06-24

arxiv.org/abs/1106.4966v1

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages, 3 figures

Scientific paper

We present a 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, we obtain 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.

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