Solving condensed-matter ground-state problems by semidefinite relaxations

Abstract

We 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, we obtain semidefinite programs (SDP). These can be solved efficiently, yielding strict 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.

8 pages, 3 figures; original title "Approaching condensed matter ground states from below"; improved numerics, added references; published version, including appendices

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• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• N-representability is QMA-complete
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