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### Condensed Matter Seminars

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The two dimensional kagome lattice is a highly frustrated spin system. When spins are placed on the vertices of the lattice with an antiferromagnetic interaction, there is no unique classical ground state. The large degeneracy of classical configurations with the same energy appear to give rise to an unusual quantum ground state. In this talk, I will discuss theoretical attempts to understand the ground state of the antiferromagnetic Heisenberg model on the kagome lattice. In the first portion of the talk, I will review several theoretical proposals for the ground state put forth over the past two decades. These fall into two basic categories: spin liquids and valence bond crystals. Theoretical methods such as series expansions, exact diagonalization, and variational studies have, at times, provided evidence for both classes of states, but no consensus has emerged in the field. Recent variational calculations using the density-matrix renormalization group produced a new bound on the ground state energy that rules out many “promising” candidates. In the second portion of the talk, I will describe more recent efforts to unravel the mystery of the ground state, including variational studies I have undertaken in collaboration with Michael Lawler, Brian Clark, Garnet Chan, and Eric Neuscamman.