THE WELLSPRING OF ALL PHASES ON THE KAGOME LATTICE University of - PowerPoint PPT Presentation

THE WELLSPRING OF ALL PHASES ON THE KAGOME LATTICE University of Illinois at Urbana Champaign with Hitesh Changlani, Dmitrii Kochkov, Krishna Kumar, Eduardo Fradkin Blue Waters Symposium Talk

Frustrated Quantum Magnets….. Insulator - Electrons don’t move Interaction between electron spins spins want to anti-align Quantum ? Materials: Frustration from triangles Herbertsmithite Vesigniette Kapellasite Volborthite

Quantum Mechanics is hard

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What we found? Hamiltoniain (i.e. matrix) with exponentially many ground states. Why it’s interesting? Each ground state represents a phase of matter (liquid, solid, gas, anti-ferromagnet, etc) This means that there is a special Hamiltonian where all phases meet. This means that it sources all interesting phases on a class of materials. Including a particularly interesting (and useful for quantum computing) phase: a spin-liquid.

In strongly correlated systems like frustrated magnets… there are a menagerie of competing phases. Z2 (or Dirac) Spin Liquid Heisenberg (White/Huse) Chiral Spin Liquid 2/3 Plateau (this work) 1/3 Plateau (Donna Sheng) Chiral Term (Bela Bauer, Andreas Ludwig) J1, J2, J3 (Donna Sheng) q=0 magnetic order √ √ 3 order 3 × Ferromagnetism … Is this a cosmic coincident or is their a deep reason behind this?

Aside: Spin Liquids are really interesting. Phil Anderson suggested that the n.n. Heisenberg model on the triangular lattice wasn’t a neel state (frustration!) J z 1 0 ∞ instead, he suggested it was a RVB state. (today we would call such a thing a spin-liquid). | "#i � | #"i

Aside: Spin Liquids are really interesting. Phil Anderson suggested that the n.n. Heisenberg model on the triangular lattice wasn’t a neel state (frustration!) J z 1 0 ∞ instead, he suggested it was a RVB state. (today we would call such a thing a spin-liquid). | "#i � | #"i + + Like Benzene

Aside: Spin Liquids are really interesting. Phil Anderson suggested that the n.n. Heisenberg model on the triangular lattice wasn’t a neel state (frustration!) J z 1 0 ∞ instead, he suggested it was a RVB state. (today we would call such a thing a spin-liquid). | "#i � | #"i + + Not actually a spin liquid - years of numerics (1970-1990) Like Benzene

Aside: Spin Liquids are really interesting. + + Beyond the Landau theory of phases - no broken symmetries! Long Range Entanglement - Can’t be produced from a product state via a short quantum circuit Fractionalized Excitations - Electron breaks into multiple emergent pieces. Topological Degeneracy - Manifold dependent geometry The search for spin liquids is truly a hunt. We haven’t had any good story for what sort of lattices should support spin liquids. The hunt for spin liquids is one of the forefront areas of condensed matter research! Would be useful for storing quantum information and topological quantum computing!

An interesting discovery…. (amazing it hasn’t been known for 30 years) X j + S y i S y X S x i S x S z i S z H = j − 0 . 5 j ij ij J z 0 -0.5 1 ∞ On the kagome: massive exact degeneracy in the XXZ model! exactly -J/4 Finding this was only possible because we could afford to explore many points on Blue Waters. What’s going on? Who ordered this?

Who ordered that? X j + S y i S y X S x i S x S z i S z H = j − 0 . 5 j ij ij These are all the ground states of a single triangle. Define 3 “colors”

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