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Solvable models of quantum matter without quasiparticles Subir Sachdev July 23, 2018 XIX International Congress on Mathematical Physics, Centre Mont-Royal, Montreal, Canada HARVARD Quasiparticles are ubiquitous: Fermi liquid theory of

  1. Solvable models of quantum matter without quasiparticles Subir Sachdev July 23, 2018 XIX International Congress on Mathematical Physics, Centre Mont-Royal, Montreal, Canada HARVARD

  2. Quasiparticles are ubiquitous: Fermi liquid theory of metals, insulators, semiconductors Theory of superconductivity (pairing of quasiparticles) Theory of disordered metals and insulators (diffusion and localization of quasiparticles) Theory of metals in one dimension (collective modes as quasiparticles) Theory of the fractional quantum Hall effect (quasiparticles which are `fractions’ of an electron)

  3. What are quasiparticles ? • Quasiparticles are additive excitations: The low-lying excitations of the many-body system can be identified as a set { n α } of quasiparticles with energy ε α E = P α n α ε α + P α , β F αβ n α n β + . . . In a lattice system of N sites, this parameterizes the energy of ∼ e α N states in terms of poly( N ) numbers. • Note: The electron liquid in one dimension and the fractional quantum Hall state both have quasiparticles; however, the quasi- particles do not have the same quantum numbers as an electron.

  4. What are quasiparticles ? • Quasiparticles eventually collide with each other. Such collisions eventually leads to thermal equilibration in a chaotic quantum state, but the equilibration takes a long time. In a Fermi liquid, this time diverges as ~ E F as T → 0, , τ eq ∼ ( k B T ) 2 where E F is the Fermi energy.

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  6. 1. Random matrix quasiparticle model q =2, complex SYK 2. Matter without quasiparticles q =4, complex SYK 3. The Schwarzian theory 4.Connections to black holes with AdS 2 horizons 5. Connections to strange metals

  7. 1. Random matrix quasiparticle model q =2, complex SYK 2. Matter without quasiparticles q =4, complex SYK 3. The Schwarzian theory 4.Connections to black holes with AdS 2 horizons 5. Connections to strange metals

  8. A simple model of a metal with quasiparticles Pick a set of random positions

  9. A simple model of a metal with quasiparticles Place electrons randomly on some sites

  10. A simple model of a metal with quasiparticles Place electrons randomly on some sites

  11. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  12. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  13. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  14. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  15. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  16. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

  17. A simple model of a metal with quasiparticles Electrons move one-by-one randomly

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