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Exploring the Strange Metal Crossover, Pomeranchuk instabilities as a complement to holography

Talk given at ICTP

Nicolás Grandi

on 4 May 2012

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Transcript of Exploring the Strange Metal Crossover, Pomeranchuk instabilities as a complement to holography

High Tc Superconductors 100 years of superconductivity Landau-Fermi Liquid Theory Pomeranchuk instabilities Generalized Pomeranchuk instabilities Holographic description of Fermi liquids Final remarks Thermodynamic potential Occupation numbers Dispersion relation Interaction function Fermi surface Ground state Excited state Isotropy Normal variables Energy as a quadratic form Gram-Schmidt Interaction function basis Exploring the strange metal crossover: Pomeranchuk instabilities as a complement to holography N. E. Grandi Conicet, Argentina Abdus Salam ICTP May 2011 Some phase diagrams s-wave interaction in the sqare lattice s-wave interaction in the honeycomb lattice d-wave interaction in the square lattice Nearest neighbor interaction
in the honeycomab lattice D. van Delft, P. Kes, 2011, Europhysics News 42 21 Holographic setup Green function Two particle Green function One particle Green function Expansion of the energy Temperature and magnetic field s-wave interaction in the square lattice
at finite temperature Spin antisymmetric interaction in the square lattice at finite magnetic field 95 years of Black Holes Schematic phase diagram Fermi Liquid Strange metal Landau theory Holography Pomeranchuk
instabiliy Crossover Complementarity of descriptions How does it look from here? Holographic Zoo Holographic setup Thanks! } Thermodynamic limit Stability condition What if we do not have isotropy? Landau-Like quasiparticle peak Renormalized energy? Effects of backreaction -Landau-like pole moves to zero frequency -It becomes ten times stronger than the NFL pole Lessons? 1- Completely defined in the framework of Landau theory

2- Nontrivial information about the phase diagram

3- The form of the interaction function is important

4- The form of the dispersion relation (lattice) is important Inclusion of a lattice Semi-holographic description Lessons? 1- A Landau Fermi liquid seems to exist in a region of parameters

2- It allows for coupling to an underlying lattice

3- The Green function can be calculated at strong coupling => we can get a dispersion relation

4- Higher order functions can be calculated at strong coupling => can we get an interaction function? Higher order functions Higher order diagrams in the bulk 1- Pomeranchuk instabilies signal the breakdown of the Landau description of a Fermi Liquid

2- They can be studied in lattice systems at finite temperature and/or magnetic field

3- Holography describes the strange metal phase with weak coupling calculations

4- In some region of parameters, holography may be describing an underlying Landau-Fermi liquid

5- In such region, one may hope to use holography to calculate the relevant functions of Landau theory

6- What would then Pomeranchuk instabilities mean, when reinterpreted in terms of the bulk quantities?
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