Gauge/Gravity Duality applied to Condensed Matter Systems Martin Ammon University of California, Los Angeles 35th Johns Hopkins Workshop on AdS/CFT and its Applications June 24th, 2011 Based on: MA, J. Erdmenger, M. Kaminski, A. O’Bannon, 1003.1134 MA, Review on AdS/CMT from top-down approach, Fortschritte der Physik, 58 (2010) 1123-1250. Martin Ammon (UCLA) AdS/CMT June 24, 2011 1 / 21
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Gauge/Gravity Duality applied toCondensed Matter Systems
Martin Ammon
University of California, Los Angeles
35th Johns Hopkins Workshop onAdS/CFT and its Applications
June 24th, 2011
Based on:
MA, J. Erdmenger, M. Kaminski, A. O’Bannon, 1003.1134
MA, Review on AdS/CMT from top-down approach,Fortschritte der Physik, 58 (2010) 1123-1250.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 1 / 21
Outline
1 Motivation
2 Applying AdS/CFT to Condensed Matter Systems
3 AdS/CMT - the top-down approach
4 Fermi Surfaces in holographic p-wave superfluids
5 Conclusion
Martin Ammon (UCLA) AdS/CMT June 24, 2011 2 / 21
Outline, part II
Motivation
Can we use string theory to study experimental observations?
is based on two cornerstones:Landau’s theory of Phase transitions
Fermi liquid theory
Martin Ammon (UCLA) AdS/CMT June 24, 2011 4 / 21
Motivation
Condensed matter physics
is based on two cornerstones:Landau’s theory of Phase transitions
- classifies different phases by their symmetries (order parameter),- Phase transitions are associated with changes in symmetry.
Fermi liquid theory
Martin Ammon (UCLA) AdS/CMT June 24, 2011 4 / 21
Motivation
Condensed matter physics
is based on two cornerstones:Landau’s theory of Phase transitions
- classifies different phases by their symmetries (order parameter),- Phase transitions are associated with changes in symmetry.
Fermi liquid theory- treats properties of electrons as small perturbations of the ground
state (filled single-particle levels up to EF ).
Martin Ammon (UCLA) AdS/CMT June 24, 2011 4 / 21
Motivation
Condensed matter physics
is based on two cornerstones:Landau’s theory of Phase transitions
- classifies different phases by their symmetries (order parameter),- Phase transitions are associated with changes in symmetry.
Fermi liquid theory- treats properties of electrons as small perturbations of the ground
state (filled single-particle levels up to EF ).
But there are also
- systems with topological phase transitions and
- strongly correlated electron systems.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 4 / 21
Motivation
Condensed matter physics
is based on two cornerstones:Landau’s theory of Phase transitions
- classifies different phases by their symmetries (order parameter),- Phase transitions are associated with changes in symmetry.
Fermi liquid theory- treats properties of electrons as small perturbations of the ground
state (filled single-particle levels up to EF ).
But there are also
- systems with topological phase transitions and
- strongly correlated electron systems.
⇒ New conceptional ideas are needed!
Martin Ammon (UCLA) AdS/CMT June 24, 2011 4 / 21
Motivation
Strongly correlated electron systems
Examples
High-Tc superconductors, e.g. cuprates like La2−xSrxCuO2,
Heavy fermion compounds such as CePd2Si2,
Fractional quantum Hall liquids,
Luttinger liquids in one-dimensional conducting systems.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 5 / 21
Motivation
Strongly correlated electron systems
Examples
High-Tc superconductors, e.g. cuprates like La2−xSrxCuO2,
Heavy fermion compounds such as CePd2Si2,
Fractional quantum Hall liquids,
Luttinger liquids in one-dimensional conducting systems.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 5 / 21
Motivation
Strongly correlated electron systems
Examples
High-Tc superconductors, e.g. cuprates like La2−xSrxCuO2,
Heavy fermion compounds such as CePd2Si2,
Fractional quantum Hall liquids,
Luttinger liquids in one-dimensional conducting systems.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 5 / 21
Motivation
Strongly correlated electron systems
Examples
High-Tc superconductors, e.g. cuprates like La2−xSrxCuO2,
Heavy fermion compounds such as CePd2Si2,
Fractional quantum Hall liquids,
Luttinger liquids in one-dimensional conducting systems.
typical (schematic)
phase diagram
Martin Ammon (UCLA) AdS/CMT June 24, 2011 5 / 21
Motivation
Quantum Phase Transitions
Definition & Consequences
Quantum Phase Transition:Phase Transition at T = 0.
Caused by non-analyticity inground state energy,
Driven by quantum fluctuations!
Quantum critical region (QCR):Temperature is the only relevantscale: ⇒ Scale invariant!
~x → λ~x ⇒ t → λz t .
[Herzog]
Martin Ammon (UCLA) AdS/CMT June 24, 2011 6 / 21
Motivation
Quantum Phase Transitions
Definition & Consequences
Quantum Phase Transition:Phase Transition at T = 0.
Caused by non-analyticity inground state energy,
Driven by quantum fluctuations!
Quantum critical region (QCR):Temperature is the only relevantscale: ⇒ Scale invariant!
~x → λ~x ⇒ t → λz t .
[Herzog]
Effective Theories in QCR-Regionare difficult to find!for example: O(N) models (Wilson-Fisher fixed point)
Martin Ammon (UCLA) AdS/CMT June 24, 2011 6 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Quantum Critical theory:
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Quantum Critical theory:strongly coupled field theory with a global U(1) symmetry(conserved current Jµ).
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Quantum Critical theory:strongly coupled field theory with a global U(1) symmetry(conserved current Jµ).described by (super-) gravity theory in asymptotically AdSspacetime with U(1) gauge fieldfinite temperature↔ (non-extremal) black hole solutionconserved current Jµ ↔ gauge field.
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Quantum Critical theory:strongly coupled field theory with a global U(1) symmetry(conserved current Jµ).described by (super-) gravity theory in asymptotically AdSspacetime with U(1) gauge fieldfinite temperature↔ (non-extremal) black hole solutionconserved current Jµ ↔ gauge field.
Charge carriers: scalars, vectors, fermions charged under U(1).
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
Applying AdS/CFT to Condensed Matter Systems:Idea
Goal
Build superconductors
Model fermi surfaces
Calculate conductivities
of the charge carriers.
Quantum Critical theory:strongly coupled field theory with a global U(1) symmetry(conserved current Jµ).described by (super-) gravity theory in asymptotically AdSspacetime with U(1) gauge fieldfinite temperature↔ (non-extremal) black hole solutionconserved current Jµ ↔ gauge field.
Charge carriers: scalars, vectors, fermions charged under U(1).
Martin Ammon (UCLA) AdS/CMT June 24, 2011 7 / 21
Applying AdS/CFT to Condensed Matter Systems
What we can learn from AdS/CMT
What AdS/CMT can achieve:Identify new phenomena at strong coupling
→ e.g. holographic superconductors do not obey BCS theory!
→ energy gap ∆ of charged excitations: 2∆ ≈ 8.4Tc 6= 3.54Tc.
Can compare dynamics of strongly coupled system with weakcoupling
⇒ Construct counterexamples to intuitive weak-couplingarguments!Find universal behaviour