Session V19: Invited Session: Holography and Strongly Correlated Electron Matter

Why black holes may be useful for condensed matter physics

I will give an overview of recent applications of black hole physics to strongly correlated electron systems, via the holographic correspondence. I will briefly review the thermodynamic nature of black hole horizons and explain how black holes exhibit quantum critical dissipation. I proceed to argue that black holes are associated with fractionalized phases of matter and provide a simple setting in which transport and other properties of such phases can be nonperturbatively studied. Black holes furthermore have natural instabilities to superconducting phases. The onset of superconductivity is described in a qualitatively different way than in BCS-derived theories of pairing. The superconductivity emerges from a non-Fermi liquid state of matter, without well-defined quasiparticles, and may suggest emphasis on different classes of observables.   

Holography and Mottness: A Discrete Marriage

Gauge-gravity duality has allowed us to solve the physics of certain strongly coupled quantum mechanical systems using gravity. I will show how a space-time consisting of a charged black hole and a bulk Pauli coupling corresponds to a boundary theory with a dynamically generated gap (with no obvious symmetry breaking) and a massive rearrangement of the spectral weight as in classic Mott systems such as VO$_2$. In this holographic set-up, the gap opens only when discrete scale invariance is present. This raises the possibility that the elusive symmetry that might be broken in Mott insulators, in general, might pertain to scale invariance. The relevance of this claim to recent theories of Mott systems that possess massless charged bosons is explored.   

Charge fractionalization and gauge-gravityduality

We discuss zero temperature phases of compressible quantum matter, i.e. phases in which the expectation value of a globally conserved $U(1)$ density, $Q$, varies smoothly as a function of parameters. Provided the global $U(1)$ and translational symmetries are unbroken, such phases are expected to have Fermi surfaces, and the Luttinger theorem relates the volumes enclosed by these Fermi surfaces to $\langle Q \rangle $. We distinguish three compressible states: Landau's Fermi Liquid (FL), the fractionalized Fermi Liquid (FL*) and the non-Fermi Liquid (NFL). The motivation for this classification stems from the fact that compressible phases seem to be the rule rather than the exception in theories studied in the context of gauge-gravity duality. We argue that the three compressible phases we identify are indeed present in two paradigmatic supersymmetric gauge-theories underlying the duality. We then describe a gravity theory with an asymptotic electric flux dual to a zero temperature gauge theory at finite chemical potential. The flux can be sourced either by explicit charged matter in the bulk, by an extremal black hole horizon, or both. We argue that these three cases show important similarities with the three compressible states of matter. By tuning a relevant parameter we can study zero temperature phase transitions between the three phases in the dual description. The work I present was done in collaboration with S. Sachdev and S. Hartnoll.   

Emergent dimensions and quantum critical points

When quantum many-body systems are strongly correlated, the underlying particles may dynamically organize themselves to show novel collective behaviors. Under certain conditions, collective fluctuations behave as if they are living in a space which has one more dimension than the space where the original particles are defined. In this talk, I will discuss about an example where an `external' space emerges at a quantum critical point of a non-abelian gauge theory. A close analogy will be drawn between this phenomenon and fractionalization which can be viewed as an example of emergent `internal' spaces. I will also discuss about non-trivial quantum orders associated with emergent dimensions.   

Embedding Fermi liquids in string theory

Evidence of Fermi surfaces in strongly coupled gauge theories comes from calculations in the gauge-string duality based on the propagation of fermion fields in charged black hole backgrounds. Most of these calculations have been done without reference to explicitly known string theory constructions. When calculations based on the most universal sector of string theory constructions were at last done, no Fermi surface was found. In addition to reviewing the work just described, I will present new work showing that Fermi surfaces do exist in the next-to-simplest string theory constructions.