[Paper Review] Holographic quantum matter

Sean A. Hartnoll, Andrew Lucas+1 more|arXiv (Cornell University)|Dec 21, 2016

Quantum, superfluid, helium dynamicsPhysics and Astronomy620 references273 citations

TL;DR

A review of theories of quantum matter without quasiparticles using holographic duality, covering transport, compressible matter, symmetry-broken phases, and non-equilibrium dynamics.

ABSTRACT

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

Motivation & Objective

• Explain states of quantum matter without quasiparticles and motivate holographic approaches.
• Summarize the AdS/CMT framework and the emergence of a dual gravitational description.
• Discuss zero-density and finite-density (compressible) quantum matter and their transport properties.
• Present unified holographic methods for transport, including memory matrix and hydrodynamics.
• Explore symmetry-broken phases, non-equilibrium dynamics, and experimental connections.

Proposed method

• Describe the holographic dictionary and GKPW correspondence.
• Outline emergent extra dimensions via Wilsonian holographic renormalization and entanglement perspectives.
• Develop holographic models for zero and nonzero density matter, with emphasis on transport and spectral functions.
• Apply bulk Maxwell and dilaton setups to compute conductivities and diffusion in quantum critical regimes.
• Utilize quasinormal modes and holographic Green’s functions to study non-quasiparticle dynamics.
• Relate holographic results to memory matrix and hydrodynamic descriptions of transport.

Experimental results

Research questions

• RQ1 How can holography model quantum matter without long-lived quasiparticles?
• RQ2 What are the universal transport signatures of holographic quantum critical and compressible phases?
• RQ3 How do holographic constructions capture symmetry-broken phases like superconductivity and striped order?
• RQ4 What is the connection between horizon dynamics in gravity and dissipative transport in the boundary theory?
• RQ5 How do holographic results inform and relate to experimental strange metals and non-Fermi liquids?

Key findings

• Holography provides a controlled framework for studying strongly interacting, non-quasiparticle states.
• Spectral functions and conductivities can be computed from bulk dynamics with infalling boundary conditions.
• Quasinormal modes replace quasiparticles in describing dissipative dynamics in holographic media.
• Compressible holographic phases exhibit varied dynamical exponents z and hyperscaling violation, with rich transport behavior.
• Memory matrix and hydrodynamic methods unify holographic transport with experimentally relevant observables.
• Symmetry-broken holographic phases, including holographic superconductors, capture pair formation and transport in ordered states.