Research Article

String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid

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Science  24 Jul 2009:
Vol. 325, Issue 5939, pp. 439-444
DOI: 10.1126/science.1174962

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String Theory and Condensed Matter

The complex interactions involving highly correlated electron systems can give rise to “exotic behavior” in electronic systems, such as quantum criticality and superconductivity. The usual theoretical tools, however, are limited when describing these states. String theory is a highly mathematical approach initially developed to describe gravity and high-energy particle physics. Certain aspects of string theory may be relevant to describe condensed matter systems. Čubrović et al. (p. 439; published online 25 June) take one such approach, and show that the characteristic properties of a Fermi liquid can emerge from string theory. The formulation may provide an approach to describing the exotic states of matter that arise in condensed matter systems.


A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high–critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti–de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

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