Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Condensed matter and AdS/CFT

Subir Sachdev A

Published Oct 31, 2015• 148 citations
OpenAlex

Abstract

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

Related papers

Fermions and the AdS/CFT correspondence: quantum phase transitions and the emergent Fermi-liquid

Mihailo Čubrović, Jan Zaanen, Koenraad Schalm

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 high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute 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.

•Apr 13, 2009•35 citations

Non-perturbative approaches to strongly correlated electron systems

Ka Wai Lo

"Strong electron correlation phenomena are ubiquitous, such as unconventional superconductivity and the metal-insulator transitions. Having a proper understanding of strongly correlated electron systems requires a non-perturbative analysis because Fermi liquid theory inevitably breaks down due to the strong correlation. In this thesis, we will study two non-perturbative approaches to tackle strongly correlated electronic system: 1.) multi-dimensional bosonization and 2.) the AdS/CFT correspondence. Multidimensional bosonization is the generalization of bosonization to spatial dimensions larger than one. The bosonized theory is an effective field theory in terms of the bosonic particle-hole fluctuations in different patches of the Fermi surface. The bosonized theory is quadratic and hence can be solved non-perturbatively. The AdS/CFT correspondence is a conjecture that d-dimensional field theory is dual to a d+1 dimensional quantum gravitational theory. Problems in strongly coupled field theory then have an equivalent description using weakly interacting gravitational theory, allowing a non-perturbative analysis. Chapter 1 will serve as an introduction. We will review several experiments which show a breakdown of Fermi liquid theory. Formalisms for multidimensional bosonization and the AdS/CFT correspondence will then be reviewed. In chapter 2, the two-orbital Hubbard model with degenerate d{xz} and d{yz} orbitals are investigated. We apply multidimensional bosonization to solve this problem exactly and discover a z=3 overdamped collective modes that emerges at the orbital-ordering quantum critical point. These modes modify the single-particle density of states and lead to non-Fermi liquid behavior which can provide a possible explanation for the recently observed zero-bias enhancement in the point contact spectroscopy signal on iron pnictides. Chapters 3, 4 and 5 discuss the applications of the AdS/CFT correspondence to model various condensed matter systems. In chapter 3, We consider an interaction term between a bulk spinor field and a gauge field in the Reissner-Nordstr\""om AdS background. When the Pauli interaction term is large enough, a dynamical gap is generated and spectral weight transfer is observed in the spectral density, mimicking the behavior of the Hubbard model. We further consider the finite temperature case and discover that the ratio between the dynamical gap and the critical temperature has the same order as that of VO^2. The Pauli coupling is also studied in the superconducting background. Chapter 4 consider the propagation of a neutral scalar field in the geometry called the electron star. The electron star has Lifshitz scaling with finite dynamical critical exponent at the interior, which is suitable for the modeling of quantum criticality and quantum phase transition with a neutral order parameter, for example for antiferromagnetism. We find that the quantum phase transition has the Berezinski-Kosterlitz-Thouless characteristic and the dynamical critical exponent can change across the quantum critical point. In chapter 5, we construct a gravity dual of the nematic phase by studying the condensation of a spin-two field in the Schwarzschild-AdS background. The condensation of a spin-two field can distort the rotational symmetry of the Fermi surface as long as the spin-two field is coupled to a probe spinor field in the bulk gravity dual."

•Jan 1, 2013•0 citations

Finite Temperature Dissipation and Transport Near Quantum Critical Points

Subir Sachdev A

I review a variety of model systems and their quantum critical points, motivated by recent experimental and theoretical developments. These are used to present a general discussion of the non-zero temperature crossovers in the vicinity of a quantum critical point. Insights are drawn from the exact solutions of quantum critical transport obtained from the AdS/CFT correspondence. I conclude with a discussion of the role of quantum criticality in the phase diagram of the cuprate superconductors

arXiv:0910.1139•Series in condensed matter physics•Nov 2, 2010•2 citations

AdS/CFT Correspondence in Condensed Matter

Antonio S. T. Pires

The goal of these notes is to introduce, in a very elementary way, the idea of the anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)- dimensional anti-de Sitter spacetime to a strongly-coupled d- dimensional quantum field theory living on its boundary. The AdS/CFT correspondence can be used to study finite temperature real time processes, such as response functions and dynamics far from equilibrium in quantum critical points in condensed matter systems. Computation of these quantities is reduced to solving classical gravitational equations in one higher dimension than the original theory.

arXiv:1006.5838•Morgan & Claypool Publishers eBooks•Jun 1, 2014•13 citations

Strange metals and the AdS/CFT correspondence

Subir Sachdev A

I begin with a review of quantum impurity models in condensed matter physics, in which a localized spin degree of freedom is coupled to an interacting conformal field theory in d = 2 spatial dimensions. Their properties are similar to those of supersymmetric generalizations which can be solved by the AdS/CFT correspondence; the low energy limit of the latter models is described by an AdS 2 geometry. Then I turn to Kondo lattice models, which can be described by a mean-field theory obtained by a mapping to a quantum impurity coupled to a self-consistent environment. Such a theory yields a 'fractionalized Fermi liquid' phase of conduction electrons coupled to a critical spin liquid state, and is an attractive mean-field theory of strange metals. The recent holographic description of strange metals with an AdS 2 × R 2 geometry is argued to be related to such mean-field solutions of Kondo lattice models.

arXiv:1010.0682•Journal of Statistical Mechanics Theory and Experiment•Nov 15, 2010•65 citations

Holography and condensed matter

Francesco Benini

Abstract This is a review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)‐Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s‐, p‐ or d‐wave holographic superconductors and “electron stars”. Finally we present a realization of local quantum criticality with an impurity problem.

arXiv:1202.6008•Fortschritte der Physik•Feb 29, 2012•12 citations
I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.
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 high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute 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.
"Strong electron correlation phenomena are ubiquitous, such as unconventional superconductivity and the metal-insulator transitions. Having a proper understanding of strongly correlated electron systems requires a non-perturbative analysis because Fermi liquid theory inevitably breaks down due to the strong correlation. In this thesis, we will study two non-perturbative approaches to tackle strongly correlated electronic system: 1.) multi-dimensional bosonization and 2.) the AdS/CFT correspondence. Multidimensional bosonization is the generalization of bosonization to spatial dimensions larger than one. The bosonized theory is an effective field theory in terms of the bosonic particle-hole fluctuations in different patches of the Fermi surface. The bosonized theory is quadratic and hence can be solved non-perturbatively. The AdS/CFT correspondence is a conjecture that d-dimensional field theory is dual to a d+1 dimensional quantum gravitational theory. Problems in strongly coupled field theory then have an equivalent description using weakly interacting gravitational theory, allowing a non-perturbative analysis. Chapter 1 will serve as an introduction. We will review several experiments which show a breakdown of Fermi liquid theory. Formalisms for multidimensional bosonization and the AdS/CFT correspondence will then be reviewed. In chapter 2, the two-orbital Hubbard model with degenerate d{xz} and d{yz} orbitals are investigated. We apply multidimensional bosonization to solve this problem exactly and discover a z=3 overdamped collective modes that emerges at the orbital-ordering quantum critical point. These modes modify the single-particle density of states and lead to non-Fermi liquid behavior which can provide a possible explanation for the recently observed zero-bias enhancement in the point contact spectroscopy signal on iron pnictides. Chapters 3, 4 and 5 discuss the applications of the AdS/CFT correspondence to model various condensed matter systems. In chapter 3, We consider an interaction term between a bulk spinor field and a gauge field in the Reissner-Nordstr\""om AdS background. When the Pauli interaction term is large enough, a dynamical gap is generated and spectral weight transfer is observed in the spectral density, mimicking the behavior of the Hubbard model. We further consider the finite temperature case and discover that the ratio between the dynamical gap and the critical temperature has the same order as that of VO^2. The Pauli coupling is also studied in the superconducting background. Chapter 4 consider the propagation of a neutral scalar field in the geometry called the electron star. The electron star has Lifshitz scaling with finite dynamical critical exponent at the interior, which is suitable for the modeling of quantum criticality and quantum phase transition with a neutral order parameter, for example for antiferromagnetism. We find that the quantum phase transition has the Berezinski-Kosterlitz-Thouless characteristic and the dynamical critical exponent can change across the quantum critical point. In chapter 5, we construct a gravity dual of the nematic phase by studying the condensation of a spin-two field in the Schwarzschild-AdS background. The condensation of a spin-two field can distort the rotational symmetry of the Fermi surface as long as the spin-two field is coupled to a probe spinor field in the bulk gravity dual."
The goal of these notes is to introduce, in a very elementary way, the idea of the anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)- dimensional anti-de Sitter spacetime to a strongly-coupled d- dimensional quantum field theory living on its boundary. The AdS/CFT correspondence can be used to study finite temperature real time processes, such as response functions and dynamics far from equilibrium in quantum critical points in condensed matter systems. Computation of these quantities is reduced to solving classical gravitational equations in one higher dimension than the original theory.
I begin with a review of quantum impurity models in condensed matter physics, in which a localized spin degree of freedom is coupled to an interacting conformal field theory in d = 2 spatial dimensions. Their properties are similar to those of supersymmetric generalizations which can be solved by the AdS/CFT correspondence; the low energy limit of the latter models is described by an AdS 2 geometry. Then I turn to Kondo lattice models, which can be described by a mean-field theory obtained by a mapping to a quantum impurity coupled to a self-consistent environment. Such a theory yields a 'fractionalized Fermi liquid' phase of conduction electrons coupled to a critical spin liquid state, and is an attractive mean-field theory of strange metals. The recent holographic description of strange metals with an AdS 2 × R 2 geometry is argued to be related to such mean-field solutions of Kondo lattice models.
Abstract This is a review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)‐Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s‐, p‐ or d‐wave holographic superconductors and “electron stars”. Finally we present a realization of local quantum criticality with an impurity problem.