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

arXiv:1209.1637 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Compressible quantum phases from conformal field theories in 2+1 dimensions

Subir Sachdev A

Published Dec 19, 2012• 32 citations
arXivHTMLPDF

Abstract

Conformal field theories (CFTs) with a globally conserved U(1) charge $\mathcal{Q}$ can be deformed into compressible phases by modifying their Hamiltonian, $\mathcal{H}$, by a chemical potential $\mathcal{H}\ensuremath{\rightarrow}\mathcal{H}\ensuremath{-}\ensuremath{\mu}\mathcal{Q}$. We study $2+1$ dimensional CFTs upon which an explicit $S$ duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called ``Bose metals'' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solids, and the product of their magnetic charge and $\mathcal{Q}$ determines the area of the unit cell. We present implications for holographic theories on asymptotically ${\mathrm{AdS}}_{4}$ spacetimes: $S$ duality and monopole/dyon fields play important roles in this connection.

DOI
10.1103/physrevd.86.126003

Related papers

Fermi surfaces and gauge-gravity duality

Liza Huijse, Subir Sachdev A

We give a unified overview of the zero temperature phases of compressible quantum matter: i.e., phases in which the expectation value of a globally conserved U(1) density, $\mathcal{Q}$, 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 $⟨\mathcal{Q}⟩$. We survey models of interacting bosons and/or fermions and/or gauge fields which realize such phases. Some phases have Fermi surfaces with the singularities of Landau's Fermi liquid theory, while other Fermi surfaces have non-Fermi liquid singularities. Compressible phases found in models applicable to condensed-matter systems are argued to also be present in models obtained by applying chemical potentials (and other deformations allowed by the residual symmetry at nonzero chemical potential) to the paradigmatic supersymmetric gauge theories underlying gauge-gravity duality: the Aharony-Bergman-Jafferis-Maldacena model in spatial dimension $d=2$, and the $\mathcal{N}=4$ super Yang-Mills theory in $d=3$.

arXiv:1104.5022•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 5, 2011•82 citations

What Can Gauge-Gravity Duality Teach Us About Condensed Matter Physics?

Subir Sachdev A

I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with nonzero temperature dynamics and transport are difficult to answer using conventional field-theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality and discuss the prospects for reliable computation of low-frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly coupled compressible quantum states.

arXiv:1108.1197•Annual Review of Condensed Matter Physics•Mar 1, 2011•246 citations

Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids

Éric Dupuis, Rufus Boyack, William Witczak‐Krempa

Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids and topological quantum spin liquids (QSLs): chiral and Z 2 QSLs.These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2 þ 1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction term.For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED 3 -GN), while for the transitions to Z 2 QSLs, it is a superconducting pairing term with general spin and valley structure (generalized QED 3 -Z 2 GN).Using the state-operator correspondence, we obtain monopole scaling dimensions to subleading order in 1=N.For monopoles with a minimal topological charge q ¼ 1=2, the scaling dimension is 2N × 0.26510 at leading order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest Z 2 case (the expression is also given for a general pairing term).Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins.The analogous result in QED 3 is also obtained, and we find a subleading contribution of -0.038138ð5Þ, which is slightly different from the value -0.0383 first obtained in the literature.The scaling dimension of a QED 3 -GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED 3 -GN with 2N ¼ 2 flavors and the CP 1 model.Additionally, nonminimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions.By studying the large-q asymptotics of the scaling dimensions in QED 3 , QED 3 -GN, and QED 3 -Z 2 GN, we verify that the constant Oðq 0 Þ coefficient precisely matches the universal nonperturbative prediction for CFTs with a global U(1) symmetry.Finally, we identify numerous open questions regarding the fate of monopoles and their hierarchies at transitions to spin liquids and ordered phases.

arXiv:2108.05922•Physical Review X•Jul 19, 2022•20 citations

Dirac quantum criticality and the web of dualities

William Witczak‐Krempa

We grow the web of dualities for conformal field theories (CFTs) in 2+1 spacetime dimensions to include quantum critical transitions of Dirac fermions. Our construction uses the seed duality, equating a free Dirac fermion with a complex boson coupled to a Chern-Simons gauge field, to express various Gross-Neveu-Yukawa (GNY) critical points of N fermions in terms of the same number of complex bosons and partner gauge fields. In some instances, monopole operators appear explicitly in the dual action, such as for the superconducting transition of a single Dirac fermion, which is a CFT with emergent supersymmetry. We match phase diagrams, symmetries and their anomalies. By further gauging certain symmetries, we derive offspring dualities. For example, starting with the duality for the regular GNY transition of 2 Dirac fermions, we arrive at the duality between a Neel-to-VBS deconfined quantum critical point and a gauged-Gross-Neveu transition. Finally, we use a large-N expansion for monopole operators, and compare with known scaling dimensions in the simplest single-flavour GNY transition.

arXiv:2305.07718•May 12, 2023•0 citations

The Landscape of the Hubbard Model

Subir Sachdev A

I present a pedagogical survey of a variety of quantum phases of the Hubbard model. The honeycomb lattice model has a conformal field theory connecting the semi-metal to the insulator with Neel order. States with fractionalized excitations are linked to the deconfined phases of gauge theories. I also consider the confining phases of such gauge theories, and show how Berry phases of monopoles induce valence bond solid order. The triangular lattice model can display a metal-insulator transition from a Fermi liquid to a deconfined spin liquid, and I describe the theory of this transition. The bilayer triangular lattice is used to illustrate another compressible metallic phase, the `fractionalized Fermi liquid'. I make numerous connections of these phases and critical points to the AdS/CFT correspondence. In particular, I argue that two recent holographic constructions connect respectively to the Fermi liquid and fractionalized Fermi liquid phases.

arXiv:1012.0299•Nov 1, 2011•23 citations

Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions

Ribhu K. Kaul, Subir Sachdev A

We consider relativistic U(1) gauge theories in $2+1$ dimensions, with ${N}_{b}$ species of complex bosons and ${N}_{f}$ species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large ${N}_{b}$ and ${N}_{f}$, but for arbitrary values of the ratio ${N}_{b}∕{N}_{f}$, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.

arXiv:0801.0723•Physical Review B•Apr 3, 2008•125 citations
Conformal field theories (CFTs) with a globally conserved U(1) charge Q\mathcal{Q}Q can be deformed into compressible phases by modifying their Hamiltonian, H\mathcal{H}H, by a chemical potential H\ensuremath→H\ensuremath−\ensuremathμQ\mathcal{H}\ensuremath{\rightarrow}\mathcal{H}\ensuremath{-}\ensuremath{\mu}\mathcal{Q}H\ensuremath→H\ensuremath−\ensuremathμQ. We study 2+12+12+1 dimensional CFTs upon which an explicit SSS duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called ``Bose metals'' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solids, and the product of their magnetic charge and Q\mathcal{Q}Q determines the area of the unit cell. We present implications for holographic theories on asymptotically AdS4{\mathrm{AdS}}_{4}AdS4​ spacetimes: SSS duality and monopole/dyon fields play important roles in this connection.
We give a unified overview of the zero temperature phases of compressible quantum matter: i.e., phases in which the expectation value of a globally conserved U(1) density, Q\mathcal{Q}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 ⟨Q⟩⟨\mathcal{Q}⟩⟨Q⟩. We survey models of interacting bosons and/or fermions and/or gauge fields which realize such phases. Some phases have Fermi surfaces with the singularities of Landau's Fermi liquid theory, while other Fermi surfaces have non-Fermi liquid singularities. Compressible phases found in models applicable to condensed-matter systems are argued to also be present in models obtained by applying chemical potentials (and other deformations allowed by the residual symmetry at nonzero chemical potential) to the paradigmatic supersymmetric gauge theories underlying gauge-gravity duality: the Aharony-Bergman-Jafferis-Maldacena model in spatial dimension d=2d=2d=2, and the N=4\mathcal{N}=4N=4 super Yang-Mills theory in d=3d=3d=3.
I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with nonzero temperature dynamics and transport are difficult to answer using conventional field-theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality and discuss the prospects for reliable computation of low-frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly coupled compressible quantum states.
Monopole operators are studied in a large family of quantum critical points between Dirac spin liquids and topological quantum spin liquids (QSLs): chiral and Z 2 QSLs.These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2 þ 1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction term.For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED 3 -GN), while for the transitions to Z 2 QSLs, it is a superconducting pairing term with general spin and valley structure (generalized QED 3 -Z 2 GN).Using the state-operator correspondence, we obtain monopole scaling dimensions to subleading order in 1=N.For monopoles with a minimal topological charge q ¼ 1=2, the scaling dimension is 2N × 0.26510 at leading order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest Z 2 case (the expression is also given for a general pairing term).Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins.The analogous result in QED 3 is also obtained, and we find a subleading contribution of -0.038138ð5Þ, which is slightly different from the value -0.0383 first obtained in the literature.The scaling dimension of a QED 3 -GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED 3 -GN with 2N ¼ 2 flavors and the CP 1 model.Additionally, nonminimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions.By studying the large-q asymptotics of the scaling dimensions in QED 3 , QED 3 -GN, and QED 3 -Z 2 GN, we verify that the constant Oðq 0 Þ coefficient precisely matches the universal nonperturbative prediction for CFTs with a global U(1) symmetry.Finally, we identify numerous open questions regarding the fate of monopoles and their hierarchies at transitions to spin liquids and ordered phases.
We grow the web of dualities for conformal field theories (CFTs) in 2+1 spacetime dimensions to include quantum critical transitions of Dirac fermions. Our construction uses the seed duality, equating a free Dirac fermion with a complex boson coupled to a Chern-Simons gauge field, to express various Gross-Neveu-Yukawa (GNY) critical points of N fermions in terms of the same number of complex bosons and partner gauge fields. In some instances, monopole operators appear explicitly in the dual action, such as for the superconducting transition of a single Dirac fermion, which is a CFT with emergent supersymmetry. We match phase diagrams, symmetries and their anomalies. By further gauging certain symmetries, we derive offspring dualities. For example, starting with the duality for the regular GNY transition of 2 Dirac fermions, we arrive at the duality between a Neel-to-VBS deconfined quantum critical point and a gauged-Gross-Neveu transition. Finally, we use a large-N expansion for monopole operators, and compare with known scaling dimensions in the simplest single-flavour GNY transition.
I present a pedagogical survey of a variety of quantum phases of the Hubbard model. The honeycomb lattice model has a conformal field theory connecting the semi-metal to the insulator with Neel order. States with fractionalized excitations are linked to the deconfined phases of gauge theories. I also consider the confining phases of such gauge theories, and show how Berry phases of monopoles induce valence bond solid order. The triangular lattice model can display a metal-insulator transition from a Fermi liquid to a deconfined spin liquid, and I describe the theory of this transition. The bilayer triangular lattice is used to illustrate another compressible metallic phase, the `fractionalized Fermi liquid'. I make numerous connections of these phases and critical points to the AdS/CFT correspondence. In particular, I argue that two recent holographic constructions connect respectively to the Fermi liquid and fractionalized Fermi liquid phases.
We consider relativistic U(1) gauge theories in 2+12+12+1 dimensions, with Nb{N}_{b}Nb​ species of complex bosons and Nf{N}_{f}Nf​ species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large Nb{N}_{b}Nb​ and Nf{N}_{f}Nf​, but for arbitrary values of the ratio Nb∕Nf{N}_{b}∕{N}_{f}Nb​∕Nf​, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.