The landscape of the Hubbard model

Subir Sachdev

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The landscape of the Hubbard model

Subir Sachdev

High Energy Physics - Theory · Submitted 1 Dec 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, I argue that two recent holographic constructions connect respectively to the Fermi liquid and fractionalized Fermi liquid phases.

how it is stated · asserted 0.66 read the record →

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.15 · mentions code or data availability 0.01.

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arXiv listing abstract v5. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	I present a pedagogical survey of a variety of quantum phases of the Hubbard model.	contribution 0.96	0.82	0.09	asserted 0.87
s1	The honeycomb lattice model has a conformal field theory connecting the semi-metal to the insulator with Neel order.	result 0.46	0.17	0.07	asserted 1.00
s2	States with fractionalized excitations are linked to the deconfined phases of gauge theories.	background 0.61	0.15	0.07	asserted 1.00
s3	I also consider the confining phases of such gauge theories, and show how Berry phases of monopoles induce valence bond solid order.	contribution 0.54	0.81	0.08	asserted 1.00
s4	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.	contribution 0.84	0.57	0.08	hedged possibility 0.83
s5	The bilayer triangular lattice is used to illustrate another compressible metallic phase, the `fractionalized Fermi liquid'.	contribution 0.81	0.46	0.05	asserted 0.99
s6	I make numerous connections of these phases and critical points to the AdS/CFT correspondence.	contribution 0.84	0.78	0.10	asserted 0.97
s7	In particular, I argue that two recent holographic constructions connect respectively to the Fermi liquid and fractionalized Fermi liquid phases.	interpretation 0.47	0.73	0.15	asserted 0.66

What kind of paper the classifier reports this is: review 1.00 · evidence from argument 0.63.

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full text
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The paper

Original abstract

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.

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References

Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
hep-th 2011-12 accept novelty 7.0 of 10

The three-sphere free energy of a 3-d gauge theory with many flavors is computed to first subleading order in 1/N_F, and the log N_F coefficient matches exact supersymmetric localization results.
Bootstrapping 3D Fermions with Global Symmetries
hep-th 2017-05 conditional novelty 6.0 of 10

Bootstrap bounds on O(N)-symmetric 3D fermion theories show kinks that track the Gross-Neveu-Yukawa fixed points, yielding conjectural critical exponents at N = 2, 3, 4 and 8.
Towards Bootstrapping QED$_3$
hep-th 2016-01 conditional novelty 6.0 of 10

Crossing equations for four monopole operators in QED3 are derived for general N and solved numerically, yielding upper bounds on the doubly charged monopole dimension that show a gap-dependent kink near large-N extra...
Semi-local quantum liquids
hep-th 2011-05 conditional novelty 6.0 of 10

A holographic analysis identifies the near-horizon AdS2 region of a charged black hole as a universal intermediate-energy phase that can order into a heavy-fermion Fermi liquid at low energies.
Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity
hep-th 2011-05 conditional novelty 6.0 of 10

A single parameter, beta plus gamma, controls whether holographic fermions in zero-entropy dilatonic black branes form a Fermi liquid, a non-Fermi liquid, or no quasiparticles at all.

Show 6 more citing papers

Conformal field theories in a periodic potential: results from holography and field theory
hep-th 2013-08 conditional novelty 5.0 of 10

Holography and free Dirac fermions in a zero-average periodic chemical potential give qualitatively similar optical conductivity, but only the fermion theory shows discrete transitions where new Dirac nodes appear.
A model of a Fermi liquid using gauge-gravity duality
hep-th 2011-07 conditional novelty 5.0 of 10

A hard-wall anti-de Sitter model with bulk fermions treated exactly yields a confining Fermi liquid whose Fermi surface area matches the charge density through Gauss's law.
Fermi surfaces and gauge-gravity duality
hep-th 2011-04 conditional novelty 5.0 of 10

Compressible quantum phases with Fermi surfaces, familiar from condensed matter, are argued to survive in the ABJM and N=4 super Yang-Mills theories when those theories are deformed by a chemical potential.
Lectures on holographic non-Fermi liquids and quantum phase transitions
hep-th 2011-10 accept novelty 3.0 of 10

A review argues that the near-horizon AdS2 region of a charged black hole defines a universal intermediate-energy phase that organizes holographic non-Fermi liquids and quantum critical points.
What can gauge-gravity duality teach us about condensed matter physics?
cond-mat.str-el 2011-08 accept novelty 3.0 of 10

Holography can compute low-frequency transport at strongly coupled quantum critical points and can generate candidate compressible quantum states, but the mapping to real condensed matter systems is not yet settled.
Hydrodynamics of electrons in graphene
cond-mat.str-el 2017-10 accept novelty 2.0 of 10

Electron-electron scattering in ultraclean graphene is fast enough for the electrons to behave as a viscous fluid, and transport measurements show signatures of that hydrodynamic flow.

How the literature uses it

25 arXiv papers cite this in 47 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 28 sentences without a confident label

Contests it 1 paper

The anticipated quantum critical phenomena of continuous SM-AFM transition [ref] are not expected to exist.

Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice · Introduction · contest 0.81

Compares with it 1 paper

This behavior is reminiscent of various theoretical models based on a large spatial dimension mean field approximation [ref] , such as the gapless quantum liquids of [ref] and the “local quantum critical point” of [ref] [1]Some suggestions for a connection have been made in [ref] ..

Lectures on holographic non-Fermi liquids and quantum phase transitions · Semi-local quantum liquids · 0.86

Cites it as background 11 papers

In particular, the possible zero-temperature phase transitions in various models of interacting electrons on the two-dimensional honeycomb lattice have recently generated intense theoretical and numerical interests [ref] .

Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice · Introduction · 0.92
We begin with a conformal field theory in 2+1 dimensions [ref] , which has a holographic description by a theory on AdS$_4$.

A model of a Fermi liquid using gauge-gravity duality · Conclusions · 0.82
We now discuss the standard understanding of such a deficit, as articulated previously by various authors [ref] .

Luttinger's theorem, superfluid vortices, and holography · Luttinger deficit · 1.00

What it cites · 125 sentences without a confident label

Builds on 1 paper

Using symmetry and gauge invariance, we can now write down the following Lagrangian density [ref] for the SU$_g$ gauge theory; this combines and generalizes the Gross-Neveu-Yukawa model in Eq. ([ref]), and the U(1) gauge theory in Eqs. ([ref]) and ([ref]). ℒ_g = Ψ γ_μ( ∂_μ+ i σ^a A^a_μ) Ψ- λΦ^a Ψ ρ^z σ^a Ψ + 1/2 [ ( ∂_μΦ^a - 2 ϵ_Abc A^b_μΦ^c )^2 + s Φ^a2 ] + u/24 ( Φ^a2 )^2 + [ (∂_μR - i A_μ^a R σ^a) (∂_μR^†+ i A_μ^a σ^a R^†) ] + s ( R R^†) + u [ ( R R^†) ]^2 .

Fluctuating spin density waves in metals · SU(2) gauge theory and a phase diagram for the half-filled honeycomb lattice · 0.95

Uses the method or tool of 3 papers

As in Nickel and Son [ref] , and in Ioffe and Larkin [ref] , this is obtained by implementing the equation of motion of the emergent gauge field $A_μ$ in Eq. ([ref]).

Deconstructing holographic liquids · Transport theory · 0.92
The analog of the transformation to a rotating reference frame in Eq. ([ref]) is now [ref] c_ α = e^-i ϑ f_αwhere we have dropped the implicit site index, and $f_α$ are neutral fermions (`spinons') which keep track of the orientation of the electron.

Slave-rotor mean field theories of strongly correlated systems and the Mott transition in finite dimensions · The Metal-insulator transition on the triangular lattice · 0.86
We transform these to the rotating reference frame by writing [ref] ( [ c_ ↑; c_ ↓ ] ) = ( [ z_↑ -z_↓^∗; z_↓ z_↑^∗ ] ) ( [ ψ_ +; ψ_ - ] )

Fluctuating spin density waves in metals · U(1) gauge theory and the valence bond solid on the honeycomb lattice · 0.96

Uses data or values from 2 papers

This number was computed in the Einstein-Maxwell theory by Kovtun et al. [ref] and found to equal $ħ/(4 πk_B)$.

Graphene - a nearly perfect fluid · The AdS/CFT correspondence · 0.94
This number was computed in the Einstein-Maxwell theory by Kovtun et al. [ref] and found to equal $ħ/(4 πk_B)$.

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics · The AdS/CFT correspondence · 0.94

Compares with 3 papers

Then structure of Eq. ([ref]) is precisely that of the semi-holographic theory of Faulkner et al. [ref] and Faulkner and Polchinski [ref] , and their IR fermion $F_α$ is chosen by essentially identical criteria.

Emergent quantum criticality, Fermi surfaces, and AdS2 · Connections to holographic metals · 0.99
Then structure of Eq. ([ref]) is precisely that of the semi-holographic theory of Faulkner et al. [ref] and Faulkner and Polchinski [ref] , and their IR fermion $F_α$ is chosen by essentially identical criteria.

Semi-Holographic Fermi Liquids · Connections to holographic metals · 0.99
The structure of Eq. ([ref]) is essentially identical to Eqs. (6) and (52) of Nickel and Son [ref] .

Deconstructing holographic liquids · Connections to holographic metals · 1.00

Cites as background 11 papers

A discussion in the context of the gauge-gravity duality appears in a recent paper [ref] .

Fermi surfaces and gauge-gravity duality · The Metal-insulator transition on the triangular lattice · 0.97
We shall focus here on the compressible state [ref] known as the fractionalized Fermi liquid (FL*).

Weak magnetism and non-Fermi liquids near heavy-fermion critical points · Fractionalized Fermi liquids · 0.83
We shall focus here on the compressible state [ref] known as the fractionalized Fermi liquid (FL*).

Fractionalized Fermi liquids · Fractionalized Fermi liquids · 0.83

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