The Landscape of the Hubbard Model

Sachdev, Subir

doi:10.1142/9789814350525_0009

Cited by 26 publications

(45 citation statements)

References 137 publications

(259 reference statements)

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“…(4.1), which is reviewed in Ref. 27. The resulting lattice model is solvable in the limit of infinite-range hopping, or infinite d, combined with a particular large N limit [69][70][71][72][73].…”

Section: Discussionmentioning

confidence: 99%

“…By "complete set" we mean that we include not only the fundamental canonical fields of the underlying Lagrangian, but also composites or fractions of the fundamental fields. Composite fields can be introduced via a suitable Hubbard-Stratonovich decoupling of an interaction term, while fractions arise in the slave-particle construction along with emergent gauge fields [27]. There is no requirement that ψ fields introduced in this manner be canonical.…”

Section: Introductionmentioning

confidence: 99%

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Fermi surfaces and gauge-gravity duality

2011

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fermi surfaces and gauge-gravity duality

2011

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“…It is well-known how to find the eigenvalues of such a Hamiltonian [1]. For (5), this was first done in [2], and a pedagogical discussion can be found in [29]. We write…”

Section: Band Structure Of the Honeycomb Latticementioning

confidence: 99%

“…There are other types of interactions one could, in principle, include. For example, one could add a Hubbard interaction, penalizing electrons of opposite spin on the same lattice site [29]:…”

Section: Electronic "Phase Diagram"mentioning

confidence: 99%

“…We have two conserved charges n a = (n, n imb ) -a, b indices will label the electric/imbalance charge indices. Still, the key observation is that nothing in the derivations of Section 4 changes if we simply replace µdN in (29) with µ a dN a , replace (30) with + P = T s + µ a n a , etc. We conclude that the nonlinear hydrodynamics with imbalance modes is given by the equations…”

Section: Hydrodynamics With An Imbalance Modementioning

confidence: 99%

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Hydrodynamics of electrons in graphene

Lucas

Fong

2018

J. Phys.: Condens. Matter

370

451

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Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the "phase diagram" of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.

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Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity

Iizuka

Kundu

Narayan

et al. 2012

J. High Energ. Phys.

158

234

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Abstract:We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasiparticles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.

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The Landscape of the Hubbard Model

Cited by 26 publications

References 137 publications

Fermi surfaces and gauge-gravity duality

Fermi surfaces and gauge-gravity duality

Hydrodynamics of electrons in graphene

Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity

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