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Extending Luttinger's theorem to Z(2) fractionalized phases of matter

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arxiv cond-mat/0406619 v1 pith:X7R5C3NX submitted 2004-06-25 cond-mat.str-el

Arun Paramekanti (KITP/UCSB) , Ashvin Vishwanath (MIT) This is my paper · ORCID
classification cond-mat.str-el
keywords fillingfractionalizedfermiluttingermomentumtheoremarisingbalance
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abstract

Luttinger's theorem for Fermi liquids equates the volume enclosed by the Fermi surface in momentum space to the electron filling, independent of the strength and nature of interactions. Motivated by recent momentum balance arguments that establish this result in a non-perturbative fashion [M. Oshikawa, Phys. Rev. Lett. {\bf 84}, 3370 (2000)], we present extensions of this momentum balance argument to exotic systems which exhibit quantum number fractionalization focussing on $Z_2$ fractionalized insulators, superfluids and Fermi liquids. These lead to nontrivial relations between the particle filling and some intrinsic property of these quantum phases, and hence may be regarded as natural extensions of Luttinger's theorem. We find that there is an important distinction between fractionalized states arising naturally from half filling versus those arising from integer filling. We also note how these results can be useful for identifying fractionalized states in numerical experiments.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 93 citations worldwide. Full citation record

  1. Thermal SU(2) lattice gauge theory for intertwined orders and hole pockets in the cuprates

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    Monte Carlo study of thermal SU(2) gauge theory with Higgs boson reconciles Fermi arcs and p/8 hole pockets while describing intertwined orders and d-wave superconductivity at lower temperatures.

  2. A microscopic model of fractionalized Fermi liquid

    cond-mat.str-el 2025-11 unverdicted novelty 4.0 of 10

    Identifies a relationship between the Kondo lattice model and the ancilla layer Hubbard model as a microscopic realization of the fractionalized Fermi liquid.

  3. Lectures on insulating and conducting quantum spin liquids

    cond-mat.str-el 2025-12 unverdicted novelty 3.0 of 10

    The notes argue that the FL* state — small pockets plus a quantized spin-liquid anomaly — resolves the ADMR pocket and v_F >> v_Delta problems that defeated holon-metal and plain fermionic-parton theories of the cuprates.

  4. Fractionalized Fermi liquids and the cuprate phase diagram

    cond-mat.str-el 2025-08 unverdicted novelty 3.0 of 10

    Reviews the FL* theory for cuprates using ancilla layer models and SU(2) gauge theories to explain pseudogap hole pockets of area p/8, Fermi arcs, and transitions to d-wave superconductivity and Fermi liquid behavior.

  5. The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions

    cond-mat.str-el 2025-01 conditional novelty 3.0 of 10

    The paper attributes the cuprate 'foot' to a disordered spin-density-wave transition and the 'fan' to a disorder-tuned FL-to-FL* Fermi-volume-changing transition described by a two-dimensional Yukawa-SYK model.

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