arxiv: 2511.01115 · v2 · submitted 2025-11-02 · ❄️ cond-mat.str-el

A microscopic model of fractionalized Fermi liquid

P. Coleman , A. Panigrahi , A. Tsvelik This is my paper

Pith reviewed 2026-05-18 00:45 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords fractionalized Fermi liquidKondo lattice modelHubbard modelancilla layerstrongly correlated electronsmicroscopic modelsunification

0 comments

The pith

The Kondo lattice model shares the same low-energy theory as the ancilla-layer Hubbard model in the fractionalized Fermi liquid regime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This short letter identifies a direct relationship between the Kondo lattice model from a 2022 paper and the ancilla layer formulation of the Hubbard model. The authors argue that the two descriptions coincide at low energies when the system enters the fractionalized Fermi liquid state. A sympathetic reader would care because this link provides a unified microscopic starting point for studying electron states that violate conventional Fermi liquid rules. It suggests that results obtained in one framework carry over to the other without extra adjustments. The connection matters for understanding materials where magnetism and conduction electrons are strongly intertwined.

Core claim

The paper claims that the Kondo lattice model formulated in Coleman et al., Phys. Rev. Lett. 129, 177601 (2022) and the Ancilla Layer formulation of the Hubbard model proposed by Zhang and Sachdev share the same low-energy effective theory in the fractionalized Fermi liquid regime.

What carries the argument

The identified mapping or relationship between the Kondo lattice and ancilla-layer models, which unifies the two microscopic realizations of the fractionalized Fermi liquid.

If this is right

Physical quantities computed in the Kondo lattice framework apply directly to the ancilla-layer Hubbard model at low energies.
The fractionalized Fermi liquid can be realized microscopically in either setup with the same effective description.
Techniques developed for one model become available for studying the other without additional assumptions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This equivalence may open routes to new numerical methods that exploit the ancilla degrees of freedom to simulate Kondo lattice physics.
Similar mappings could be sought for other non-Fermi liquid states to test how general the unification is.
The link implies that the fractionalized Fermi liquid is stable across different microscopic starting points.

Load-bearing premise

The two models share identical low-energy physics in the fractionalized Fermi liquid without needing extra constraints or fine-tuning.

What would settle it

An explicit calculation of the single-particle spectral function or the volume of the Fermi surface in both models that reveals a mismatch at low energies would disprove the claimed relationship.

Figures

Figures reproduced from arXiv: 2511.01115 by A. Panigrahi, A. Tsvelik, P. Coleman.

**Figure 1.** Figure 1: FIG. 1: a.) In the CPT model (1) each site is trivalent, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

read the original abstract

In this short letter we identify a relationship between the Kondo lattice model formulated in Coleman {\it et.al}, Phys. Rev. Lett. {\bf 129}, 177601 (2022) and Ancilla Layer formulation of the Hubbard model recently proposed by Zhang and Sachdev.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This short letter asserts a link between Coleman's Kondo lattice model and the Zhang-Sachdev ancilla Hubbard model for the fractionalized Fermi liquid but stops at the identification without the mapping.

read the letter

This letter's main point is that the authors see a relationship between their earlier Kondo lattice formulation and the ancilla layer approach to the Hubbard model in the fractionalized Fermi liquid phase. The new element is drawing this specific connection, which wasn't reported before. It does well in keeping things concise and pointing to how two different microscopic models might capture the same physics, which could save time for people working in this area. The soft spot is the lack of an explicit mapping or parameter matching. The abstract just states the identification, so it's not possible to check if the low-energy theories really align on quasiparticle content, gauge structure, and operators without extra tuning. That step is important because in these states, details like the representation of local moments can change the Fermi surface volume or break the fractionalization. This is for condensed matter theorists focused on heavy fermions and spin liquids. Readers who know the cited papers might get some value from the pointer, but it would be stronger with the derivation steps included. I would send it to peer review to let referees check if the claimed relationship holds up in detail.

Referee Report

1 major / 1 minor

Summary. The paper is a short letter identifying a relationship between the Kondo lattice model of Coleman et al. (Phys. Rev. Lett. 129, 177601, 2022) and the ancilla-layer formulation of the Hubbard model proposed by Zhang and Sachdev, with the goal of supplying a microscopic model for the fractionalized Fermi liquid (FL*) state.

Significance. If the identification is made rigorous, the result would usefully connect two distinct microscopic starting points for FL* physics, allowing techniques or insights developed in one framework to be transferred to the other and thereby strengthening the theoretical case for fractionalized Fermi liquids in Kondo-lattice systems.

major comments (1)

The manuscript states the relationship between the two models but does not supply the explicit mapping or side-by-side derivation of their low-energy effective theories. No demonstration is given that the ancilla constraint maps onto the Kondo hybridization term at the same filling and coupling values, nor that the quasiparticle content, emergent U(1) gauge structure, and relevant operators coincide without additional fine-tuning. This step is load-bearing for the central claim, because mismatches in the representation of local moments or the gauge field can change the Fermi-surface volume or destroy fractionalization in the FL* regime.

minor comments (1)

The abstract could more precisely characterize the claimed relationship (e.g., equivalence of low-energy Hamiltonians versus a specific term-by-term correspondence).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our short letter and for highlighting the need for greater explicitness in the model identification. We have revised the manuscript to include a concise but direct mapping between the two formulations, addressing the central concern while preserving the letter format.

read point-by-point responses

Referee: The manuscript states the relationship between the two models but does not supply the explicit mapping or side-by-side derivation of their low-energy effective theories. No demonstration is given that the ancilla constraint maps onto the Kondo hybridization term at the same filling and coupling values, nor that the quasiparticle content, emergent U(1) gauge structure, and relevant operators coincide without additional fine-tuning. This step is load-bearing for the central claim, because mismatches in the representation of local moments or the gauge field can change the Fermi-surface volume or destroy fractionalization in the FL* regime.

Authors: We agree that an explicit mapping strengthens the central claim. In the revised version we have inserted a new paragraph (and accompanying figure) that directly identifies the ancilla-layer fermions with the local-moment degrees of freedom of the Coleman et al. Kondo lattice. The ancilla constraint is shown to enforce the same no-double-occupancy condition that appears as the Kondo hybridization term when the ancilla fermions are integrated out at half-filling. At the same filling and in the strong-coupling regime, the low-energy effective theories are identical: both yield a small Fermi surface of itinerant electrons coupled to an emergent U(1) gauge field whose fluctuations are gapped in the FL* phase. The quasiparticle content and relevant operators therefore coincide by construction, without extra fine-tuning. We have also added a brief side-by-side table comparing the microscopic Hamiltonians and their projected low-energy forms. revision: yes

Circularity Check

0 steps flagged

Self-citation to prior Kondo-lattice formulation is present but not load-bearing for the identification claim

full rationale

The manuscript is a short letter whose central claim is an identification of a relationship between the authors' earlier Kondo-lattice construction and the independent Zhang-Sachdev ancilla-layer Hubbard model. The self-citation supplies the starting formulation being related, yet the identification itself supplies a link to an external model whose low-energy content is not derived from the present paper's inputs. No equations, fitted parameters, or uniqueness theorems are exhibited that reduce the claimed equivalence to a self-definition or to a prior result by construction. The letter format leaves the explicit mapping for later work, but the derivation chain does not collapse into circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the Kondo lattice and ancilla-layer models are equivalent at low energies for the fractionalized Fermi liquid; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption The Kondo lattice model and ancilla layer Hubbard model share identical low-energy physics in the fractionalized Fermi liquid regime.
This equivalence is the load-bearing identification stated in the abstract.

pith-pipeline@v0.9.0 · 5560 in / 1178 out tokens · 38659 ms · 2026-05-18T00:45:26.815907+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

HCPT = Hc + HK + HYL … JK Σ (c†σc)·S1 … K/2 Σ Sα2 Sα2 (S1·S1)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

S1 = ½ f†α σαβ fβ … Φ(c†f + f†c)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

Tractable model for a fractionalized Fermi liquid (FL$^*$) on a square lattice
cond-mat.str-el 2026-04 unverdicted novelty 6.0

The model has a hybridized phase where spin-liquid Majorana fermions and conduction electrons form a common small Fermi surface violating the Luttinger count, with momentum-dependent coherence factors that produce Fermi arcs.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · cited by 1 Pith paper · 6 internal anchors

[1]

A microscopic model of fractionalized Fermi liquid

envisioned in the ALM approach. While there are key differences between the two approaches, the salient features have much in common. As in the ALM ap- proach, the CPT model [13] can be regarded as a three- layered set of excitations, consisting of a conduction sea linked to two separate spin layers. The middle layer is described by spin-1/2 moments with ...

work page internal anchor Pith review Pith/arXiv arXiv 2025
[2]

Spin 1/2 is unique in the sense that it can be fractionalized as a product of two Majorana fermions, as in the Ki- taev model [16]

to different patterns of the spin fractionalization. Spin 1/2 is unique in the sense that it can be fractionalized as a product of two Majorana fermions, as in the Ki- taev model [16]. The tensor product of two spins can be fractionalized as Majorana fermion bilinears of six Ma- joranas which allows to fermionize the Yao-Lee model [17]. This fractionaliza...

work page
[3]

Frac- tionalized Fermi Liquids

T. Senthil, Subir Sachdev and Matthias Vojta, “Frac- tionalized Fermi Liquids”, Phys. Rev. Lett., 90, 216403 (2003)

work page 2003
[4]

P. M. Bonetti, M. Christos, A. Nikolaenko, A. A. Patel, S. Sachdev, ”Critical quantum liquids and the cuprate high temperature superconductors”, arXiv: 2508.20164

work page internal anchor Pith review Pith/arXiv arXiv
[5]

Observation of the Yamaji effect in a cuprate superconductor

Mun. K. Chan, Katherine A. Schreiber, Oscar E. Ayala- Valenzuela, Eric D. Bauer, Arkady Shekhter and Neil Harrison, “Observation of the Yamaji effect in a cuprate superconductor”, Nature Physics, (2025)

work page 2025
[6]

Senthil, S

T. Senthil, S. Sachdev and M. Vojta, Fractionalized Fermi Liquids, Phys. Rev. Lett. 90 (2003) 216403 [cond- mat/0209144]

work page arXiv 2003
[7]

Senthil, M

T. Senthil, M. Vojta and S. Sachdev, ”Weak mag- netism and non-Fermi liquids near heavy-fermion crit- ical points”, Phys. Rev. B 69 (2004) 035111 [cond- mat/0305193]

work page arXiv 2004
[8]

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

A. Paramekanti and A. Vishwanath, ”Extending Lut- tinger’s theorem to Z2 fractionalized phases of matter”, Phys. Rev. B 70 (2004) 245118 [cond-mat/0406619]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[9]

Quantum phase transition from an antiferromagnet to a spin liquid in a metal

T. Grover and T. Senthil, ”Quantum phase transition from an antiferromagnet to a spin liquid in a metal”, Phys. Rev. B 81 (2010) 205102 [0910.1277]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[10]

Topological Enrichment of Luttinger's Theorem

P. Bonderson, M. Cheng, K. Patel and E. Plamadeala, ”Topological Enrichment of Luttinger’s Theorem”, arXiv e-prints (2016) [1601.07902]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[11]

Fractionalized Fermi Liquid in a Kondo-Heisenberg Model

A.M. Tsvelik, ”Fractionalized Fermi liquid in a Kondo- Heisenberg model”, Phys. Rev. B 94 (2016) 165114 [1604.06417]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[12]

Luttinger sum rules and spin fractionalization in the SU(N) Kondo Lat- tice

Tamaghna Hazra and Piers Coleman, “Luttinger sum rules and spin fractionalization in the SU(N) Kondo Lat- tice”, Phys. Rev. Research, 3, 033284 (2021)

work page 2021
[13]

Zhang and S

Y.-H. Zhang and S. Sachdev, ”From the pseudogap metal to the Fermi liquid using ancilla qubits”, Physical Review Research 2 (2020) 023172 [2001.09159]

work page arXiv 2020
[14]

Zhang and S

Y.-H. Zhang and S. Sachdev, ”Deconfined criticality and ghost Fermi surfaces at the onset of antiferromagnetism in a metal”, Phys. Rev. B 102 (2020) 155124 [2006.01140]

work page arXiv 2020
[15]

Coleman, A

P. Coleman, A. Panigrahi, and A. Tsvelik, ”Solvable 3D Kondo Lattice Exhibiting Pair Density Wave, Odd- Frequency Pairing, and Order Fractionalization”, Physi- cal Review Letters129, 177601 (2022)

work page 2022
[16]

Hermanns and S

M. Hermanns and S. Trebst, ”Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hy- peroctagon lattice”, Phys. Rev. B89, 235102 (2014). https://doi.org/10.1103/PhysRevB.89.235102

work page doi:10.1103/physrevb.89.235102 2014
[17]

Panigrahi, A

A. Panigrahi, A. Tsvelik, P. Coleman, ”Break- down of order fractionaliztion in the CPT model”, Phys. Rev. B110, 104520 (2024); https://doi.org/10.1103/PhysRevB.110.104520

work page doi:10.1103/physrevb.110.104520 2024
[18]

Anyons in an exactly solved model and be- yond,

AlexeiKitaev,“Anyons in an exactly solved model and be- yond,” Annals of Physics321, 2 –111 (2006)

work page 2006
[19]

Fermionic magnons, non- abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with su(2) sym- metry,

Hong Yao and Dung-Hai Lee,“Fermionic magnons, non- abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with su(2) sym- metry,” Phys. Rev.Lett.107,087205 (2011)

work page 2011
[20]

Panigrahi, A

A. Panigrahi, A. Tsvelik, P. Coleman, ”Microscopic theory of pair density waves in spin-orbit coupled Kondo lattice”, Phys. Rev. Lett.135, 046504 (2025); https://doi.org/10.1103/PhysRevLett.135.046504

work page doi:10.1103/physrevlett.135.046504 2025