Fractionalized Fermi liquids with the ghost-Gutzwiller Ansatz

Carlos Mejuto-Zaera; Ivan Pasqua; Michele Fabrizio

A simple ghost-Gutzwiller Ansatz yields a fractionalized Fermi liquid phase and a cuprate-like diagram in the single-band t-J model.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-15 06:18 UTC pith:FFBDTUQW

load-bearing objection Abstract-only claim of FL* from ghost-Gutzwiller on t-J; technique-level interest, but emergence vs. Ansatz artifact cannot be checked yet. the 3 major comments →

arxiv 2607.12410 v1 pith:FFBDTUQW submitted 2026-07-14 cond-mat.str-el cond-mat.supr-con

Fractionalized Fermi liquids with the ghost-Gutzwiller Ansatz

Ivan Pasqua , Carlos Mejuto-Zaera , Michele Fabrizio This is my paper

classification cond-mat.str-el cond-mat.supr-con

keywords fractionalized Fermi liquidFL*ghost-Gutzwiller Ansatzt-J modelcupratespseudogapd-wave superconductivityLuttinger's theorem

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper claims that a fractionalized Fermi liquid (FL*) phase arises naturally in the single-band t-J model when the ground state is approximated by a ghost-Gutzwiller variational Ansatz that can be optimized at mean-field cost. FL* metals combine fractionalized quasiparticles with ordinary ones and violate Luttinger's theorem; they have long been proposed as candidates for the pseudogap of underdoped cuprates. The authors report that the optimized Ansatz produces a temperature-doping phase diagram containing a low-doping FL* region, a d-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby recovering the main qualitative features of cuprate phenomenology from a single, inexpensive variational calculation. If correct, the result shows that the essential physics of fractionalization and the cuprate diagram can be captured without heavy numerical machinery once the right fractionalization channels are built into the trial wave function.

Core claim

A FL* phase emerges in the single-band t-J model through a simple ghost-Gutzwiller Ansatz optimized at mean-field cost. The resulting temperature-doping phase diagram encompasses a low-doping FL*, a d-wave superconducting dome, and an overdoped conventional Fermi liquid, reproducing key qualitative features of cuprate phenomenology.

What carries the argument

The ghost-Gutzwiller Ansatz: a variational wave function that introduces auxiliary "ghost" fractionalization channels inside a Gutzwiller projected state, allowing simultaneous treatment of conventional and fractionalized quasiparticles and optimized by a mean-field calculation.

Load-bearing premise

That the ghost-Gutzwiller channels, once mean-field optimized, faithfully capture the true low-energy physics of the t-J model rather than forcing FL*-like features by construction of the trial state.

What would settle it

A controlled numerical benchmark (exact diagonalization on small clusters or high-accuracy DMRG/ variational Monte Carlo without ghost channels) showing that the t-J ground state at low doping remains a conventional Fermi liquid or lacks the FL* signatures predicted by the optimized ghost-Gutzwiller Ansatz.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Abstract-only claim of FL* from ghost-Gutzwiller on t-J; technique-level interest, but emergence vs. Ansatz artifact cannot be checked yet.

read the letter

The one thing to know: this abstract claims that a simple ghost-Gutzwiller Ansatz, optimized at mean-field cost, produces an FL* phase inside the single-band t-J model and a T–doping diagram with low-doping FL*, a d-wave SC dome, and overdoped FL. That combination, if it holds up in the full paper, is a useful technique-level result for cuprate/pseudogap work. It is not a first-principles proof that FL* is the true t-J ground state.

What looks new is the packaging: ghost channels plus Gutzwiller projection, cheap enough to scan temperature and doping, and reported to land on the qualitative cuprate sequence. Gutzwiller and slave-particle treatments of t-J, and FL* as a pseudogap candidate, are established; the contribution is that this particular variational route is claimed to deliver the whole diagram without heavy numerics. Credit that if the full text shows clean diagnostics (Luttinger volume, energy comparisons, phase boundaries) and honest comparison to known t-J benchmarks.

The soft spot is real and load-bearing for the “emerges in the t-J model” language. Ghost fractionalization channels can put FL*-like states inside the variational manifold by construction. Without the paper showing that FL* survives when those channels are constrained or removed, or that the same signatures appear in unbiased methods, the low-doping FL* may be an artifact of the trial state rather than a property of the Hamiltonian. Mean-field variational treatments of t-J are known to over-stabilize ordered or fractionalized phases; that is a standard caveat, not a manufactured one. Free parameters (J/t, longer-range hoppings, ghost hybridizations) will also matter for how much of the diagram is robust.

We only have the abstract, so derivation, diagnostics, and benchmarks cannot be inspected. The stress-test concern about forced fractionalization is the right one to carry into the full text; it may or may not land once the math is visible.

Who it is for: people who already work on variational/slave-particle approaches to doped Mott systems and want a cheap FL* route for phase-diagram scans. Not for someone looking for a definitive resolution of the t-J ground state. It deserves a serious referee if the full paper ships the Ansatz details, Luttinger diagnostics, and energy comparisons; desk-reject only if those are missing. I would not cite from the abstract alone, and I would not put it in reading group until the full text is out. Send to peer review when the manuscript is complete—the claim is important enough inside the field to warrant referee time, even if revision will demand tighter controls on the ghost sector.

Referee Report

3 major / 0 minor

Summary. The manuscript claims that a fractionalized Fermi liquid (FL*) phase emerges in the single-band t-J model from a mean-field-optimized ghost-Gutzwiller variational Ansatz. The resulting temperature-doping phase diagram is reported to contain a low-doping FL* region, a d-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology. Because only the abstract is available, the explicit form of the Ansatz, the optimization procedure, the Luttinger-volume diagnostics, energy comparisons, and any benchmarks against exact or high-accuracy t-J results cannot be inspected.

Significance. If the central claim is substantiated, the work would supply a computationally inexpensive variational route to FL* physics inside the single-band t-J model and a compact cuprate-like T-doping diagram. That would be of clear interest to the strongly correlated community, provided the FL* is shown to be a genuine property of the t-J low-energy physics rather than an artifact of the ghost channels. The abstract advertises a simple mean-field cost and a parameter-light construction; those practical strengths would be valuable if the fidelity of the Ansatz is established.

major comments (3)

Only the abstract is available for review. The load-bearing claim that FL* 'emerges' in the t-J model therefore cannot be verified: the explicit ghost-Gutzwiller wavefunction, the mean-field free-energy functional, the Luttinger-volume diagnostic, the energy comparisons that place FL* below competing states, and any checks against exact diagonalization or high-accuracy t-J benchmarks are all inaccessible. Without those elements the emergence claim cannot be assessed.
The abstract's emergence language is in tension with the structure of ghost-Gutzwiller constructions. Ghost fractionalization channels introduce auxiliary degrees of freedom that can violate Luttinger's theorem by design. For the reported low-doping FL* to be attributed to the t-J model rather than to the variational manifold, the manuscript must demonstrate that FL* survives when the ghost channels are constrained or removed, or that the same diagnostics appear in unbiased methods. No such control is described in the abstract; this is the central fidelity assumption that must be tested before the phase diagram can be read as a property of the t-J model.
Mean-field variational treatments of the t-J model are known to over-stabilize ordered or fractionalized phases. The abstract asserts a full temperature-doping diagram (FL*, d-wave dome, overdoped FL) obtained at mean-field cost. Without finite-size scaling, comparison to known t-J ground-state energies, or an assessment of the variational bias, it is unclear whether the reported sequence of phases is robust or an artifact of the mean-field approximation.

Circularity Check

0 steps flagged

No demonstrable circularity from the abstract; FL* via ghost-Gutzwiller is a variational claim, not a by-construction reduction.

full rationale

Only the abstract is available, so no derivation chain, equations, or self-citations can be inspected for load-bearing reductions. The abstract states that an FL* phase emerges in the single-band t-J model through a mean-field-optimized ghost-Gutzwiller Ansatz and that the resulting T–doping diagram includes low-doping FL*, a d-wave SC dome, and overdoped FL. That is a standard variational claim: an Ansatz is chosen, optimized, and phases are reported. Under the circularity criteria, this is not self-definitional (no quote shows X defined as Y), not a fitted input renamed as prediction (no experimental curve-fitting is reported), and not a self-citation uniqueness or ansatz-smuggling chain (no citations appear). Concerns that ghost fractionalization channels might force FL*-like violations of Luttinger’s theorem by construction are fidelity/correctness risks about the trial manifold versus the true t-J ground state; they cannot be elevated to circularity without equations exhibiting that the reported FL* diagnostics are identical to the Ansatz inputs by definition. Honest non-finding: score 0, empty steps.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 1 invented entities

The central claim rests on the t-J Hamiltonian plus a variational ghost-Gutzwiller wavefunction whose ghost sector is introduced to allow fractionalization at mean-field cost. No experimental curve-fitting is stated in the abstract, but the Ansatz form and the identification criteria for FL* are modeling choices that carry the result.

free parameters (2)

t-J microscopic ratios (J/t and any longer-range hoppings)
Standard model parameters whose chosen values set the relative scales of magnetism and kinetic energy and therefore move phase boundaries.
ghost-sector variational parameters / hybridizations
Amplitudes and channels optimized in the mean-field procedure; their number and form control whether fractionalization is allowed and how it couples to physical electrons.

axioms (3)

domain assumption The single-band t-J model is an adequate effective description of doped cuprate CuO2 planes for the phases under discussion.
Invoked throughout the abstract as the microscopic setting in which FL* and the cuprate-like diagram are obtained.
ad hoc to paper A mean-field-optimized ghost-Gutzwiller Ansatz faithfully represents the low-energy physics of the t-J model, including possible fractionalization.
The abstract’s emergence claim and phase diagram rest on this variational approximation; its fidelity is not independently established in the abstract.
domain assumption FL* is identified by coexistence of fractionalized and conventional quasiparticles together with violation of Luttinger’s theorem.
Standard field definition used to label the low-doping phase; diagnostics themselves are not shown in the abstract.

invented entities (1)

ghost degrees of freedom in the Gutzwiller Ansatz no independent evidence
purpose: Provide fractionalization channels so that an FL*-like mean-field solution can appear while preserving the no-double-occupancy constraint.
Introduced as part of the Ansatz; the abstract does not supply an independent experimental handle (e.g., a predicted spectral feature unique to the ghosts) outside the phase diagram itself.

pith-pipeline@v1.1.0-grok45 · 6022 in / 2762 out tokens · 45051 ms · 2026-07-15T06:18:37.800922+00:00 · methodology

0 comments

read the original abstract

Fractionalized Fermi liquids ($\mathrm{FL}^{\!*}$), elusive metallic states characterized by fractionalized quasiparticles alongside conventional ones and defying Luttinger's theorem, are prime candidates for the pseudogap regime of underdoped cuprates. We show that a $\mathrm{FL}^{\!*}$ phase emerges in the single-band $t$-$J$ model through a simple ghost-Gutzwiller Ansatz, optimized at the cost of a mean-field calculation. The resulting temperature-doping phase diagram encompasses a low-doping $\mathrm{FL}^{\!*}$, a $d$-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology.

Fractionalized Fermi liquids with the ghost-Gutzwiller Ansatz

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)