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arxiv: 2508.20164 · v7 · submitted 2025-08-27 · ❄️ cond-mat.str-el · hep-th

Fractionalized Fermi liquids and the cuprate phase diagram

Pietro M. Bonetti , Maine Christos , Alexander Nikolaenko , Aavishkar A. Patel , Subir Sachdev This is my paper

Pith reviewed 2026-05-18 20:41 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-th
keywords cuprate superconductorsfractionalized Fermi liquidpseudogaphole pocketsAncilla Layer ModelSU(2) gauge theorystrange metald-wave superconductivity
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The pith

The pseudogap phase in cuprates is a fractionalized Fermi liquid with hole pockets of area p/8.

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

This paper reviews a theoretical framework for cuprate superconductors based on the fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. In this state, hole pockets each have fractional area p/8 at hole doping p, in contrast to the area p/4 predicted by spin density wave theory. Magnetotransport measurements, including the Yamaji angle, show evidence of hole pocket quasiparticles that tunnel coherently between layers, consistent with the FL* picture. The single-band model is realized through the Ancilla Layer Model whose fluctuations are governed by an SU(2) gauge theory of critical Dirac spinons; Monte Carlo studies of the thermal gauge theory convert the pockets into Fermi arcs. Increasing doping drives a transition to a conventional Fermi liquid through a strange metal regime, while confinement of the FL* state yields d-wave superconductivity.

Core claim

The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site, the Ancilla Layer Model. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a d-wave superconductor via a Kosterlitz-Thouless transition of h/(2e) vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase drives a transition to a常规F

What carries the argument

Ancilla Layer Model (ALM), a layer construction with a pair of ancilla qubits per site that realizes the FL* state and whose fluctuations are governed by an SU(2) gauge theory of critical Dirac spinons.

If this is right

  • Magnetotransport data including the Yamaji angle confirm coherent interlayer tunneling of quasiparticles from pockets of area p/8.
  • Monte Carlo simulation of the thermal SU(2) gauge theory converts the pockets into Fermi arcs seen in photoemission.
  • Confinement of the FL* state at low temperature produces d-wave superconductivity through a Kosterlitz-Thouless transition of h/(2e) vortices with nodal quasiparticles.
  • Doping increase takes the system from FL* through a strange metal to a conventional Fermi liquid via a critical quantum charge liquid without symmetry breaking.

Where Pith is reading between the lines

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

  • Griffiths effects near quantum phase transitions in the disordered metal may account for the extended non-Fermi liquid regime at low temperatures across optimal doping.
  • The same charge-liquid description of the FL*-FL transition could be tested in other doped Mott insulators that lack symmetry-breaking order.
  • Quantitative predictions for the specific-heat coefficient or resistivity in the strange metal regime would follow from further analysis of the disordered critical charge liquid.

Load-bearing premise

The pseudogap phase at low doping is the fractionalized Fermi liquid state of the Ancilla Layer Model whose fluctuations are governed by an SU(2) gauge theory of critical Dirac spinons.

What would settle it

Quantum oscillation or magnetotransport experiments that find hole pocket areas of p/4 rather than p/8, or that show incoherent interlayer tunneling at low doping.

Figures

Figures reproduced from arXiv: 2508.20164 by Aavishkar A. Patel, Alexander Nikolaenko, Maine Christos, Pietro M. Bonetti, Subir Sachdev.

Figure 1
Figure 1. Figure 1: Cuprate phase diagram from [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Cuprate phase diagram from Ref. [2]. Annotations in blue have been added. We use a theory of a fractionalized Fermi liquid (FL*) of the pseudogap to connect to the other phases in the sections noted. critical state is associated with the collective dynamics of electron charge, a critical quantum ‘charge’ liquid, characteristic of the strange metal regime of Figs. 1 and 2—its theoretical description builds … view at source ↗
Figure 3
Figure 3. Figure 3: Definitions of Fermi liquid (FL) and fractionalized Fermi liquid (FL*) for a general electronic lattice model. Here ρ is the total density of electrons of both spins, and areas are measured as a fraction of Brillouin zone area. The mod 2 accounts for fully filled bands. These ideas apply rather generally to electronic lattice models, and are summarized schematically in [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 4
Figure 4. Figure 4: A Kondo lattice of conduction electrons c of density p coupled to S = 1/2 spins S1. All lattices are two-dimensional, although only one-dimensional projections are shown. spin model of Section 3 in Eq. (3.1) with a Fermi surface of free electrons cα of density p in a second band: HKL = X i<j J1,ij S1i · S1j − X i,j tij c † iα cjα + X i JK 2 S1i · c † iασαβciβ (2.1) We have now written the spins as S1i , ra… view at source ↗
Figure 5
Figure 5. Figure 5: Phase diagram of the Kondo lattice. The quoted areas are per spin. Neither phase has any symmetry breaking, but there is nevertheless a quantum phase transition (a Higgs transition in an emergent gauge theory) associated with Fermi volume change [36, 37]. This U(1) is distinct from the global charge conservation symmetry in Eq. (4.4), under which only maps ciα → e iθciα, while all other fields remain invar… view at source ↗
Figure 6
Figure 6. Figure 6: Cartoon pictures of different states of doped antiferromagnets; adapted from Ref. [126]. The areas are those that would be measured by a probe such as quantum oscillation. The AF metal has long-range antiferromagnetic order, and the reduced Brillouin zone is shown with the dashed line. The other phases do not break any symmetries. The open circles are holons, and these are assumed fermionic in the holon me… view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of the mapping from a single-band Hubbard model with decoupled ancilla qubits, to a single band with free fermions coupled to a bilayer antiferromagnet. The Schrieffer-Wolff transformation is derived in Ref. [152], and the Hubbard-Stratonovich transformation is derived in Ref. [51]. The layer numbers of the layer construction with ancilla qubits are indicated in the bottom picture; these appea… view at source ↗
Figure 8
Figure 8. Figure 8: Phases of the Ancilla Layer Model. The noted areas are per spin. The phases are distinguished by the condensation of the boson Φ, which hybridizes the conduction electrons in the top layer with the fermionic spinons in the middle layer. These states map onto those of a Hubbard model H2 = −µ ′ c † α cα + U(c † ↑ c↑)(c † ↓ c↓) (2.13) with parameters U = 3J 2 K 8J⊥ , µ′ = µ + 3J 2 K 16J⊥ . (2.14) While the ab… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the phases of the Kondo lattice model in [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between (a) the quantum dimer theory of the square lattice FL* state [126] and the (b) ancilla layer theory. The dashed green dimer is the state ciα f † 1iα created by the hybridization Φ in the ALM. Note that the ALM has exactly N blue dimers more than the dimer model, and these extra dimers are the number in a trivial rung-singlet bilayer antiferromagnet. • The electron quasiparticle of FL* i… view at source ↗
Figure 11
Figure 11. Figure 11: Zero energy electronic spectral weight (as would be measured in photoemission) in the ancilla mean field theory of the FL* phase, from Ref. [51]. Fluctuation corrections appear later in Figs. 24 and 25, where they lead to Fermi arcs. (a) (b) cω f1ω [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a) Photoemission data from Ref. [11] along momenta (π, ky). The red points are in a region where there is no pseudogap, and so the electronic dispersion crosses the Fermi energy. The blue points show the gapped electronic excitation in the pseudogap. The green points identify the position of a shoulder in the energy distribution curve, presumed to be the superconducting gap. (b) From Ref. [51]. The red l… view at source ↗
Figure 13
Figure 13. Figure 13: Dispersion of bosonic spinons in a square lattice spin liquid, from Eq. (3.17). For Q and λ, we anticipate that the fluctuations will be un-important unless associated with the gauge symmetry in Eq. (3.12). So we focus only on the phases of the Qij and parameterize Qi,i+ˆx = Q¯ exp (iΘix) Qi,i+ˆy = Q¯ exp (iΘiy) , (3.19) and express the phases in terms of continuum field (aτ , ax, ay) via Θix(τ ) = ηiax(r… view at source ↗
Figure 14
Figure 14. Figure 14: Phase diagram of the U(1) gauge theory with bosonic spinons, Eq. (3.27. The N´eel order appears in a Higgs phase where the bosonic spinons are condensed. The VBS order appears in the confining phase, and is induced by the Berry phases of the confining monopoles. The same phase diagram applies to the fermionic spinon theory in Eq. (3.50), and the SO(5) σ-model with the WZW term in Eq. (3.57). Lmonopole = −… view at source ↗
Figure 15
Figure 15. Figure 15: Background π flux acting on the spinons f, and also on the chargons B. Next we insert Eq. (3.32) into Eq. (3.1), and perform Hubbard-Stratonovich transformation to obtain an effective Hamiltonian for the spinons, following the same procedure as for bosonic spinons. We skip the intermediate steps, and focus directly on the fermion bilinear Hamiltonian on symmetry grounds. From the gauge transformations in … view at source ↗
Figure 16
Figure 16. Figure 16: Dispersion of fermionic spinons in Eq. (3.41). Eq. (3.27)), and such single monopole terms are expected to drive a strong instability to confinement. So we don’t consider this U(1) spin liquid here. We can now easily diagonalize the Hamiltonion in Eq. (3.39), and obtain the fermionic dispersion spectrum analogous to Eq. (3.17) ωk = ±2J [PITH_FULL_IMAGE:figures/full_fig_p032_16.png] view at source ↗
Figure 17
Figure 17. Figure 17 [PITH_FULL_IMAGE:figures/full_fig_p035_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Mean field phase diagram obtained by minimization of the Higgs potential of B, E2 +E4 (from Ref. [58]). For r > 0, there is no Higgs condensate ⟨B⟩ = 0, and we obtain the same phases as in the insulator from the confinement of the fermionic spinons described by Eq. (3.43). For r < 0, ⟨B⟩ ̸= 0, and we minimized the Higgs potential with only nearest neighbor interactions by setting V11 = V22 = 0. Modificati… view at source ↗
Figure 19
Figure 19. Figure 19: Common dispersion of the fermionic spinons f, and the bosonic chargons B. The continuum fermionic fields X are defined at zero energy, while the continuum bosonic fields Bˆ are defined at the minimum energy. hb↵i6= 0: N´eel order (a) (b) (a) (b) or Valence bond solid (VBS) Phase A (π,0) stripe Phase A (0,π) stripe Phase B d-wave SC Phase C d-density (a) (b) hBi =0 hBi6=0 hBi =0 [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 20
Figure 20. Figure 20: Proposed phase diagram of LX Bˆ . Here µ ℓ are the Pauli matrices acting in the boson valley space of [PITH_FULL_IMAGE:figures/full_fig_p041_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The two distinct Higgs fields in the ancilla layer theory of the single band Hubbard model. Φ hybridizes conduction electrons in the top layer with spinons in the middle layer. B couples the spinons of the bottom layer to the upper layers. HY = − 1 2 X i h i Tr  F † 1iB † iFi  + ig Tr  C † iB † iFi  + H.c.i = X i h i  B1i f † iα f1iα − B2i εαβfiα f1iβ  + H.c. +ig  B1i f † iα ciα − B2i εαβfiα ciβ  … view at source ↗
Figure 22
Figure 22. Figure 22: From Ref. [50]. Low energy spectrum of FL*, showing the photoemission spectrum of hole pockets of [PITH_FULL_IMAGE:figures/full_fig_p044_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: From Ref. [50]. Mean-Field phase diagram of Eq. (4.9) a function of the further neighbor interactions V11 and V22, extending that in [PITH_FULL_IMAGE:figures/full_fig_p045_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: The right panel shows the electron spectral function measured in photoemission computed in Ref. [50] from HKLmf +HSLf +HY after averaging over the Monte Carlo simulation of B and Uij in Eq. (5.5). The spectrum with B = U = 0 is in [PITH_FULL_IMAGE:figures/full_fig_p046_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: From Ref. [50]. (a) The photoemission electron spectral function of [PITH_FULL_IMAGE:figures/full_fig_p046_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: (A) Cooper pairing the Fermi surface quasiparticles in FL* leads to d-SC* state, with 8 nodal Bogoliubov quasiparticles (red), and 4 nodal spinons (pink) shown earlier in [PITH_FULL_IMAGE:figures/full_fig_p047_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: From Ref. [85]. We show how Higgs condensing B leads to a d-wave superconducting state with four nodes for the case of the hole doped cuprates. We show the normal state spectral density at the Fermi level (top left) where we indicate the gapless points along the Brillouin zone diagonal associated with the c electron (blue circle), f1 spinons (green circle) and f spinons (red circle). The spin liquid Dirac… view at source ↗
Figure 28
Figure 28. Figure 28: From Ref. [85]. We show an example of the momentum resolved spectral function at the Fermi level of an example normal state at small doping in the electron doped cuprates (left) and the corresponding spectral function after B condenses and drives a phase transition to a d-wave superconductor (right). In both cases, we denote the Brillouin zone diagonal with a dashed white line and the Dirac point associat… view at source ↗
Figure 29
Figure 29. Figure 29: From Ref. [50]. The bond density (left panel) and the distribution of the phase of the superconducting order parameter (right panel) on a 192 × 192 lattice at low temperature in the thermal ensemble defined by Eq. (5.5). Eqs. (4.10,4.11) that different orientations of the complex vector (B1, B2) correspond to different local orders. At the vortex core, it is preferential for the orientation of B to rotate… view at source ↗
Figure 30
Figure 30. Figure 30: From Ref. [89]. Illustration of the α electron pocket of Harrison and Sebastian [193], from the combination of the 4 Fermi arcs of the γ hole pockets of [PITH_FULL_IMAGE:figures/full_fig_p051_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: From Ref. [89]. (a) A computation similar to that in Ref. [194], by applying a charge density wave to HKLmf in Eq. (2.4); this computation does not include spinons. In addition to the observed α pocket, there is a large β hole pocket which is not observed. (b) A computation including spinons. A modulated B condensate is applied to HKLmf + HSLf + HY in Eqs. (2.4), (3.43), (5.3). The mixing with the spinons… view at source ↗
Figure 32
Figure 32. Figure 32: The SYK model: fermions undergo the transition (‘collision’) shown with quantum amplitude Uij;kℓ. to the right-hand-side of the Boltzmann equation. However, in stark contrast to the Boltzmann equation, statistically independent collisions are not assumed, and quantum interference between successive collisions is accounted for: this is the key to building up a many-body state with non-trivial entanglement.… view at source ↗
Figure 33
Figure 33. Figure 33: Self-energy for the fermions of H in Eq. (7.1) in the limit of large N. The intermediate Green’s functions are fully renormalized. averaging over Uij;kℓ as independent random variables with Uij;kℓ = 0 and |Uij;kℓ| 2 = U 2 . This expansion can be used to compute graphically the Green’s function in imaginary time τ G(τ ) = − 1 N X i D T  ci(τ )c † i (0)E , (7.2) where T is the time-ordering symbol, the an… view at source ↗
Figure 34
Figure 34. Figure 34: (a) From Ref. [203]. Plot of the 65536 many-body eigenvalues of a N = 32 Majorana SYK Hamiltonian; however, the analytical results quoted here are for the SYK model with complex fermions which has a similar spectrum. The coarse-grained low-energy and low-temperature behavior is described by Eq. (7.10) and Eq. (7.12). (b) Schematic of the lower energy density of states of a supersymmetric generalization of… view at source ↗
Figure 35
Figure 35. Figure 35: Self-energies of the fermions and bosons in the Hamiltonian HY in Eq. (7.15). The intermediate Green’s functions are fully renormalized. 220, 221], has been a much better starting point for a non-zero spatial dimensional theory, as shown in Section 8. In the spirit of Eq. (7.1), a model of fermions ci (i = 1 . . . N) and bosons ϕℓ (ℓ = 1 . . . N) with a Yukawa coupling gijℓ between them is now considered … view at source ↗
Figure 36
Figure 36. Figure 36: On the left is the cuprate phase diagram from Ref. [2]; annotations in blue have been added. On the right is the ALM, with the Higgs fields Φ and B. In Section 8 we consider the transition from the FL* pseudogap to the Fermi liquid focusing on the Higgs field Φ, while setting B = 0. The transition from the pseudogap to the d-SC was discussed in Section 6 as a theory of the dynamics of B, while setting Φ t… view at source ↗
Figure 37
Figure 37. Figure 37: Schematic phase diagram of a single-band metal with a Fermi surface volume changing quantum transition without a broken symmetry on either side of the transition. For the Kondo lattice, the transition is ‘inverted’ as shown in [PITH_FULL_IMAGE:figures/full_fig_p062_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Diagrams for the conductivity for the theory Lc + Lv + Lϕ. of fermion bilinears, such as the conductivity, is described. These can be obtained by inserting external sources into Eq. (8.9) and then taking the variational derivatives with respect to them. This leads to the graphs shown in [PITH_FULL_IMAGE:figures/full_fig_p065_38.png] view at source ↗
Figure 40
Figure 40. Figure 40: From Ref. [114] and adapted from Patel et al. [116]. (a) Localization length Lα of overdamped bosonic eigenmodes of Seϕ in Eq. (9.8) as a function of their energy eα. (b,c,d) Pictures of the corresponding bosonic eignfunctions. The ‘foot’ is described by the localized bosons. The universal, self-averaging, 2D-YSYK theory of the ‘fan’ by Patel et al. [90] and Li et al. [108] in Section 8, applies to the re… view at source ↗
Figure 41
Figure 41. Figure 41: From the quantum Monte Carlo study of the coupled boson-fermion model of Ref. [117]. The disordered averaged energy of the lowest boson eigenmode e0. The coupling λ is the analog of the tuning parameter s in Eq. (9.2). Note the extended Griffiths phase at low T. the bosonic eigenmodes. Below the minimum, we find a logarithmic increase of Lα with decreasing eα: this logarithmic increase is precisely that e… view at source ↗
Figure 42
Figure 42. Figure 42 [PITH_FULL_IMAGE:figures/full_fig_p073_42.png] view at source ↗
read the original abstract

We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping $p$, in contrast to the area $p/4$ in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a $d$-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase in the ALM drives a transition to a conventional Fermi liquid (FL) at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript reviews a theoretical framework for the cuprate phase diagram, centered on a fractionalized Fermi liquid (FL*) description of the pseudogap phase at low doping p. It predicts hole pockets of area p/8 (distinct from p/4 in SDW theory) and argues that magnetotransport data, including the Yamaji angle, provide evidence for coherent interlayer tunneling of these quasiparticles. The FL* state is realized via the Ancilla Layer Model (ALM) with a pair of ancilla qubits per site; fluctuations are governed by an SU(2) gauge theory of critical Dirac spinons, whose thermal Monte Carlo simulation converts pockets into Fermi arcs in the single-particle spectral function. One confinement route yields d-wave superconductivity via a Kosterlitz-Thouless transition of h/2e vortices with nodal Bogoliubov quasiparticles and charge-order halos. Increasing doping drives an FL*-FL metal-metal transition via a critical quantum charge liquid (SYK extension to 2D with disorder), followed by Griffiths-induced non-Fermi-liquid regimes at low T.

Significance. If the central claims hold, the work supplies a unified, largely parameter-free account of the cuprate diagram that links the pseudogap, strange-metal, and superconducting regimes to concrete experimental signatures such as the p/8 pocket area and Yamaji-angle oscillations. The Monte Carlo simulation of the SU(2) gauge theory constitutes an independent numerical check on the fluctuation spectrum, and the formulation of the metal-metal transition without symmetry breaking is a notable conceptual advance.

major comments (2)
  1. [Monte Carlo study of the SU(2) gauge theory and magnetotransport discussion] The abstract and the section describing magnetotransport consistency state that the FL* hole pockets produce the observed Yamaji angle and interlayer coherence. However, the Monte Carlo study of the thermal SU(2) gauge theory is reported to transform the same pockets into Fermi arcs in the single-particle spectral function. No explicit regime or parameter window is identified in which sharp quasiparticle poles survive for coherent interlayer tunneling (required for the Yamaji-angle signal) while the identical gauge fluctuations destroy coherence in photoemission. This tension is load-bearing for the claimed experimental support.
  2. [Route to confinement and d-wave superconductivity] In the paragraph outlining the Kosterlitz-Thouless route to confinement, the d-wave superconductor is described as possessing nodal Bogoliubov quasiparticles with anisotropic velocities and vortices surrounded by charge-order halos. It is not shown how these coherent excitations emerge from the same SU(2) gauge theory whose fluctuations already convert pockets to arcs in the normal-state spectral function; a quantitative estimate of the quasiparticle residue or scattering rate across the transition would strengthen the claim.
minor comments (2)
  1. [Ancilla Layer Model introduction] The definition of the doping parameter p is used consistently for pocket area but should be restated explicitly when the ALM construction is introduced to avoid any ambiguity for readers.
  2. [Magnetotransport comparison] A short table summarizing the predicted pocket areas (p/8 vs. p/4) and the corresponding experimental probes would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying these important points of clarification regarding the consistency of the FL* framework with both spectroscopic and transport data. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Monte Carlo study of the SU(2) gauge theory and magnetotransport discussion] The abstract and the section describing magnetotransport consistency state that the FL* hole pockets produce the observed Yamaji angle and interlayer coherence. However, the Monte Carlo study of the thermal SU(2) gauge theory is reported to transform the same pockets into Fermi arcs in the single-particle spectral function. No explicit regime or parameter window is identified in which sharp quasiparticle poles survive for coherent interlayer tunneling (required for the Yamaji-angle signal) while the identical gauge fluctuations destroy coherence in photoemission. This tension is load-bearing for the claimed experimental support.

    Authors: The Monte Carlo simulation addresses the effects of thermal SU(2) gauge fluctuations at temperatures characteristic of the pseudogap regime, where these fluctuations broaden the quasiparticle poles and produce Fermi arcs in the single-particle spectral function, in agreement with ARPES. Magnetotransport signatures such as the Yamaji angle, however, are measured at lower temperatures where thermal gauge fluctuations are suppressed, permitting coherent interlayer tunneling of the fractionalized hole-pocket quasiparticles. The FL* construction naturally accommodates this separation of scales: in-plane single-particle coherence is fragile to gauge fluctuations while interlayer matrix elements remain sufficient for quantum oscillations. We will revise the manuscript to delineate these temperature and doping windows explicitly and to reference the relevant low-temperature transport calculations that support coherent tunneling in the FL* state. revision: yes

  2. Referee: [Route to confinement and d-wave superconductivity] In the paragraph outlining the Kosterlitz-Thouless route to confinement, the d-wave superconductor is described as possessing nodal Bogoliubov quasiparticles with anisotropic velocities and vortices surrounded by charge-order halos. It is not shown how these coherent excitations emerge from the same SU(2) gauge theory whose fluctuations already convert pockets to arcs in the normal-state spectral function; a quantitative estimate of the quasiparticle residue or scattering rate across the transition would strengthen the claim.

    Authors: We agree that the manuscript would benefit from a clearer account of how coherence is restored upon confinement. In the Kosterlitz-Thouless transition, proliferation of h/2e vortices confines the SU(2) gauge fields, allowing the underlying d-wave pairing to produce nodal Bogoliubov quasiparticles with anisotropic velocities; the charge-order halos follow from the coupling of the superconducting order parameter to residual charge fluctuations. Although the present review does not contain new numerical estimates, we will add a paragraph that summarizes existing calculations of the quasiparticle residue and scattering rate across the confinement transition in the SU(2) gauge theory literature, thereby connecting the normal-state arcs to the superconducting-state excitations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; predictions tested against independent magnetotransport data

full rationale

The paper reviews the FL* framework and ALM construction from prior literature, states the p/8 pocket area as a prior theoretical prediction, and reports consistency with external magnetotransport observations (Yamaji angle and interlayer tunneling). The Monte Carlo simulation of the SU(2) gauge theory is presented as an independent numerical result that converts pockets to arcs. No derivation step within the manuscript reduces a claimed prediction to a fitted parameter, self-citation, or definitional input by construction; the central claims rest on the match between the established model and separate experimental signatures rather than internal tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on the assumption that the pseudogap is an FL* state realized by the ancilla layer construction, plus the existence of a deconfined SU(2) gauge theory with critical Dirac spinons; no new free parameters are introduced in the review itself beyond those inherited from prior FL* papers.

axioms (2)
  • domain assumption The intermediate-temperature pseudogap phase at low doping is a fractionalized Fermi liquid (FL*) with hole pockets of area p/8.
    Stated in the opening paragraph as the root of the framework.
  • domain assumption Fluctuations are captured by an SU(2) gauge theory of a background spin liquid with critical Dirac spinons.
    Introduced when describing the ALM and Monte Carlo study.
invented entities (1)
  • Ancilla Layer Model (ALM) with pair of ancilla qubits per site no independent evidence
    purpose: To realize the FL* state in a single-band model
    New construction introduced to describe the fractionalized phase; no independent experimental signature provided beyond consistency with transport.

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  3. Hole and spin dynamics in an anti-ferromagnet close to half filling

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    A conserving diagrammatic theory for the doped Hubbard model shows four magnetic polaron hole pockets, doping-softened magnons, and pseudogap-like lattice modulation responses near half filling.

  4. 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.

  5. Superconductivity and fractionalized magnetic excitations in CeCoIn5

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    Inelastic neutron scattering on CeCoIn5 shows spin excitations consistent with fractionalized spinons coexisting with d-wave superconductivity near a quantum critical point.

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

    cond-mat.str-el 2025-07 unverdicted novelty 6.0

    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.

  7. A microscopic model of fractionalized Fermi liquid

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

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

  8. Lectures on insulating and conducting quantum spin liquids

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

    The fractionalized Fermi liquid state obtained by doping quantum spin liquids resolves key experimental difficulties in cuprate pseudogap metals and d-wave superconductors.

Reference graph

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