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Electrons Lost in Phase Space

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Pith's one-line read Patch bosonization cannot describe the 2D critical metal at N ~ 1; only synthetic limits are solvable.

desk verdict A genuinely useful negative result about patch bosonization at quantum criticality, with a clean cutoff-inconsistency argument and an honest admission that the strongest no-go claim rests on an unproved sum-versus-integral step. read the letter →

arxiv 2412.00924 v2 pith:O5BI5SSC submitted 2024-12-01 cond-mat.str-el hep-th

Tomer Ravid This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords patchbosonizationnon-FermiliquidquantumcriticalmetalFermisurfacesmall-Nlimitlarge-Ncutoffconsistencyboson-fermionmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Two-dimensional metals at a quantum critical point are among the simplest models with no Landau quasiparticles, and patch bosonization has often been used to solve them exactly. The paper argues that this method is fundamentally inapplicable to the physical case: the critical regime is not semiclassical, so the patched theory only works by treating its momentum cutoff inconsistently. Bosonization becomes exact only in synthetic limits, a small-$N$ limit already known in the literature and a new random double-large-$N$ limit, and neither is perturbatively connected to $N=1$. If the paper is right, the widely used bosonized non-Fermi liquid solution is an artifact, and controlled results for the critical metal must come from other methods. The paper also shows where bosonization does remain exact, namely in the high-frequency transport regime, where it agrees with anomaly-based exact results.

What carries the argument

Patch bosonization rewrites the Fermi surface as a set of discrete patches labelled by angle $\chi$ and tangential position $x_\parallel$, with cutoffs linked by $\Lambda_\parallel = \frac{1}{2}k_F\Delta\chi$; the resulting continuum of chiral bosons $\zeta(t,x,\chi)$ describes electron-hole pairs. The paper's argument rests on that cutoff structure: scale invariance forces dynamical uncertainty in $\chi$ and $x_\parallel$ to scale with the same power of energy, so the semiclassical separation of scales that justifies the continuum limit cannot hold in the critical regime. To make the failure quantitative, the paper uses the Euler-Maclaurin formula to show that a discrete sum over patches and its continuum integral differ by terms smaller than any power of the patch spacing, which is what blocks any perturbative expansion from the continuum bosonized solution back to the physical model.

What would settle it

Compute the exact difference between the discrete sum and continuum integral in the one-loop boson and fermion self-energy integrals at finite $\Delta\chi$; if the difference decays as a power of $\Delta\chi$ rather than faster than every power, the claimed nonperturbative barrier to reaching $N=1$ is absent. A complementary check is to compare the bosonized zero-frequency fermion propagator at nonzero momentum with a numerically exact calculation of the physical critical metal: the paper predicts the two disagree already at leading order.

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Extended reading notes

Core claim

The paper's central claim is that Fermi-surface patch bosonization is fundamentally inapplicable to a two-dimensional metal at a quantum critical point, except in synthetic limits that are not adiabatically connected to the physical model. The bosonized action (18) is quadratic, exactly solvable, and yields a scale-invariant non-Fermi liquid with fermion propagator (36); the paper argues that this solution is an artifact of treating the cutoff inconsistently. In the critical regime, the boson self-energy requires a continuum of patches with $\omega^{1/3}\gg \Lambda$, while the fermion self-energy requires $\Lambda \gg \omega^{1/3}$; no honest cutoff can satisfy both. The formalism is exact only in a small-$N$ limit ($N\to0$) or in a random double-large-$N$ limit, and perturbative expansions around either cannot cross over to $N=1$ because the discrete sum over patches differs from its continuum integral by terms smaller than any power of the patch spacing.

Load-bearing premise

The conclusion rests on the assertion that the difference between a discrete sum over patches and its continuum integral vanishes faster than every power of the patch spacing; if the mismatch were polynomial, a perturbative expansion around the continuum solution could in principle reach the realistic $N=1$ model.

Editorial extensions

If this is right

  • The bosonized non-Fermi liquid solution, including the anomalous fermion propagator (36), is not the physics of the physical $N=1$ critical metal; it is the exact solution of a different, synthetic model.
  • Only synthetic limits are controllable: the small-$N$ limit ($N\to0$), and the proposed random double-large-$N$ limit with many more bosonic than fermionic flavors; in both, bosonization is exact or effectively solvable.
  • Perturbation theory around these limits (the intra-patch curvature as a cubic $\zeta$ vertex, with Klein factors) is formally constructible but cannot converge to the correct $N=1$ answer once nonperturbative discrete-patch effects set in.
  • In the transport regime $\omega \gg v_F k$, bosonization is exact and reproduces anomaly-based results for the boson mass and the free Drude optical conductivity; the failure is specific to the critical regime $\omega \ll v_F k$.
  • The renormalized electron-hole continuum found in the bosonized theory is a consequence of its quadraticity and should not be assumed to be the true excitation spectrum of the critical metal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If this argument is right, any transport or spectral calculation for strange metals that starts from a bosonized critical Fermi surface inherits the same cutoff inconsistency, even if it dresses the result with higher loops; the problem is in the starting semiclassical description, not in the loop order.
  • The Euler-Maclaurin argument suggests a precise mathematical test: if a rigorous comparison of patch sums and integrals shows only exponential, not polynomial, suppression, then the crossover from continuum bosonization to the discrete patch model is genuinely nonperturbative, which would support the paper's main claim.
  • One could try to use anomaly-derived exact constraints at nonzero frequency and momentum; any discrepancy with the bosonized solution outside the transport regime would give an independent falsifier of the bosonized critical theory.
  • The proposed large-$N$ random model, though complicated, is the only solvable bosonizable non-Fermi liquid found; it may serve as a benchmark for testing whether non-bosonizable corrections at $N\sim1$ change critical exponents, which the paper leaves open.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper argues that patch bosonization of Fermi surfaces cannot describe the two-dimensional metal at a quantum critical point for N=1, except in contrived small-N and large-N limits. The argument has three parts: (i) Section 4.1 presents an internal-consistency check showing that the boson self-energy requires the continuum patch limit with ω^(1/3) much larger than the patch spacing, while the fermion self-energy requires the opposite inequality; (ii) Section 4.2 introduces a small-N bosonizable limit and claims that the crossover from the continuum of patches to the discrete-patch N=1 model is nonperturbative because the sum-integral difference vanishes faster than any power of the spacing; (iii) Sections 4.3-4.4 outline a random-coupling large-N bosonizable theory and an expansion in intra-patch curvature, with the caveat that the expansion has not been completed. The paper concludes that bosonization is fundamentally inapplicable except in synthetic limits.

Significance. If correct, the paper would be an important and timely critique of a widely used formalism; it also makes a constructive proposal for a new large-N bosonizable model. The paper is commendably explicit about its own open issues (e.g., Section 4.4) and about the distinction between internal inconsistency and mere disagreement with conventional wisdom. However, the central no-go claim depends on a nonperturbative sum-versus-integral assertion that is not proved for the singular propagators of the theory; the paper's strength is therefore more in the clear formulation of the cutoff problem than in a definitive demonstration of the nonperturbative conclusion.

major comments (2)
  1. [Section 4.2, after Eq. (66)] The assertion that the difference between the discrete sum over patches and the continuum integral is smaller than any power of δx is essential for the claim that the small-N continuum theory is not perturbatively connected to the N=1 model, but it is not established for the actual integrands. The Euler-Maclaurin argument assumes the summand is smooth on the integration domain, while the boson self-energy in Eq. (19) has a pole at ω = v_F k cosχ regulated only by iε, and the fermion self-energy in Eq. (53) inherits the same singular structure. The Matlab check on generic smooth functions does not probe this regime. For singular integrands, the discrepancy typically decays as a power of δx (or is O(1) if the pole and the patch spacing scale incompatibly), which would turn the claimed nonperturbative crossover into a perturbatively controlled expansion in the patch spacing and invalidate the conclusion that the continuum limits are fundamentally disconnected from the discrete model. Please provide a proof or careful analytic/numerical treatment of the sum-integral discrepancy for the actual propagators, or weaken the conclusion accordingly.
  2. [Abstract and Section 4.4] The abstract states that it is 'at least formally possible to construct perturbative expansions around these synthetic limits,' but Section 4.4 (final paragraph) reports that one of the two order-γ² patch-local diagrams was not calculated and concludes that 'it is clear that more work is required to determine whether the perturbation theory around linearized bosonization is sensible.' This is an internal inconsistency between the level of confidence in the abstract and the evidence presented. Either provide the missing calculation and a demonstration that the C(γ) counterterm renders the expansion well-defined, or explicitly reformulate the abstract as a conjecture rather than a shown result.
minor comments (5)
  1. [Section 2.2, Eq. (18)] The word 'one-dimensinoal' should read 'one-dimensional'; also, the phrase 'the latter of which' is used ambiguously in the following sentence.
  2. [Section 4.2, Eq. (66)] The name 'Euler-Macluarin' is a typo for 'Euler-Maclaurin'.
  3. [Section 4.2, after Eq. (62)] The sentence using 'dχdy = 1/N' would benefit from specifying that this holds in the rescaled units with the cutoffs in Eq. (56); as written, the measure appears dimensionally inconsistent.
  4. [Section 4.3, Eq. (73)] The summation index n in the geometric series is overloaded with the number of fermion flavors n; consider renaming one of them to avoid confusion.
  5. [Section 3.4, Eq. (49)] The notation 'iη∂t' is introduced without defining η; a sentence explaining that η is the coefficient of the irrelevant kinetic term would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central no-go argument is a self-consistency check; acknowledged technical gaps are correctness risks, not circular reductions.

full rationale

The paper's central claim—that patch bosonization is fundamentally inapplicable to the physical critical metal—is an internal consistency argument, not a reduction to its inputs. In §4.1 it derives, from the RPA/patched propagators and the scaling of Eqs. (37)/(48), that the boson self-energy requires a continuum of patches with δχ ≫ Λ while the fermion self-energy requires Λ ≫ ω^{1/3}, so no single cutoff can satisfy both. This is a contradiction within the bosonized framework; it does not define bosonization in terms of the conclusion. The small-N and double-large-N constructions are explicitly presented as synthetic limits whose expansions are separate (§4.2–4.4), and the claim that no perturbative expansion connects them to N=1 rests on the Euler–Maclaurin argument after Eq. (66). That step is asserted and checked numerically rather than proved—a correctness gap, not a circular identification: the nonperturbative crossover does not follow by construction from a fitted parameter or from an earlier self-citation. The paper also openly flags missing support at §4.2 ('This conclusion is confirmed by playing with discretized integrals on Matlab') and §4.4 ('It is clear that more work is required'); these are limitations, not circularity. No load-bearing self-citation or imported uniqueness theorem is used to forbid alternatives; the 'only bosonizable model I have been able to find' is an explicitly personal statement. I find no step in which a 'prediction' is equivalent by construction to its inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central negative claim does not rely on fitted numerical parameters; it is a consistency argument built from scaling and cutoff logic. The main unproved inputs are the one-loop scaling at the critical point and the asserted nonperturbative character of the sum-to-integral crossover. The proposed synthetic limits introduce ad hoc random couplings and a tunable C-term whose values are undetermined. No new particles, fields, or forces are postulated.

free parameters (3)
  • bare boson mass m0^2 = set to cancel the reverse-screening shift in Eq. (19)
    In Section 3.1 the bare mass is chosen by hand to cancel the negative 'reverse screening' contribution and tune the metal to criticality. This is a tuning choice rather than a fit to data, and it is part of the bosonized solution rather than the central negative claim.
  • random coupling variance g^2 = not fitted; chosen with zero mean and variance g^2 delta_ij delta_IJ
    The double-large-N model in Section 4.3 introduces Gaussian random couplings giJ as an ad hoc device to suppress flavor-changing processes. The distribution is chosen by hand to make bosonization work, and its variance is absorbed into a 't Hooft-like coupling.
  • bare coefficient C0(gamma) = unknown; to be tuned at each order in gamma
    In Section 4.4 the author introduces a (d_y^2 zeta)^2 term with an initially unknown bare coefficient C0(gamma) to regulate UV divergences. The value is not derived or measured; it is a parameter that would require tuning for the proposed perturbation theory to be consistent.
assumptions (4)
  • domain assumption The one-loop self-consistent RPA calculation in the patched theory gives the correct low-energy scaling of fermion and boson self-energies at the critical point, including omega^(1/3) broadening of the patch angle.
    Section 4.1 uses this scaling to derive the contradictory cutoff requirements. If higher-loop effects changed the scaling, the inconsistency could disappear, so this is a load-bearing premise.
  • ad hoc to paper The difference between a discrete sum over patches and its continuum integral is smaller than any power of the spacing, making the crossover to discrete patches nonperturbative.
    Section 4.2, after Eq. (66), asserts this based on Euler-Maclaurin boundary terms and Matlab checks rather than providing a proof. The conclusion that physical N=1 cannot be reached from the continuum limit depends on this property.
  • domain assumption Random Gaussian couplings self-average so that the boson self-energy series remains a sum of single-body diagrams, and the 't Hooft scaling n/N controls the expansion.
    Section 4.3 borrows the SYK-style random-coupling device and assumes it does not qualitatively alter the physics at finite N. This is needed for the proposed large-N bosonizable model.
  • domain assumption The chiral anomaly of the patch U(1) symmetry gives exact constraints on the critical metal, as used in Section 5.2.
    The paper invokes anomaly-based exact results from the cited literature to check the bosonized gap and the optical conductivity. If this anomaly reasoning were incorrect, parts of the discussion would need revision, though the central inconsistency argument is largely independent.

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Cite this review

Pith. "Pith review of Electrons Lost in Phase Space." pith.science (2026). https://pith.science/paper/O5BI5SSC

@misc{pith2026241200924,
  author       = {Pith},
  title        = {Pith review of: Electrons Lost in Phase Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O5BI5SSC}},
  note         = {Machine review of arXiv:2412.00924}
}
abstract

I review the formalism of patch bosonization of Fermi surfaces, with a focus on the problem of a two-dimensional metal at a quantum critical point. I argue that this formalism is fundamentally inapplicable to the problem, except in synthetic limits. One such limit is the small-$N$ limit, which was already discussed in early studies of the problem; a similar but slightly less unphysical large-$N$ limit is proposed. I show that it is at least formally possible to construct perturbative expansions around these synthetic limits. However, I argue that nonperturbative effects become important when $N\sim1$.

Figures

Figures reproduced from arXiv: 2412.00924 by the authors.

Figure 1
Figure 1. The Fermi surface is broken into patches (indicated by red dashed lines) at angular intervals of ∆χ. Momenta within the patch are labeled by the normal and tangential coordinates k⊥ and k∥. In order for the patches to fully cover the Fermi surface without overlapping, one must impose a cutoff on k∥ such that kF ∆χ = 2Λ∥. and with the sums over χ and y∥ appropriately discretized in accordance with (4). By contrast, x… view at source ↗
Figure 2
Figure 2. An electron-hole pair of momentum k can have a continuum of energies: if k is locally tangential to the Fermi surface, then the pair’s energy vanishes, whereas if k is locally normal to the Fermi surface, then the energy is vF k. and the tangential position x∥ and patch angle χ as flavor labels. The result is a bosonic action for an infinite collection of linearly dispersing electron-hole fields. The continuum of bo… view at source ↗
Figure 3
Figure 3. The only boson self-energy diagram in the bosonized theory. Wavy lines are bare bosonic propagators, while dashed lines are bare electron-hole propagators. 3 Properties of the Bosonized Solution 3.1 Boson Propagator Since the bosonized action (18) is quadratic, the only thing a boson can do is turn into an electron-hole pair of the same energy and momentum but of any patch, and the only thing this electron-hole pair… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The only two diagrams contributing to the electron-hole propagator. A dashed line is a bare electron-hole propagator, while a wavy line with a bubble is a full boson propagator. 3.2 Electron-Hole Propagator and Renormalized Electron-Hole Contin￾uum Similarly to the abo…
Figure 5
Figure 5. Figure 5: The two patch-local (i.e., initial χ equal to final χ) corrections to the electron-hole propagator to order γ 2 . Dashed lines are bare electron-hole propagators. The wavy line with the filled bubble is a full linearized ϕ-propagator from (22), with all corrections fro…

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Forward citations

Cited by 2 Pith papers

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

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Reference graph

Works this paper leans on

31 extracted references · 22 canonical work pages · cited by 2 Pith papers

  1. [1]

    A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics. Courier Corporation, 2012

    work page 2012

  2. [2]

    QuantumPhaseTransitionsofMetalsinTwoSpatial Dimensions. I. Ising-Nematic Order,

    M.A.MetlitskiandS. Sachdev,“QuantumPhaseTransitionsofMetalsinTwoSpatial Dimensions. I. Ising-Nematic Order,”Phys. Rev. B, vol. 82, p. 075127, 7 2010.doi: 10.1103/PhysRevB.82.075127 . [Online]. Available:https://link.aps.org/doi/ 10.1103/PhysRevB.82.075127

    doi:10.1103/physrevb.82.075127 2010

  3. [3]

    Low-Energy Dynamics of the Spinon-Gauge System,

    J. Polchinski, “Low-Energy Dynamics of the Spinon-Gauge System,”Nuclear Physics B, vol. 422, no. 3, pp. 617–633, 1994,issn: 0550-3213. doi: https://doi.org/10. 1016/0550- 3213(94)90449- 9. [Online]. Available:https://www.sciencedirect. com/science/article/pii/0550321394904499

    arXiv 1994

  4. [4]

    Low-Energy Effective Theory of Fermi Surface Coupled with U(1) Gauge Field in 2 + 1Dimensions,

    S.-S. Lee, “Low-Energy Effective Theory of Fermi Surface Coupled with U(1) Gauge Field in 2 + 1Dimensions,” Phys. Rev. B, vol. 80, p. 165102, 16 2009.doi: 10.1103/ PhysRevB.80.165102. [Online]. Available:https://link.aps.org/doi/10.1103/ PhysRevB.80.165102

    work page 2009

  5. [5]

    Large-N Theory of Critical Fermi Surfaces,

    I. Esterlis, H. Guo, A. A. Patel, and S. Sachdev, “Large-N Theory of Critical Fermi Surfaces,” Physical Review B, vol. 103, no. 23, 2021, issn: 2469-9969. doi: 10 . 1103/physrevb.103.235129 . [Online]. Available:http://dx.doi.org/10.1103/ PhysRevB.103.235129

    work page 2021

  6. [6]

    Luttinger’s Theorem and Bosonization of the Fermi Surface,

    F. D. M. Haldane, “Luttinger’s Theorem and Bosonization of the Fermi Surface,” arXiv preprint cond-mat/0505529, 2005

    arXiv 2005

  7. [7]

    Bosonization of Fermi Liquids,

    A. C. Neto and E. Fradkin, “Bosonization of Fermi Liquids,” Physical Review B, vol. 49, no. 16, p. 10877, 1994

    work page 1994

  8. [8]

    Bosonized Fermions in Three Dimensions,

    A Luther, “Bosonized Fermions in Three Dimensions,”Physics Reports, vol. 49, no. 2, pp. 261–266, 1979

    work page 1979

Show all 31 references
  1. [9]

    Low-Energy Properties of Fermions with Singular Interactions,

    B. L. Altshuler, L. B. Ioffe, and A. J. Millis, “Low-Energy Properties of Fermions with Singular Interactions,”Phys. Rev. B, vol. 50, pp. 14048–14064, 19 1994.doi: 10.1103/PhysRevB.50.14048. [Online]. Available:https://link.aps.org/doi/10. 1103/PhysRevB.50.14048. 42

    1994 doi

  2. [10]

    Nonpertur- bative Behavior of the Quantum Phase Transition to a Nematic Fermi Fluid,

    M. J. Lawler, D. G. Barci, V. Fern’andez, E. Fradkin, and L. Oxman, “Nonpertur- bative Behavior of the Quantum Phase Transition to a Nematic Fermi Fluid,”Phys. Rev. B, vol. 73, p. 085101, 8 2006.doi: 10.1103/PhysRevB.73.085101 . [Online]. Available: https://link.aps.org/doi/10...

    2006 doi

  3. [11]

    Geometrical Approach to Bosonization of D > 1 Dimensional (Non)-Fermi Liquids,

    D. Khveshchenko, “Geometrical Approach to Bosonization of D > 1 Dimensional (Non)-Fermi Liquids,”Physical Review B, vol. 52, no. 7, p. 4833, 1995

    1995

  4. [12]

    Bosonization of Current-Current Interactions,

    D. V. Khveshchenko, “Bosonization of Current-Current Interactions,”Physical Review B, vol. 49, no. 24, 16893–16898, Jun. 1994,issn: 1095-3795.doi: 10.1103/physrevb. 49.16893. [Online]. Available:http://dx.doi.org/10.1103/PhysRevB.49.16893

    1994 doi

  5. [13]

    Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits,

    L. V. Delacrétaz, Y.-H. Du, U. Mehta, and D. T. Son, “Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits,”Physical Review Research, vol. 4, no. 3, p. 033131, 2022

    2022

  6. [14]

    Postmodern Fermi Liquids,

    U. B. Mehta, “Postmodern Fermi Liquids,” Ph.D. dissertation, The University of Chicago, 2023

    2023

  7. [15]

    (Pre-)Modern(Non-)Fermiliquids,

    D.Khveshchenko,“(Pre-)Modern(Non-)Fermiliquids,” arXiv preprint arXiv:2409.02316, 2024

    2024 arXiv

  8. [16]

    Renormalization Group for Non-Relativistic Fermions: II,

    R. Shankar, “Renormalization Group for Non-Relativistic Fermions: II,” inQuantum Field Theory and Condensed Matter: An Introduction. Cambridge University Press, 2017, 305–318. doi: 10.1017/9781139044349.017

    2017 doi

  9. [17]

    Effective Field Theory and the Fermi Surface,

    J. Polchinski, “Effective Field Theory and the Fermi Surface,” arXiv preprint hep- th/9210046, 1992

    1992

  10. [18]

    Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals,

    D. V. Else, R. Thorngren, and T Senthil, “Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals,” Physical Review X, vol. 11, no. 2, p. 021005, 2021

    2021

  11. [19]

    Phe- nomenology of the Normal State of Cu-O High-Temperature Superconductors,

    C. Varma, P. B. Littlewood, S Schmitt-Rink, E Abrahams, and A. Ruckenstein, “Phe- nomenology of the Normal State of Cu-O High-Temperature Superconductors,”Phys- ical Review Letters, vol. 63, no. 18, p. 1996, 1989

    1996

  12. [20]

    Universal Theory of Strange Metals from Spatially Random Interactions,

    A. A. Patel, H. Guo, I. Esterlis, and S. Sachdev, “Universal Theory of Strange Metals from Spatially Random Interactions,”Science, vol. 381, no. 6659, pp. 790–793, 2023. 43

    2023

  13. [21]

    Effect of Fermi Surface Curvature on Low- Energy Properties of Fermions with Singular Interactions,

    A. V. Chubukov and D. V. Khveshchenko, “Effect of Fermi Surface Curvature on Low- Energy Properties of Fermions with Singular Interactions,”Phys. Rev. Lett., vol. 97, p. 226403, 22 2006. doi: 10 . 1103 / PhysRevLett . 97 . 226403. [Online]. Available: https://link.aps.org/doi/...

    2006 doi

  14. [22]

    Path Integral Formulation of Chiral Invariant Fermion Models in Two-Dimensions,

    K. Furuya, R. E. Gamboa Saravi, and F. A. Schaposnik, “Path Integral Formulation of Chiral Invariant Fermion Models in Two-Dimensions,”Nucl. Phys. B, vol. 208, pp. 159–181, 1982.doi: 10.1016/0550-3213(82)90191-2

    1982 doi

  15. [23]

    Path-Integral Measure for Gauge-Invariant Fermion Theories,

    K. Fujikawa, “Path-Integral Measure for Gauge-Invariant Fermion Theories,”Phys. Rev. Lett., vol. 42, pp. 1195–1198, 18 1979.doi: 10.1103/PhysRevLett.42.1195 . [Online]. Available:https://link.aps.org/doi/10.1103/PhysRevLett.42.1195

    1979 doi

  16. [24]

    Gifts from Anomalies: Exact Results for Landau Phase Transitions in Metals,

    Z. D. Shi, H. Goldman, D. V. Else, and T. Senthil, “Gifts from Anomalies: Exact Results for Landau Phase Transitions in Metals,” SciPost Physics, vol. 13, no. 5, p. 102, 2022

    2022

  17. [25]

    Fluctuation Spectrum of2 + 1D Critical Fermi Surface and its Aplication to Optical Conductivity and Hydrodynamics,

    H. Guo, “Fluctuation Spectrum of2 + 1D Critical Fermi Surface and its Aplication to Optical Conductivity and Hydrodynamics,”arXiv preprint arXiv:2311.03458, 2023

    2023 arXiv

  18. [26]

    Chiral Non-Fermi Liquids,

    S. Sur and S.-S. Lee, “Chiral Non-Fermi Liquids,”Physical Review B, vol. 90, no. 4, p. 045121, 2014

    2014

  19. [27]

    Perturbative Non-Fermi Liquids From Nonlinear Bosonization,

    U. B. Mehta, “Perturbative Non-Fermi Liquids From Nonlinear Bosonization,” talk given at KITP donference on Correlated Gapless Quantum Matter, 2024. [Online]. Available: https://online.kitp.ucsb.edu/online/gapless24/mehta/

    2024

  20. [28]

    An Introduction to Bosonization,

    D. Sénéchal, “An Introduction to Bosonization,” inTheoretical Methods for Strongly Correlated Electrons, Springer, 2004, pp. 139–186

    2004

  21. [29]

    Bosonization for Beginners—Refermionization for Experts,

    J. Von Delft and H. Schoeller, “Bosonization for Beginners—Refermionization for Experts,” Annalen der Physik, vol. 510, no. 4, pp. 225–305, 1998

    1998

  22. [30]

    An Exact Method for Bosonizing the Fermi Surface in Arbitrary Dimensions,

    T. Park and L. Balents, “An Exact Method for Bosonizing the Fermi Surface in Arbitrary Dimensions,” SciPost Physics, vol. 16, no. 3, p. 069, 2024

    2024

  23. [31]

    Loop Current Fluctuations and Quantum Critical Transport,

    Z. D. Shi, D. V. Else, H. Goldman, and T. Senthil, “Loop Current Fluctuations and Quantum Critical Transport,”SciPost Physics, vol. 14, no. 5, p. 113, 2023. 44

    2023

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