arxiv: 2512.19480 · v2 · submitted 2025-12-22 · ✦ hep-th · cond-mat.str-el

Recognition: 2 theorem links

· Lean Theorem

Quantum critical theories in a periodic potential: strange metallic thermoelectric and magnetotransport

Eric Nilsson , Koenraad Schalm

Authors on Pith no claims yet

Pith reviewed 2026-05-16 20:26 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el

keywords quantum critical theoriesholographic transportstrange metalsmagnetoresistancethermoelectric transporttranslational symmetry breakingperiodic potentialAdS black holes

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The pith

Holographic models show 2D quantum critical systems with zero-average periodic potentials conduct better and show B-linear magnetoresistance.

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

The paper examines DC and AC thermoelectric and magnetotransport in two-dimensional quantum critical theories with strong translational symmetry breaking from a periodic chemical potential lattice that averages to zero. Using holographic models of near-extremal AdS black holes, the authors show these systems become better conductors, with currents flowing around lattice obstacles in two dimensions. Electrical transport follows bad-metal behavior while thermal transport is Drude-like though not strictly Drude, and longitudinal magnetoresistance grows approximately linearly with magnetic field at large values, matching effective medium theory. These signatures arise from the interplay of quantum criticality and the missing average chemical potential scale, and may hold more generally for large potential variance or strong symmetry breaking.

Core claim

In holographic models of 2D quantum critical theories with strong translational symmetry breaking from a zero-average periodic chemical potential lattice, the systems become better conductors because currents flow around obstacles. They exhibit bad-metal electrical transport with Drude-like thermal transport, and display approximately B-linear longitudinal magnetoresistance at large fields similar to effective medium theory. The findings cover DC and AC transport and are expected to apply when the average chemical potential is nonzero.

What carries the argument

Near-extremal AdS black holes that model the DC and AC thermoelectric and magnetotransport of 2D quantum critical theories under strong translational symmetry breaking from zero-average periodic chemical potential lattices.

Load-bearing premise

Near-extremal AdS black holes accurately capture the DC and AC thermoelectric and magnetotransport of 2D quantum critical theories with strong translational symmetry breaking from a zero-average periodic chemical potential lattice.

What would settle it

Observation of strictly Drude electrical conductivity or quadratic-in-B longitudinal magnetoresistance in a real 2D quantum critical material with a zero-average periodic potential would contradict the results.

read the original abstract

We study DC and AC thermoelectric and magneto-transport in 2D quantum critical theories with strong translational symmetry breaking due to a % varying chemical potential lattice with zero average $\bar{\mu}=0$. The combination of quantum criticality and the absence of the average natural scale implies that such systems have idiosyncratic signatures that may apply more generally when the variance in the lattice potential far exceeds the average or for strong translational symmetry breaking in general. We model such theories holographically through near-extremal AdS black holes. We find that these systems (a) become \emph{better} conductors. In a 2D lattice, this can be explained by currents flowing around obstacles; (b) exhibit bad-metal electrical transport with Drude-like thermal transport, though it is not Drude, and, notably, (c) display an approximately $B$-linear longitudinal magnetoresistance at large fields, similar to Effective Medium Theory. We comment on how these results may apply when $\bar{\mu}\neq 0$.

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

The holographic calculation for zero-average periodic potentials yields B-linear magnetoresistance and a split between bad-metal electrical and more Drude-like thermal transport, but the 'better conductor via currents around obstacles' claim needs tighter support from the bulk geometry.

read the letter

The core result is that near-extremal AdS black holes with a zero-mean periodic chemical potential source produce three transport features: improved DC conductivity, bad-metal resistivity paired with thermal transport that looks closer to Drude, and roughly linear longitudinal magnetoresistance at large B. These are extracted from standard horizon or membrane-paradigm formulas applied to the Einstein-Maxwell system with the lattice potential imposed on the boundary. The absence of a nonzero average scale is what the authors argue drives the idiosyncratic signatures, and they note possible extensions to cases with nonzero mean mu. That combination of observables is not standard in the earlier holographic literature they cite, so the specific application is new enough to be worth checking. The numerics appear to follow established methods for holographic lattices, which makes the DC and AC coefficients reproducible in principle if the code and parameter choices are documented. The B-linear MR matching effective-medium expectations is the cleanest part, since it comes directly from the large-field asymptotics of the bulk solution. The weaker link is the physical story for why conductivity improves. The abstract ties it to currents flowing around obstacles in a 2D lattice, but the bulk geometry does not explicitly compute real-space current distributions or percolation paths; conductivity is read off from horizon data. Without an additional check showing how the effective medium result maps to microscopic flow patterns beyond the hydrodynamic regime, that interpretation stays one step removed from the calculation. The other two claims rest more directly on the model equations, so they are less exposed. This is aimed at condensed-matter theorists who use holography for strange-metal transport or who want concrete signatures to compare against experiments on disordered quantum critical systems. A reader already comfortable with AdS/CMT techniques will get the most out of the concrete numbers and the zero-mean case. It is solid enough on the technical side to merit a serious referee, mainly to verify the numerics and to see whether the current-path interpretation can be sharpened or replaced by a purely effective description.

Referee Report

2 major / 2 minor

Summary. The manuscript studies DC and AC thermoelectric and magnetotransport in 2D quantum critical theories with strong translational symmetry breaking induced by a periodic chemical potential lattice of zero average, modeled holographically via near-extremal AdS black holes. It reports that such systems become better conductors (attributed to currents flowing around obstacles in 2D), exhibit bad-metal electrical transport with Drude-like thermal transport, and display approximately B-linear longitudinal magnetoresistance at large fields, with parallels drawn to effective medium theory.

Significance. If the holographic results hold, the work offers a controlled framework for idiosyncratic transport signatures in quantum critical systems where potential variance dominates the average, potentially relevant to strange metals with strong inhomogeneity. The zero-average setup isolates effects that may generalize beyond the specific lattice.

major comments (2)

[Abstract and results section] Abstract and results section: The central claim that the systems become better conductors because currents flow around obstacles in a 2D lattice is an interpretive step not directly supported by the holographic calculation. Conductivity is extracted from horizon data or the membrane paradigm, but no explicit computation or visualization of real-space current distributions, percolation paths, or obstacle avoidance is provided to justify the mapping beyond the hydrodynamic regime.
[Holographic setup] Holographic setup: The near-extremal AdS black hole model is assumed to capture the DC/AC thermoelectric and magnetotransport without explicit checks that the duality assumptions remain independent of post-hoc choices in the zero-average periodic potential; this underpins all three claims and requires demonstration that the extracted quantities are not artifacts of the bulk geometry.

minor comments (2)

[Introduction] The notation for the zero-average chemical potential (denoted with overbar) should be introduced and used consistently from the introduction onward to avoid ambiguity.
[Discussion] Add explicit references to effective medium theory literature when comparing the B-linear magnetoresistance in claim (c).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive comments. We address each major comment below and indicate the revisions we plan to make.

read point-by-point responses

Referee: [Abstract and results section] Abstract and results section: The central claim that the systems become better conductors because currents flow around obstacles in a 2D lattice is an interpretive step not directly supported by the holographic calculation. Conductivity is extracted from horizon data or the membrane paradigm, but no explicit computation or visualization of real-space current distributions, percolation paths, or obstacle avoidance is provided to justify the mapping beyond the hydrodynamic regime.

Authors: We agree that the statement in the abstract and results regarding currents flowing around obstacles represents a physical interpretation rather than a direct output of the holographic computation. Our calculation shows an increase in conductivity for the zero-average periodic potential relative to the homogeneous case, obtained via the membrane paradigm. This enhancement is consistent with known behavior in 2D inhomogeneous media from effective medium theory, where current paths can avoid high-potential regions. We did not compute or visualize explicit real-space current distributions, as the focus was on integrated transport coefficients. In the revised manuscript we will rephrase the claim to present it explicitly as an analogy supported by effective medium considerations in 2D, add supporting references, and clarify that it is not a direct holographic visualization. revision: partial
Referee: [Holographic setup] Holographic setup: The near-extremal AdS black hole model is assumed to capture the DC/AC thermoelectric and magnetotransport without explicit checks that the duality assumptions remain independent of post-hoc choices in the zero-average periodic potential; this underpins all three claims and requires demonstration that the extracted quantities are not artifacts of the bulk geometry.

Authors: The near-extremal AdS black hole with a periodic chemical potential of zero average is a standard holographic setup for quantum critical systems with strong momentum relaxation. Transport coefficients are obtained from established methods (horizon data for DC, linearized bulk perturbations for AC) that apply generally to this class of geometries. We have verified that the reported qualitative features persist across a range of lattice amplitudes and periods. To address the concern directly, the revised manuscript will include a short robustness subsection demonstrating that the key transport signatures remain stable under modest variations in the potential profile, confirming they are not artifacts of the specific bulk geometry chosen. revision: partial

Circularity Check

0 steps flagged

Holographic derivation of transport coefficients is self-contained with no circular reduction

full rationale

The paper models 2D quantum critical theories via near-extremal AdS black holes sourced by a zero-average periodic chemical potential. DC/AC thermoelectric and magnetotransport coefficients are obtained by solving the bulk Einstein-Maxwell equations and extracting response functions from horizon data or the membrane paradigm. These quantities are direct outputs of the gravitational dynamics under the stated boundary conditions, not inputs or reparameterizations of the target observables. No self-citation chain, fitted parameter, or ansatz is invoked to force the reported signatures (better conductivity, bad-metal resistivity with Drude-like thermal transport, B-linear MR). The post-hoc geometric interpretation of currents around obstacles is not part of the derivation and does not alter the computed results. The chain is therefore independent.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; ledger therefore limited to the modeling assumption stated in the text. No free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)

domain assumption The AdS/CFT correspondence applies to near-extremal black holes modeling 2D quantum critical theories with periodic potentials
Invoked to justify the holographic computation of transport coefficients.

pith-pipeline@v0.9.0 · 5474 in / 1302 out tokens · 42945 ms · 2026-05-16T20:26:39.273117+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

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

We model such theories holographically through near-extremal AdS black holes... Stokes equations... σDC ≥ σ∞ = 1
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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

2D charge-neutral lattices... currents flowing around obstacles... Effective Medium Theory

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.

Reference graph

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