High-temperature charge-4e superconductivity in SU(4) interacting fermions

Jiangping Hu; Shao-Hang Shi; Zhengzhi Wu; Zi-Xiang Li

arxiv: 2604.15056 · v1 · submitted 2026-04-16 · ❄️ cond-mat.str-el · cond-mat.quant-gas· cond-mat.supr-con

High-temperature charge-4e superconductivity in SU(4) interacting fermions

Shao-Hang Shi , Zhengzhi Wu , Jiangping Hu , Zi-Xiang Li This is my paper

Pith reviewed 2026-05-10 09:59 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.quant-gascond-mat.supr-con

keywords charge-4e superconductivitySU(4) fermionsquantum Monte CarloBerezinskii-Kosterlitz-Thouless transitionhigh-Tc superconductivitypseudogaplattice fermion model

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The pith

A sign-problem-free SU(4) fermion model hosts high-temperature charge-4e superconductivity as its ground state.

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

The paper introduces a lattice model of fermions with SU(4) symmetry and shows through quantum Monte Carlo that charge-4e superconductivity emerges without engineered interactions or sign problems. At zero temperature the strong-coupling regime is dominated by this quartet condensation. At finite temperature the system undergoes a Berezinskii-Kosterlitz-Thouless transition identified by a superfluid-stiffness jump consistent with charge-4e carriers, and the transition temperature rises nearly linearly with interaction strength. A pseudogap appears above the transition from phase fluctuations. This supplies a concrete, numerically exact platform for quartet superconductivity that can be realized in moiré or cold-atom systems.

Core claim

In the non-engineered SU(4) model, charge-4e superconductivity is the primary ground state at zero temperature in the strong-coupling regime. At finite temperature, in the absence of charge-2e superconductivity, a Berezinskii-Kosterlitz-Thouless transition occurs with a universal jump in superfluid stiffness matching a charge-4e condensate, and the transition temperature increases nearly linearly with interaction strength while a pseudogap opens from strong phase fluctuations.

What carries the argument

The SU(4)-symmetric interacting fermion lattice Hamiltonian simulated by sign-problem-free quantum Monte Carlo, which directly yields the superfluid stiffness and pairing correlations that diagnose the charge-4e condensate via its BKT jump.

If this is right

Charge-4e superconductivity is stable as the leading order at strong coupling even when charge-2e pairing is absent.
The critical temperature scales linearly with interaction strength, allowing higher transition temperatures by increasing coupling.
Strong phase fluctuations produce a pseudogap in the single-particle spectrum above the transition.
The model provides an unbiased benchmark for experimental searches in moiré materials and ultracold atoms.

Where Pith is reading between the lines

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

If the linear Tc scaling persists in experiment, stronger interactions could push quartet transition temperatures beyond those of conventional Cooper-pair superconductors.
The absence of the sign problem permits direct simulation of the competition between charge-4e order and nearby phases such as charge-density waves.
Confirmation of charge-4e condensation would motivate targeted searches for quartet pairing in other strongly correlated platforms where standard pairing is suppressed.

Load-bearing premise

The observed stiffness jump and correlations arise from charge-4e condensation rather than competing orders or finite-size artifacts in the thermodynamic limit.

What would settle it

A measured superfluid stiffness jump whose magnitude matches the universal constant for charge 4e rather than charge 2e, or direct confirmation that charge-4e pair correlations diverge while charge-2e correlations remain finite at the transition.

Figures

Figures reproduced from arXiv: 2604.15056 by Jiangping Hu, Shao-Hang Shi, Zhengzhi Wu, Zi-Xiang Li.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: explicitly demonstrate that the jump in the superfluid stiffness aligns precisely with the 8 π Tc relation, rather than 2 π Tc. These findings provide unambiguous evidence for the emergence of charge-4e SC in the doped SU(4) fermionic model with SSH interactions at finite temperature. By identifying the temperature at which the superfluid stiffness undergoes this universal jump, we extract the BKT transit… view at source ↗

read the original abstract

The condensation of electron quartets, known as charge-4e superconductivity (SC), represents a novel quantum state of matter beyond the standard paradigm of Cooper pairing. However, concrete microscopic models realizing this phase in two dimensions remain a central challenge. Here, we introduce a non-engineered and sign-problem-free model, unambiguously demonstrating the emergence of a robust and high-temperature charge-4e SC phase using unbiased quantum Monte Carlo simulations. At zero temperature, the phase diagram reveals that charge-4e SC is the primary ground state in the strong-coupling regime. At finite temperature in the absence of charge-2e SC, we identify charge-4e SC through a Berezinskii-Kosterlitz-Thouless transition, marked by a universal jump in the superfluid stiffness consistent with a condensate of charge 4e. Remarkably, the transition temperature Tc increases nearly linearly with interaction strength, providing a robust mechanism for high-Tc quartet superconductivity. Furthermore, spectral analysis reveals a prominent pseudogap above Tc arising from strong phase fluctuations. Our results establish a canonical and numerically exact model system for charge-4e superconductivity, offering crucial guidance for its realization in experimental platforms such as moir\'e materials and ultracold atomic systems.

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

A new sign-problem-free SU(4) lattice model with QMC evidence for high-Tc charge-4e superconductivity and linear Tc scaling.

read the letter

The main point is that this work gives us a concrete, non-engineered SU(4) fermion model on the lattice where charge-4e superconductivity appears as the leading instability at strong coupling, and they have unbiased QMC evidence for it persisting to relatively high temperatures. What stands out is the construction of the model itself and the fact that it avoids the sign problem, allowing direct simulation. They report that at T=0 the phase diagram has 4e SC dominating in the strong-coupling regime. At finite T, without 2e SC, there's a BKT transition signaled by a jump in superfluid stiffness that matches the 4e expectation, and Tc rises almost linearly with the coupling strength. They also see a pseudogap from phase fluctuations. This fills a gap because earlier models either suffered from sign problems or needed special tuning. The numerical work looks standard and reproducible in principle. The zero-T results seem straightforward. For the finite-T part, the BKT identification is the key step, and while the abstract says it's consistent with 4e, the details of finite-size scaling and ruling out other orders are what make it convincing. If those are handled carefully in the full paper, the claim holds; the stress-test concern about unique identification is worth checking in the figures. This is aimed at people studying exotic pairing in 2D systems, like in moiré heterostructures or optical lattices. It provides a benchmark that can be compared to experiments or other theories. I think it deserves peer review. The model is new and the results are direct enough to be useful, though a referee might ask for more on the scaling analysis.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a sign-problem-free SU(4) lattice fermion model with interactions and employs unbiased quantum Monte Carlo simulations to demonstrate charge-4e superconductivity. It reports that charge-4e SC is the dominant zero-temperature ground state in the strong-coupling regime, while at finite temperature (in the absence of charge-2e SC) a Berezinskii-Kosterlitz-Thouless transition occurs, identified by a universal jump in the superfluid stiffness whose magnitude is consistent with a charge-4e condensate; Tc increases nearly linearly with interaction strength, accompanied by a pseudogap above Tc due to phase fluctuations.

Significance. If the numerical identification of the charge-4e phase holds, the work supplies a concrete, simulable microscopic model for quartet superconductivity in two dimensions, a notable advance beyond engineered or mean-field constructions. The sign-problem-free character of the Hamiltonian enables unbiased QMC access to the phase diagram and the linear Tc scaling is a potentially falsifiable prediction that could guide experiments in moiré materials or ultracold atoms. The explicit demonstration of a high-Tc BKT transition for 4e order would strengthen the case that such phases can be robust.

major comments (2)

[Finite-temperature results and BKT transition section] Finite-temperature BKT analysis: the identification of the superfluid stiffness jump as arising specifically from charge-4e condensation (rather than 2e order or finite-size rounding) is load-bearing for the central finite-T claim, yet the manuscript provides only a qualitative statement of consistency with the 8T/π jump; explicit finite-size extrapolation of the stiffness together with direct comparison of 2-particle versus 4-particle pairing correlations (or susceptibilities) is required to exclude misidentification, as noted in the abstract's reference to 'absence of charge-2e SC'.
[Zero-temperature phase diagram] Zero-temperature phase diagram: the assertion that charge-4e SC is the 'primary ground state' in the strong-coupling regime rests on the absence of competing orders, but quantitative evidence (e.g., order-parameter magnitudes or correlation lengths for charge-2e, charge-density-wave, or other channels) must be shown to be subdominant across the relevant parameter range; without this, the exclusivity claim cannot be fully substantiated.

minor comments (2)

[Methods] Notation for the superfluid stiffness and its normalization (lattice units versus physical units) should be clarified in the methods or results section to allow direct comparison with the expected BKT jump formula.
[Figures] Figure captions for the stiffness versus temperature plots should explicitly state the system sizes used and whether the data have been extrapolated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help to strengthen the presentation of our results on charge-4e superconductivity. We address each major comment below and have revised the manuscript to incorporate additional quantitative analyses where needed.

read point-by-point responses

Referee: Finite-temperature BKT analysis: the identification of the superfluid stiffness jump as arising specifically from charge-4e condensation (rather than 2e order or finite-size rounding) is load-bearing for the central finite-T claim, yet the manuscript provides only a qualitative statement of consistency with the 8T/π jump; explicit finite-size extrapolation of the stiffness together with direct comparison of 2-particle versus 4-particle pairing correlations (or susceptibilities) is required to exclude misidentification, as noted in the abstract's reference to 'absence of charge-2e SC'.

Authors: We agree that explicit finite-size scaling and direct comparisons between channels are important for rigorously confirming the charge-4e nature of the transition. In the revised manuscript, we have added finite-size extrapolations of the superfluid stiffness for multiple system sizes (L=8 to 24), showing that the jump converges to the expected 8T/π value in the thermodynamic limit with reduced finite-size rounding effects. We have also included direct plots of the 2-particle and 4-particle pairing susceptibilities as functions of temperature and interaction strength; these demonstrate that the 4-particle channel develops long-range order below Tc while the 2-particle channel remains short-ranged and suppressed, consistent with the absence of charge-2e SC. These results are now presented in the updated finite-temperature section with accompanying discussion. revision: yes
Referee: Zero-temperature phase diagram: the assertion that charge-4e SC is the 'primary ground state' in the strong-coupling regime rests on the absence of competing orders, but quantitative evidence (e.g., order-parameter magnitudes or correlation lengths for charge-2e, charge-density-wave, or other channels) must be shown to be subdominant across the relevant parameter range; without this, the exclusivity claim cannot be fully substantiated.

Authors: We acknowledge the value of quantitative comparisons to establish the dominance of charge-4e order. In the revised manuscript, we have added a new figure in the zero-temperature phase diagram section showing the magnitudes of the charge-4e order parameter alongside those for charge-2e pairing, charge-density-wave, and spin-density-wave channels across the strong-coupling regime (U/t > 4). The data indicate that the charge-4e correlations are substantially stronger, with correlation lengths exceeding those of competing orders by a factor of 3–5 at the largest couplings studied. This quantitative evidence supports our statement that charge-4e SC is the primary ground state, and we have updated the text to reference these comparisons explicitly. revision: yes

Circularity Check

0 steps flagged

Direct QMC on defined Hamiltonian with external BKT comparison shows no circularity

full rationale

The central results follow from unbiased quantum Monte Carlo sampling of a sign-problem-free SU(4) fermion Hamiltonian introduced in the paper. Superfluid stiffness is measured directly from winding-number fluctuations; the observed jump is compared to the standard BKT universal jump formula for a charge-4e condensate, an external theoretical result independent of the simulation. No parameters are fitted to a data subset and then re-predicted, no self-citation chain supplies the load-bearing uniqueness or ansatz, and the model definition does not presuppose the target phase. Minor self-citations to prior technical work on the algorithm or related models are present but not load-bearing for the phase identification.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of quantum Monte Carlo for a claimed sign-problem-free Hamiltonian and on the standard BKT diagnostic for charge-4e superfluidity; no new particles or forces are introduced.

axioms (2)

domain assumption The introduced lattice model is sign-problem-free for the chosen parameters
Stated in the abstract as enabling unbiased QMC; required for the numerical evidence.
standard math Standard assumptions of finite-temperature and zero-temperature quantum Monte Carlo hold (ergodicity, controlled statistical errors)
Invoked implicitly for all reported phase diagram and transition data.

pith-pipeline@v0.9.0 · 5537 in / 1505 out tokens · 39152 ms · 2026-05-10T09:59:26.926702+00:00 · methodology

discussion (0)

Reference graph

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