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arXiv:2610.42103

Charge Pumping Leptogenesis from the Symmetric Mass Generation Phase on a Four-Leg Ladder Lattice

Runze Chi, Meng Zeng, Tao Xiang, Yi-Zhuang You, Bertrand I. Halperin, Juven Wang

cond-mat.str-elquant-phSubmitted Oct 30, 2026• Announced Nov 2, 2026
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Abstract

Quantized charge pumping in quantum Hall systems is a bulk topological property, typically manifesting on gapless boundaries as spectral flow through chiral edge modes upon flux insertion. When the boundary is anomaly-free, it can be symmetrically gapped by symmetric mass generation (SMG) interactions. However, the effects on quantized charge pumping at an interacting gapped boundary are unclear. We address this using density-matrix renormalization group simulations of a four-leg ladder quasi-(2+1)d realization of the (1+1)d 3-4-5-0 lattice chiral fermion model with six-fermion interactions at one edge. We find gapless modes near the interacting edge for both weak and strong couplings, but the edge can be in a fully gapped SMG phase at intermediate coupling. We also identify spontaneous breaking of the model's $\mathbb{Z}_2$ symmetry above a critical interaction strength. Across all three boundary phases, we find quantized charge pumping with the same pumped charge per flux quantum. The spatial distribution of the pumped charge varies between phases. Besides charge pumping, we study how a single injected fermion propagates under open boundary conditions. In the SMG phase, an interaction-induced flavor-mixing current develops at the endpoints of the gapped edge, which is absent in the weak- and strong-coupling limits. This current reveals a charge-redistribution mechanism unique to the SMG phase. Additionally, we propose an analogy between charge pumping in this model and a topological leptogenesis scenario in the (3+1)d Standard Model. The anomaly-free chiral U(1) symmetries of the 3-4-5-0 model play a role analogous to the baryon-minus-lepton symmetry of the Standard Model. In both settings, charge pumping can be associated with a continuous deformation along a classically defined but quantum-anomalous direction, while a discrete subgroup remains an exact quantum symmetry.

AI Summary

The paper asks how quantized charge pumping behaves when an anomaly-free chiral boundary is gapped by symmetric mass generation (SMG). It studies the four-flavor 3-4-5-0 lattice model, with six-fermion interactions confined to one edge of a Chern-insulator ladder, using DMRG primarily on $L_x=8$, $L_y=4$ systems, supplemented by smaller-system calculations, exact diagonalization, and strong-coupling analysis. The numerical results support an intermediate symmetric, gapped-edge regime around $g\simeq5$–$6$, between weak-coupling gapless behavior and a symmetry-broken strong-coupling regime. Channel-exchange symmetry breaking appears near $g\simeq6$. At sufficiently strong coupling, the interacting row effectively decouples and gapless modes emerge on the adjacent row. The isolated interacting edge admits a monomer–dimer reduction to a constrained PXP chain, with numerical evidence for four symmetry-related ground states. Removing a $\mathbb Z_{10}$ flux quantum along the flavor-charge direction $(2,1,-2,1)$ pumps conserved charges $(2,1)$ away from the noninteracting edge across the studied regimes, consistent with the bulk mixed Hall response. The receiving charge’s spatial distribution depends on the boundary regime. A different continuous interpolation of the same discrete twist produces zero net conserved-charge pumping. Static added-particle calculations also show enhanced endpoint flavor-conversion currents in the proposed SMG regime. The accessible sizes do not resolve the strong-side transitions or establish thermodynamic phase boundaries; finite-width hybridization remains a caveat. Real-time interface scattering is left open. A proposed Standard-Model leptogenesis connection is an anomaly-based analogy, not a demonstrated cosmological mechanism.

Little sign of AI-generated textIncrementalOverclaims

Central claim may not hold: The claim of quantized pumping across a fully gapped SMG boundary phase is conditional because the four-leg calculations do not conclusively establish that phase in the thermodynamic limit. The abstract describes injected-fermion propagation, but the reported calculations measure static ground-state charge and current profiles rather than propagation dynamics.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

Comments
30 pages, many figures

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Quantized charge pumping in quantum Hall systems is a bulk topological property, typically manifesting on gapless boundaries as spectral flow through chiral edge modes upon flux insertion. When the boundary is anomaly-free, it can be symmetrically gapped by symmetric mass generation (SMG) interactions. However, the effects on quantized charge pumping at an interacting gapped boundary are unclear. We address this using density-matrix renormalization group simulations of a four-leg ladder quasi-(2+1)d realization of the (1+1)d 3-4-5-0 lattice chiral fermion model with six-fermion interactions at one edge. We find gapless modes near the interacting edge for both weak and strong couplings, but the edge can be in a fully gapped SMG phase at intermediate coupling. We also identify spontaneous breaking of the model's Z2\mathbb{Z}_2Z2​ symmetry above a critical interaction strength. Across all three boundary phases, we find quantized charge pumping with the same pumped charge per flux quantum. The spatial distribution of the pumped charge varies between phases. Besides charge pumping, we study how a single injected fermion propagates under open boundary conditions. In the SMG phase, an interaction-induced flavor-mixing current develops at the endpoints of the gapped edge, which is absent in the weak- and strong-coupling limits. This current reveals a charge-redistribution mechanism unique to the SMG phase. Additionally, we propose an analogy between charge pumping in this model and a topological leptogenesis scenario in the (3+1)d Standard Model. The anomaly-free chiral U(1) symmetries of the 3-4-5-0 model play a role analogous to the baryon-minus-lepton symmetry of the Standard Model. In both settings, charge pumping can be associated with a continuous deformation along a classically defined but quantum-anomalous direction, while a discrete subgroup remains an exact quantum symmetry.
The paper asks how quantized charge pumping behaves when an anomaly-free chiral boundary is gapped by symmetric mass generation (SMG). It studies the four-flavor 3-4-5-0 lattice model, with six-fermion interactions confined to one edge of a Chern-insulator ladder, using DMRG primarily on Lx=8L_x=8Lx​=8, Ly=4L_y=4Ly​=4 systems, supplemented by smaller-system calculations, exact diagonalization, and strong-coupling analysis.
The numerical results support an intermediate symmetric, gapped-edge regime around g≃5g\simeq5g≃5–666, between weak-coupling gapless behavior and a symmetry-broken strong-coupling regime. Channel-exchange symmetry breaking appears near g≃6g\simeq6g≃6. At sufficiently strong coupling, the interacting row effectively decouples and gapless modes emerge on the adjacent row. The isolated interacting edge admits a monomer–dimer reduction to a constrained PXP chain, with numerical evidence for four symmetry-related ground states.
Removing a Z10\mathbb Z_{10}Z10​ flux quantum along the flavor-charge direction (2,1,−2,1)(2,1,-2,1)(2,1,−2,1) pumps conserved charges (2,1)(2,1)(2,1) away from the noninteracting edge across the studied regimes, consistent with the bulk mixed Hall response. The receiving charge’s spatial distribution depends on the boundary regime. A different continuous interpolation of the same discrete twist produces zero net conserved-charge pumping. Static added-particle calculations also show enhanced endpoint flavor-conversion currents in the proposed SMG regime.
The accessible sizes do not resolve the strong-side transitions or establish thermodynamic phase boundaries; finite-width hybridization remains a caveat. Real-time interface scattering is left open. A proposed Standard-Model leptogenesis connection is an anomaly-based analogy, not a demonstrated cosmological mechanism.
Lattice regularization of chiral fermions has been a long-standing problem in physics. In this Letter, we present the density matrix renormalization group simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multilayer Chern insulator, whose finite width implies the quantum system is effectively (1+1)D. By introducing two sets of carefully designed six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.
Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter KKK) that reduces the scaling dimension of the 3-4-5-0 interaction from 555 to 5K5K5K, making it relevant for K<2/5K<2/5K<2/5. Density-matrix renormalization group calculations show the opening of an excitation gap in this regime without the appearance of a degenerate ground state, the hallmark of symmetric mass generation.
Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by nonperturbative interactions without generating any fermion bilinear condensation. The previous studies of SMG have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this paper, we generalize the concept of SMG to Fermi liquid (FL) with a finite Fermi volume and discuss how to gap out the Fermi surfaces (FSs) by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of FS SMG in both (1+1)(1+1)(1+1)-dimensional [(1+1)D][(1+1)\mathrm{D}][(1+1)D] and (2+1)(2+1)(2+1)-dimensional FL systems when several FSs together cancel the FS anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the (1+1)D(1+1)\mathrm{D}(1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.
We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (V1{V}_{1}V1​ and V2{V}_{2}V2​), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate V2<V1{V}_{2}<{V}_{1}V2​<V1​ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.
We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of the underlying topological phases change between noninteracting fermions and a bosonic system in the strong coupling limit, the symmetry-protection argument enforces a gap closing and thereby predicts a breakdown of the topological pumping. We also demonstrate that, even in the weakly interacting regime where the bulk topological pumping is still robust, the interaction effects manifest themselves in the edge density profiles, leading to a unique feature of the pumping in open boundary conditions. Furthermore, an extension of the above results indicates that an analog of an interaction-induced phase of Weyl semimetals can be realized in the setup of the topological pumping. Our results provide a systematic understanding for the stability of topological pumping against strong interactions, to which the conventional perturbative argument cannot be applied.
Strong interactions can give rise to new fermionic symmetry protected topological phases which have no analogs in free fermion systems. As an example, we have systematically studied a spinless fermion model with U(1) charge conservation and time reversal symmetry on a three-leg ladder using density-matrix renormalization group. In the non-interacting limit, there are no topological phases. Turning on interactions, we found two gapped phases. One is trivial and is adiabatically connected to a band insulator, while another one is a nontrivial symmetry protected topological phase resulting from strong interactions.