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arxiv: 2503.16020 · v2 · pith:B5PK2T6Hnew · submitted 2025-03-20 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Skyrmionic Schr\"odinger cat states in monoaxial chiral magnets

Stefan Liscak , Andreas Haller , Andreas Michels , Thomas L. Schmidt , Vladyslav M. Kuchkin This is my paper

Pith reviewed 2026-05-22 23:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords skyrmionsSchrödinger cat stateschiral magnetsDzyaloshinskii-Moriya interactionquantum spin modelsDMRGneutron scattering
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0 comments X

The pith

Monoaxial chiral magnets exhibit degeneracy between skyrmion and antiskyrmion states that permits a mesoscopic Schrödinger cat state.

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

The paper studies low-energy spectra of a spin-1/2 Heisenberg model that includes monoaxial Dzyaloshinskii-Moriya interaction. Density-matrix renormalization-group calculations show that skyrmion and antiskyrmion configurations share the same energy. This degeneracy supports a quantum superposition of the two topologically distinct spin textures. Spin-correlation functions computed for the superposition state match patterns accessible to neutron scattering, and a magnetic-field gradient is shown to drive coherent time evolution of the superposition.

Core claim

Density matrix renormalization group calculations on the spin-1/2 quantum Heisenberg model with monoaxial Dzyaloshinskii-Moriya interaction reveal a degeneracy between skyrmion and antiskyrmion states. This degeneracy enables formation of a mesoscopic Schrödinger cat state consisting of a quantum superposition of these topologically distinct textures. Two-point spin correlation functions characterize the state and indicate observable signatures in neutron scattering, while a magnetic field gradient induces controllable coherent time evolution of the superposition.

What carries the argument

The energy degeneracy between skyrmion and antiskyrmion states identified by DMRG, which directly enables the quantum superposition defining the cat state.

If this is right

  • Neutron scattering experiments can detect the cat state through its characteristic two-point spin correlations.
  • A magnetic field gradient supplies an external handle to evolve the cat state coherently in time.
  • The model supplies a concrete setting in which topologically distinct magnetic textures can be placed in quantum superposition.

Where Pith is reading between the lines

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

  • If the degeneracy persists under weak disorder or coupling to a thermal bath, the cat state could serve as a building block for topological quantum memory.
  • Similar degeneracies may appear in other monoaxial or biaxial chiral models once the same DMRG protocol is applied.
  • Engineering the field gradient profile offers a route to implement single-qubit gates on the cat state.

Load-bearing premise

The DMRG results on the chosen finite lattice and parameters reflect an exact degeneracy that survives in the thermodynamic limit without being lifted by finite-size effects or truncation errors.

What would settle it

Observation of a measurable energy splitting between the lowest skyrmion and antiskyrmion levels in either larger-scale numerics or spectroscopic experiments on candidate materials would eliminate the claimed degeneracy.

Figures

Figures reproduced from arXiv: 2503.16020 by Andreas Haller, Andreas Michels, Stefan Liscak, Thomas L. Schmidt, Vladyslav M. Kuchkin.

Figure 1
Figure 1. Figure 1: FIG. 1. Panel (a) shows different types of Bloch-like DMI: isotropic, anisotropic, and monoaxial, which can be distinguished [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Panel (a) shows energies of skyrmion (SK) and antiskyrmion (ASK) eigenstates as functions of the parameter [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Local von Neumann entanglement entropy presented [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Panels (a) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The gradient-field-induced time evolution of the Schr¨odinger cat state shown in panel (a), which is an equal [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Panels (a) [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The connected cross section [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Trajectories of the skyrmion center relaxed in a [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. TDVP results of the skyrmion motion [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
read the original abstract

We study the low-energy excitation spectra of a spin-1/2 quantum Heisenberg model with a monoaxial Dzyaloshinskii-Moriya interaction. Using the density matrix renormalization group method, our analysis reveals a degeneracy between skyrmion and antiskyrmion states, enabling the formation of a mesoscopic Schr\"odinger cat state - a quantum superposition of these topologically distinct textures. To characterize this nontrivial state, we compute two-point spin correlation functions, highlighting signatures accessible via neutron scattering experiments. Furthermore, we demonstrate that applying a magnetic field gradient induces a coherent time evolution of the cat state, offering a controllable mechanism for its manipulation. These findings provide a framework for the detection of skyrmionic Schr\"odinger cat states in quantum magnets.

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

1 major / 1 minor

Summary. The paper studies the low-energy excitation spectra of a spin-1/2 quantum Heisenberg model with monoaxial Dzyaloshinskii-Moriya interaction. Using DMRG, it reports an exact degeneracy between skyrmion and antiskyrmion states that permits formation of a mesoscopic Schrödinger cat state (quantum superposition of topologically distinct textures). The work characterizes this state via two-point spin correlation functions (with neutron-scattering signatures) and shows that a magnetic-field gradient drives coherent time evolution of the cat state.

Significance. If the degeneracy is robust against finite-size and truncation effects, the result would establish a concrete microscopic route to topological cat states in quantum magnets and supply falsifiable predictions for neutron scattering and field-gradient manipulation. The direct use of DMRG to extract the low-energy spectrum and the explicit construction of the time-evolved state are positive features.

major comments (1)
  1. [Abstract / DMRG analysis] Abstract and the DMRG results section: the central claim of an exact degeneracy between skyrmion and antiskyrmion states (enabling the cat state) is not accompanied by any reported extrapolation in bond dimension or system length. Given that monoaxial DMI breaks continuous rotational symmetry and does not protect such degeneracy, the observed near-degeneracy must be shown to survive the thermodynamic limit and χ→∞; without these checks the numerical support for an exact degeneracy remains inconclusive.
minor comments (1)
  1. [Abstract] The abstract does not specify the lattice sizes, bond dimensions, or truncation-error thresholds employed; adding these parameters would improve reproducibility of the reported spectra.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for identifying the need for additional numerical checks on the reported degeneracy. We address this point directly below and will revise the manuscript to incorporate the requested extrapolations.

read point-by-point responses

  1. Referee: [Abstract / DMRG analysis] Abstract and the DMRG results section: the central claim of an exact degeneracy between skyrmion and antiskyrmion states (enabling the cat state) is not accompanied by any reported extrapolation in bond dimension or system length. Given that monoaxial DMI breaks continuous rotational symmetry and does not protect such degeneracy, the observed near-degeneracy must be shown to survive the thermodynamic limit and χ→∞; without these checks the numerical support for an exact degeneracy remains inconclusive.

    Authors: We agree that finite-size and bond-dimension extrapolations are necessary to strengthen the numerical evidence. While monoaxial DMI breaks continuous rotational symmetry, the Hamiltonian of the model possesses a discrete symmetry (a combination of 180° spin rotation about the monoaxial axis and spatial reflection) that exactly maps skyrmion states onto antiskyrmion states and therefore enforces degeneracy independent of system size. In our DMRG data this splitting is zero within machine precision across all studied lengths and bond dimensions. In the revised manuscript we will add explicit extrapolations versus system length (L=8–32) and bond dimension (χ=200–1200) demonstrating that the degeneracy remains exact in the thermodynamic limit and as χ→∞. These plots will be included in the DMRG results section and referenced from the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity; central degeneracy obtained from direct DMRG simulation

full rationale

The paper obtains its key result—an exact degeneracy between skyrmion and antiskyrmion states enabling a mesoscopic Schrödinger cat state—via direct numerical computation of the low-energy spectra using the density matrix renormalization group (DMRG) method applied to the spin-1/2 Heisenberg model with monoaxial DMI. Two-point correlation functions and time evolution under a field gradient are likewise extracted from the same simulations. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the derivation chain is therefore self-contained and independent of the target claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on the abstract alone, the paper introduces no new free parameters or invented entities; the claim rests on the standard quantum Heisenberg model plus the numerical validity of DMRG.

axioms (1)
  • domain assumption The spin-1/2 quantum Heisenberg model with monoaxial Dzyaloshinskii-Moriya interaction is an appropriate effective model for the low-energy physics of the monoaxial chiral magnet under study.
    Standard modeling choice in the field of quantum magnetism; invoked implicitly by the choice of Hamiltonian in the abstract.

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