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arxiv: 2411.13651 · v3 · submitted 2024-11-20 · ❄️ cond-mat.str-el · cond-mat.stat-mech· cond-mat.supr-con· hep-th· quant-ph

Certain BCS wavefunctions are quantum many-body scars

Kiryl Pakrouski , Zimo Sun This is my paper

Pith reviewed 2026-05-23 16:40 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.stat-mechcond-mat.supr-conhep-thquant-ph
keywords many-body scarsBCS wavefunctionfermionic lattice modelseta-pairingsuperconductivitythermalizationquantum simulatorsscar subspace
0
0 comments X

The pith

BCS wavefunctions are many-body scars in multi-flavour fermionic lattice models and stay protected from thermalization.

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

The paper constructs scar states in fermionic systems whose correlations are fixed by a unitary matrix A. One such state is the BCS wavefunction, which maximizes one-point correlations over the full space and becomes the ground state once the correlations are added as a pairing potential. The part of any eligible Hamiltonian that controls the scar subspace exactly matches the BCS mean-field Hamiltonian. Its eigenstates are therefore scars that remain decoupled from the rest of the Hilbert space. This construction works for both superconducting and unconventional magnetic cases and supplies an explicit route to initialize scar states in fermionic quantum simulators.

Core claim

In any Hamiltonian that supports group-invariant scars, the BCS wavefunction can be made the ground state by adding the specified correlations as a pairing potential. The exact dynamics inside the scar subspace then coincide with those of the BCS mean-field Hamiltonian, so the eigenstates of that mean-field operator are scars that are decoupled from the thermalizing bulk of the Hilbert space.

What carries the argument

The scar subspace whose exact dynamics coincide with the BCS mean-field Hamiltonian.

If this is right

  • Eigenstates of the BCS mean-field Hamiltonian become scars in the full model.
  • The scars remain decoupled from the rest of the Hilbert space and are protected from thermalization.
  • The same construction applies to both superconducting and unconventional magnetic correlations.
  • The protocol supplies the first feasible way to prepare a fermionic scar state in a quantum simulator experiment.

Where Pith is reading between the lines

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

  • Similar pairing-potential additions might turn other mean-field ground states into scars in bosonic or spin models.
  • The link suggests that mean-field descriptions of superconductivity could be reinterpreted as exact scar dynamics in certain lattices.
  • Experimental tests could begin by preparing the eta-pairing combination in a single-flavour spinful chain and measuring its overlap with the thermal bulk.

Load-bearing premise

Any Hamiltonian supporting group-invariant scars can have the BCS state made its ground state by adding the correlations as a pairing potential while preserving the exact coincidence of scar-subspace dynamics with the BCS mean-field Hamiltonian.

What would settle it

An explicit check that the time evolution generated inside the proposed scar subspace deviates from the BCS mean-field evolution or that the states thermalize under the full Hamiltonian.

read the original abstract

We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $\eta$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

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 / 2 minor

Summary. The paper constructs many-body scar states in multi-flavour fermionic lattice models possessing strong magnetic or superconducting correlations specified by a unitary matrix A. One such state is a BCS wavefunction that maximizes one-point correlations; it can be made the ground state of any Hamiltonian supporting group-invariant scars by adding the correlations as a pairing potential. In examples (single-flavour spinful fermions with superconducting A, multi-orbital fermions with unconventional magnetic correlations), the BCS scar is a linear combination of eta-pairing states or maximizes magnetic correlations. The portion of the Hamiltonian governing scar-subspace dynamics coincides with the BCS mean-field Hamiltonian, implying the eigenstates are decoupled scars protected from thermalization. The work connects superconductivity to weak ergodicity breaking and offers an experimental initialization protocol.

Significance. If the central construction holds, the result links superconductivity and many-body scars, identifies a broad class of conventional condensed-matter Hamiltonians supporting scars, and supplies a concrete protocol for preparing fermionic scar states in quantum simulators. The explicit identification of the scar-subspace dynamics with the BCS mean-field Hamiltonian is a notable structural feature.

major comments (1)
  1. [Abstract / construction] The load-bearing step is the claim that, for arbitrary Hamiltonians supporting group-invariant scars, addition of the pairing potential always preserves exact subspace invariance and makes the intra-subspace dynamics coincide with the BCS mean-field Hamiltonian. The abstract asserts this holds universally, but the skeptic concern correctly identifies that off-subspace matrix elements or modified intra-subspace elements would destroy the decoupling; without explicit verification of the matrix elements under the modified Hamiltonian (or a general proof that they remain zero), the central claim that the eigenstates are decoupled scars cannot be assessed.
minor comments (2)
  1. Notation for the unitary matrix A and the precise definition of 'group-invariant scars' should be introduced with an equation or short paragraph before the examples.
  2. The statement that the eligible Hamiltonians 'include many conventional condensed matter interactions' would benefit from one or two explicit examples with their interaction terms written out.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work's significance, and for identifying the load-bearing aspect of the central construction. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract / construction] The load-bearing step is the claim that, for arbitrary Hamiltonians supporting group-invariant scars, addition of the pairing potential always preserves exact subspace invariance and makes the intra-subspace dynamics coincide with the BCS mean-field Hamiltonian. The abstract asserts this holds universally, but the skeptic concern correctly identifies that off-subspace matrix elements or modified intra-subspace elements would destroy the decoupling; without explicit verification of the matrix elements under the modified Hamiltonian (or a general proof that they remain zero), the central claim that the eigenstates are decoupled scars cannot be assessed.

    Authors: We agree this is the central claim requiring careful justification. The pairing potential is constructed explicitly as a sum of one-point correlation operators defined by the unitary matrix A; these operators generate the group under which the scar subspace is invariant by construction. Consequently, the potential commutes with the group generators, ensuring that its action maps the subspace to itself and produces no off-subspace matrix elements. The intra-subspace matrix elements are computed directly and shown to reproduce the BCS mean-field Hamiltonian. To address the concern that this argument may not be sufficiently explicit, we will revise the manuscript to include a dedicated subsection (or appendix) with the general proof that the modified Hamiltonian preserves exact subspace invariance for any group-invariant scar-supporting parent Hamiltonian, together with the explicit verification that off-subspace elements remain zero. revision: yes

Circularity Check

0 steps flagged

Forward construction from BCS form and group-invariant scars; no reduction of claims to fitted inputs or self-referential definitions.

full rationale

The paper constructs scar states by design: BCS wavefunctions are embedded into Hamiltonians supporting group-invariant scars via addition of a pairing term, with the intra-subspace dynamics defined to coincide with the BCS mean-field. This is an explicit forward construction rather than a statistical prediction or self-definition that equates output to input by construction. No load-bearing self-citations, uniqueness theorems imported from the same authors, or ansatzes smuggled via citation are evident in the abstract or described derivation. The central result follows from the stated assumptions about invariance preservation, which are presented as part of the construction rather than derived from external benchmarks or fits.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of Hamiltonians that support group-invariant scars and on the mathematical property that the BCS form maximizes the specified correlations for a given unitary matrix A.

axioms (1)
  • domain assumption Existence of Hamiltonians supporting group-invariant scars to which a pairing potential can be added
    The paper states that the BCS state may always be made the ground state by adding the correlations as a pairing potential to any such Hamiltonian.

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Reference graph

Works this paper leans on

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    Single-orbital: Eta subspace With respect to the symmetry groups of the |η⟩ and |η⟩′ states the H0 part of the Hamiltonian is given by eq. (III.7) Let’s write it (consider the case of eta states with O† = η† j = c† j↑c† j↓) using the type-I spinor (II.25) and µ = (U/2 + µH) H η 0 = X j c† j↑ cj↓ µ −γeiθ −γe−iθ −µ cj↑ c† j↓ + µN (A.1) Observe that this Ham...

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    Single-orbital: Zeta subspace With respect to the symmetry group of the |ζ⟩ states the H0 part of the Hamiltonian is given by eq. (III.12). Using the type-II spinor (II.26) we write it as 11 H ζ 0 = X j c† j↑ c† j↓ 0 −γeiθ −γe−iθ 0 cj↑ cj↓ + µN (A.9) The transformation is the same as in the eta case (re- placing µ = 0 and using definitions (A.6), (II.22))...

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