Effective Bethe Ansatz for Spin-1 Non-integrable Models

Rui-Dong Zhu; Zhuohang Wang

arxiv: 2604.04640 · v1 · submitted 2026-04-06 · ❄️ cond-mat.stat-mech · hep-th· nlin.SI

Effective Bethe Ansatz for Spin-1 Non-integrable Models

Zhuohang Wang , Rui-Dong Zhu This is my paper

Pith reviewed 2026-05-10 20:08 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech hep-thnlin.SI

keywords Effective Bethe Ansatzspin-1 bilinear-biquadratic chainnon-integrable quantum spin chainsvariational wavefunctionsfidelityentanglement entropylevel crossingsexact diagonalization benchmark

0 comments

The pith

Deforming exact Bethe wavefunctions from integrable points yields accurate variational states for nearby non-integrable spin-1 chains.

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

The paper benchmarks a variational method called Effective Bethe Ansatz on the spin-1 bilinear-biquadratic chain in its non-integrable regime. Starting from the two known integrable endpoints, the method deforms the exact Bethe wavefunctions to approximate ground and first-excited states, then compares energies, wavefunction overlaps, and entanglement entropies against exact diagonalization on small lattices. Agreement holds near the integrable points and degrades controllably with increasing perturbation, while still registering sharp fidelity drops at finite-size level crossings. This positions the approach as a semi-analytical route to low-energy physics in systems that lack exact solutions.

Core claim

The Effective Bethe Ansatz supplies a reliable variational description of the low-energy sector in the non-integrable regime of the spin-1 bilinear-biquadratic chain. When initialized at either the Takhtajan-Babujian or Lai-Sutherland point and deformed variationally, the resulting states reproduce the exact energies, fidelities, and entanglement entropies obtained by full diagonalization sufficiently close to integrability, with fidelity dropping smoothly as the perturbation grows and exhibiting abrupt drops precisely where level crossings occur.

What carries the argument

Effective Bethe Ansatz (EBA), a variational ansatz formed by continuously deforming the exact Bethe wavefunctions of an integrable point to fit a nearby non-integrable Hamiltonian.

If this is right

The method captures finite-size level crossings through abrupt fidelity drops, offering a diagnostic for nearby phase boundaries.
It supplies a computationally cheap way to track entanglement entropy and excitation gaps without full matrix diagonalization.
Accuracy remains high near integrability and falls off gradually, defining a practical window of applicability.
The same deformation procedure can be repeated from either integrable endpoint to cross-check results.

Where Pith is reading between the lines

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

The same deformation strategy could be tried on other one-dimensional models that sit close to known integrable points.
For stronger perturbations one would likely need to enlarge the variational manifold or combine EBA with other techniques.
If the low-energy spectrum remains dominated by the integrable structure even moderately far from the endpoint, the approach may generalize to quasi-one-dimensional materials.

Load-bearing premise

That a modest variational deformation of the Bethe wavefunctions from an integrable endpoint remains a good trial state once the Hamiltonian is perturbed away from integrability.

What would settle it

Exact diagonalization on chains of length 20 or larger showing that the EBA energy deviates by more than a few percent or the fidelity falls below 0.7 at moderate perturbation strengths where small-system agreement still holds.

read the original abstract

This work presents a comprehensive benchmark and validation of a recently proposed method called Effective Bethe Ansatz (EBA). It is a variational method that deforms the exact Bethe wavefunctions of one-dimensional spin chains at integrable points to approximate non-integrable systems. We apply this method to the non-integrable regime of the spin-1 bilinear-biquadratic chain. By performing EBA method starting from the two integrable endpoints, the Takhtajan-Babujian point and the Lai-Sutherland point, we systematically evaluate the accuracy of the EBA for the ground state and first excited state. Our validation is based on a direct comparison with exact diagonalization, assessing energy, fidelity, and entanglement entropy. The results confirm that the EBA provides a physically accurate description near integrability, with fidelity decreasing controllably as the perturbation increases. The method successfully captures key finite-size effects, such as level crossings, manifested as sharp drops in fidelity, and provides a probe to potential phase transitions. This study establishes the EBA as a reliable and efficient semi-analytical tool, clarifying its scope and limitations for studying low-energy physics in non-integrable quantum spin chains.

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

Solid small-system benchmark of EBA on the spin-1 chain, but validation stops where ED does.

read the letter

The paper benchmarks the Effective Bethe Ansatz on the spin-1 bilinear-biquadratic chain by starting from the Takhtajan-Babujian and Lai-Sutherland integrable points, variationally deforming the Bethe states, and comparing energies, fidelities, and entanglement entropy to exact diagonalization for the ground and first excited states. It reports that accuracy holds near the integrable endpoints and that fidelity drops sharply at level crossings, which the authors suggest could flag finite-size effects or phase boundaries. That supplies new concrete numbers for this model that were not in the earlier EBA literature. The comparisons are direct and the degradation away from integrability looks controlled on the systems they can check. The soft spot is that all the evidence comes from exact diagonalization on small chains. ED is feasible only up to modest N, exactly where finite-size effects and level crossings are most pronounced, so the agreement does not yet show whether the deformed ansatz remains faithful once N grows and those artifacts recede. No cross-checks against DMRG or other methods that reach larger sizes appear in the work. This is incremental but honest validation work. Readers who follow variational methods for one-dimensional magnets will find the benchmark data useful for deciding whether to try EBA themselves. It deserves a serious referee because the comparisons are systematic and the results for this specific chain are new, even if the paper will likely be asked to add larger-system tests or more implementation details before publication.

Referee Report

2 major / 1 minor

Summary. The manuscript benchmarks the Effective Bethe Ansatz (EBA), a variational deformation of exact Bethe wavefunctions from the integrable Takhtajan-Babujian and Lai-Sutherland points, as an approximation for the ground and first excited states of the spin-1 bilinear-biquadratic chain in its non-integrable regime. Accuracy is assessed through direct numerical comparisons to exact diagonalization on energies, fidelities, and entanglement entropies, with the central claim that EBA remains physically accurate near integrability, exhibits controllable fidelity degradation with increasing perturbation, captures finite-size effects such as level crossings, and functions as a reliable semi-analytical tool for low-energy physics.

Significance. If the EBA approach can be shown to remain faithful beyond the small-system regime, it would supply an efficient semi-analytical route to low-energy states in non-integrable 1D spin models, bridging integrable and perturbed regimes and enabling studies of phase transitions and finite-size scaling where full exact diagonalization becomes intractable.

major comments (2)

[Numerical results and validation sections] The validation rests exclusively on exact-diagonalization comparisons for small chain lengths accessible to ED. No data or scaling analysis is provided for larger N (where finite-size effects recede), nor are orthogonal benchmarks (e.g., DMRG or other variational methods) reported. This leaves the extrapolation to “physically accurate description” and “reliable semi-analytical tool” unsecured, as agreement on small N does not automatically guarantee faithful correlations once finite-size artifacts diminish.
[Methods and abstract] The manuscript supplies no quantitative information on the system sizes N employed, the precise optimization procedure for the variational deformation parameters, or any error analysis. These omissions are load-bearing because the claimed “controlled degradation” and capture of level crossings cannot be assessed for robustness or reproducibility without them.

minor comments (1)

[Abstract] The abstract states that the method “systematically evaluate[s] the accuracy” yet gives no numerical ranges for N, perturbation strengths, or number of states considered; adding these would improve immediate readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the positive overall assessment of our work on the Effective Bethe Ansatz. We address each major comment point by point below. Revisions have been made to improve methodological transparency and to clarify the scope of our claims.

read point-by-point responses

Referee: [Numerical results and validation sections] The validation rests exclusively on exact-diagonalization comparisons for small chain lengths accessible to ED. No data or scaling analysis is provided for larger N (where finite-size effects recede), nor are orthogonal benchmarks (e.g., DMRG or other variational methods) reported. This leaves the extrapolation to “physically accurate description” and “reliable semi-analytical tool” unsecured, as agreement on small N does not automatically guarantee faithful correlations once finite-size artifacts diminish.

Authors: We agree that the direct numerical validation is restricted to system sizes where exact diagonalization remains feasible, which is the standard and necessary approach for establishing the accuracy of a new variational ansatz against an exact reference. The EBA is formulated to remain computationally tractable for larger chains where ED is unavailable; however, we acknowledge that the manuscript does not contain explicit scaling data or DMRG comparisons. In the revised version we have added a dedicated paragraph in the Discussion section that (i) explains why finite-size effects are expected to diminish in a controlled manner as the deformation parameters remain small near integrability, and (ii) explicitly qualifies the claim of a “reliable semi-analytical tool” to the regime of small-to-moderate system sizes accessible to benchmarking. We have also softened the abstract and conclusion accordingly. revision: partial
Referee: [Methods and abstract] The manuscript supplies no quantitative information on the system sizes N employed, the precise optimization procedure for the variational deformation parameters, or any error analysis. These omissions are load-bearing because the claimed “controlled degradation” and capture of level crossings cannot be assessed for robustness or reproducibility without them.

Authors: We thank the referee for highlighting these omissions. The revised manuscript now contains a new subsection in Methods that reports: the precise chain lengths used for each integrable starting point, the numerical algorithm and convergence criteria employed to optimize the variational deformation parameters, and a brief error analysis (including the spread obtained from multiple random initializations and direct comparison with ED eigenvalues). These additions make the reported fidelity degradation and level-crossing signatures reproducible and allow readers to judge the robustness of the results. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to prior EBA proposal; validation against ED is independent

full rationale

The paper applies the Effective Bethe Ansatz (described as a recently proposed variational deformation of integrable Bethe states) to the spin-1 bilinear-biquadratic chain and benchmarks it via direct numerical comparison of energies, fidelities, and entanglement entropies against exact diagonalization on small systems. These benchmarks constitute independent external checks rather than any reduction of outputs to fitted inputs or self-referential equations. The sole self-citation is to the method's original proposal and is not load-bearing for the accuracy claims, which rest on the ED agreement. No equations, ansatzes, or uniqueness arguments collapse by construction to the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The benchmark relies on the core EBA deformation idea (introduced elsewhere) and standard exact diagonalization; no new free parameters, ad-hoc axioms, or invented entities are introduced in this validation study.

axioms (1)

domain assumption Bethe wavefunctions at integrable points can be variationally deformed to approximate nearby non-integrable systems.
This is the foundational premise of the EBA method invoked throughout the abstract.

pith-pipeline@v0.9.0 · 5510 in / 1299 out tokens · 81615 ms · 2026-05-10T20:08:50.207349+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

[1]

Bethe,On the theory of metals

H. Bethe,On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain,Z. Phys.71(1931) 205–226

work page 1931
[2]

W. Zhao, Y. Jiang, and R.-D. Zhu,The Roaming Bethe Roots: An Effective Bethe Ansatz Beyond Integrability,to appear(2026)

work page 2026
[3]

H. M. Babujian,Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spin S,Phys. Lett. A90(1982) 479–482

work page 1982
[4]

L. A. Takhtajan,The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins,Phys. Lett. A87(1982) 479–482

work page 1982
[5]

C. K. Lai,Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics,Journal of Mathematical Physics15(10, 1974) 1675–1676

work page 1974
[6]

Sutherland,Model for a multicomponent quantum system,Phys

B. Sutherland,Model for a multicomponent quantum system,Phys. Rev. B12(Nov,

work page
[7]

Yang,Some exact results for the many body problems in one dimension with repulsive delta function interaction,Phys

C.-N. Yang,Some exact results for the many body problems in one dimension with repulsive delta function interaction,Phys. Rev. Lett.19(1967) 1312–1314

work page 1967
[8]

Affleck, T

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,Rigorous Results on Valence Bond Ground States in Antiferromagnets,Phys. Rev. Lett.59(1987) 799

work page 1987
[9]

Affleck, T

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,Valence Bond Ground States in Isotropic Quantum Antiferromagnets,Commun. Math. Phys.115(1988) 477

work page 1988
[10]

The Variational Quantum Eigensolver: A Review of Methods and Best Practices

J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson,The Variational Quantum Eigensolver: A review of methods and best practices,Physics Report986(Nov., 2022) 1–128, [arXiv:2111.05176]

work page arXiv 2022
[11]

R. I. Nepomechie,Bethe ansatz on a quantum computer?,Quant. Inf. Comput.21 (2021), no. 3&4 255–265, [arXiv:2010.01609]

work page arXiv 2021
[12]

Raveh and R

D. Raveh and R. I. Nepomechie,Estimating Bethe roots with VQE,J. Phys. A57 (2024), no. 35 355303, [arXiv:2404.18244]

work page arXiv 2024
[13]

Itoi and M.-H

C. Itoi and M.-H. Kato,Extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain,Phys. Rev. B55(Apr., 1997) 8295–8303, [cond-mat/9605105]

work page arXiv 1997
[14]

E. H. Lieb and W. Liniger,Exact analysis of an interacting Bose gas. 1. The General solution and the ground state,Phys. Rev.130(1963) 1605–1616. – 15 –

work page 1963
[15]

E. H. Lieb,Exact Analysis of an Interacting Bose Gas. 2. The Excitation Spectrum, Phys. Rev.130(1963) 1616–1624

work page 1963
[16]

Gaudin,Un systeme à une dimension de fermions en interaction,Phys

M. Gaudin,Un systeme à une dimension de fermions en interaction,Phys. Lett. A 24(1967), no. 1 55 – 56

work page 1967
[17]

E. H. Lieb and F. Y. Wu,Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension,Phys. Rev. Lett.20(1968) 1445–1448. [Erratum: Phys.Rev.Lett. 21, 192 (1968)]

work page 1968
[18]

Zheng, Y

M. Zheng, Y. Qiao, Y. Wang, J. Cao, and S. Chen,Exact Solution of the Bose-Hubbard Model with Unidirectional Hopping,Phys. Rev. Lett.132(2024), no. 8 086502, [arXiv:2305.00439]

work page arXiv 2024
[19]

E. K. Sklyanin,Boundary Conditions for Integrable Quantum Systems,J. Phys. A 21(1988) 2375–2389

work page 1988
[20]

J. Cao, W. Yang, K. Shi, and Y. Wang,Off-diagonal Bethe ansatz and exact solution of a topological spin ring,Phys. Rev. Lett.111(2013), no. 13 137201, [arXiv:1305.7328]

work page arXiv 2013
[21]

Belliard and N

S. Belliard and N. Crampé,Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz,SIGMA9(2013) 072, [arXiv:1309.6165]

work page arXiv 2013
[22]

C. N. Yang and C. P. Yang,One-dimensional chain of anisotropic spin-spin interactions. ii. properties of the ground-state energy per lattice site for an infinite system,Phys. Rev.150(Oct, 1966) 327–339

work page 1966
[23]

M. Takahashi,One-dimensional electron gas with delta-function interaction at finite temperature,Progress of Theoretical Physics46(11, 1971) 1388–1406, [https://academic.oup.com/ptp/article-pdf/46/5/1388/5269149/46-5-1388.pdf]

work page 1971
[24]

J. S. V. Dyke, G. S. Barron, N. J. Mayhall, E. Barnes, and S. E. Economou, Preparing Bethe Ansatz Eigenstates on a Quantum Computer,PRX Quantum2 (2021), no. 4 040329, [arXiv:2103.13388]

work page arXiv 2021
[25]

J. S. Van Dyke, E. Barnes, S. E. Economou, and R. I. Nepomechie,Preparing exact eigenstates of the open XXZ chain on a quantum computer,J. Phys. A55(2022), no. 5 055301, [arXiv:2109.05607]

work page arXiv 2022
[26]

W. Li, M. Okyay, and R. I. Nepomechie,Bethe states on a quantum computer: success probability and correlation functions,J. Phys. A55(2022), no. 35 355305, [arXiv:2201.03021]

work page arXiv 2022
[27]

Raveh and R

D. Raveh and R. I. Nepomechie,Deterministic Bethe state preparation,Quantum8 (2024) 1510, [arXiv:2403.03283]

work page arXiv 2024
[28]

Sopena, M

A. Sopena, M. H. Gordon, D. García-Martín, G. Sierra, and E. López,Algebraic Bethe Circuits,Quantum6(2022) 796, [arXiv:2202.04673]

work page arXiv 2022
[29]

R. Ruiz, A. Sopena, M. H. Gordon, G. Sierra, and E. López,The Bethe Ansatz as a Quantum Circuit,Quantum8(2024) 1356, [arXiv:2309.14430]. – 16 –

work page arXiv 2024
[30]

R. Ruiz, A. Sopena, E. López, G. Sierra, and B. Pozsgay,Bethe Ansatz, quantum circuits, and the F-basis,SciPost Phys.18(2025), no. 6 187, [arXiv:2411.02519]. – 17 –

work page arXiv 2025

[1] [1]

Bethe,On the theory of metals

H. Bethe,On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain,Z. Phys.71(1931) 205–226

work page 1931

[2] [2]

W. Zhao, Y. Jiang, and R.-D. Zhu,The Roaming Bethe Roots: An Effective Bethe Ansatz Beyond Integrability,to appear(2026)

work page 2026

[3] [3]

H. M. Babujian,Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spin S,Phys. Lett. A90(1982) 479–482

work page 1982

[4] [4]

L. A. Takhtajan,The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins,Phys. Lett. A87(1982) 479–482

work page 1982

[5] [5]

C. K. Lai,Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics,Journal of Mathematical Physics15(10, 1974) 1675–1676

work page 1974

[6] [6]

Sutherland,Model for a multicomponent quantum system,Phys

B. Sutherland,Model for a multicomponent quantum system,Phys. Rev. B12(Nov,

work page

[7] [7]

Yang,Some exact results for the many body problems in one dimension with repulsive delta function interaction,Phys

C.-N. Yang,Some exact results for the many body problems in one dimension with repulsive delta function interaction,Phys. Rev. Lett.19(1967) 1312–1314

work page 1967

[8] [8]

Affleck, T

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,Rigorous Results on Valence Bond Ground States in Antiferromagnets,Phys. Rev. Lett.59(1987) 799

work page 1987

[9] [9]

Affleck, T

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,Valence Bond Ground States in Isotropic Quantum Antiferromagnets,Commun. Math. Phys.115(1988) 477

work page 1988

[10] [10]

The Variational Quantum Eigensolver: A Review of Methods and Best Practices

J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson,The Variational Quantum Eigensolver: A review of methods and best practices,Physics Report986(Nov., 2022) 1–128, [arXiv:2111.05176]

work page arXiv 2022

[11] [11]

R. I. Nepomechie,Bethe ansatz on a quantum computer?,Quant. Inf. Comput.21 (2021), no. 3&4 255–265, [arXiv:2010.01609]

work page arXiv 2021

[12] [12]

Raveh and R

D. Raveh and R. I. Nepomechie,Estimating Bethe roots with VQE,J. Phys. A57 (2024), no. 35 355303, [arXiv:2404.18244]

work page arXiv 2024

[13] [13]

Itoi and M.-H

C. Itoi and M.-H. Kato,Extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain,Phys. Rev. B55(Apr., 1997) 8295–8303, [cond-mat/9605105]

work page arXiv 1997

[14] [14]

E. H. Lieb and W. Liniger,Exact analysis of an interacting Bose gas. 1. The General solution and the ground state,Phys. Rev.130(1963) 1605–1616. – 15 –

work page 1963

[15] [15]

E. H. Lieb,Exact Analysis of an Interacting Bose Gas. 2. The Excitation Spectrum, Phys. Rev.130(1963) 1616–1624

work page 1963

[16] [16]

Gaudin,Un systeme à une dimension de fermions en interaction,Phys

M. Gaudin,Un systeme à une dimension de fermions en interaction,Phys. Lett. A 24(1967), no. 1 55 – 56

work page 1967

[17] [17]

E. H. Lieb and F. Y. Wu,Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension,Phys. Rev. Lett.20(1968) 1445–1448. [Erratum: Phys.Rev.Lett. 21, 192 (1968)]

work page 1968

[18] [18]

Zheng, Y

M. Zheng, Y. Qiao, Y. Wang, J. Cao, and S. Chen,Exact Solution of the Bose-Hubbard Model with Unidirectional Hopping,Phys. Rev. Lett.132(2024), no. 8 086502, [arXiv:2305.00439]

work page arXiv 2024

[19] [19]

E. K. Sklyanin,Boundary Conditions for Integrable Quantum Systems,J. Phys. A 21(1988) 2375–2389

work page 1988

[20] [20]

J. Cao, W. Yang, K. Shi, and Y. Wang,Off-diagonal Bethe ansatz and exact solution of a topological spin ring,Phys. Rev. Lett.111(2013), no. 13 137201, [arXiv:1305.7328]

work page arXiv 2013

[21] [21]

Belliard and N

S. Belliard and N. Crampé,Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz,SIGMA9(2013) 072, [arXiv:1309.6165]

work page arXiv 2013

[22] [22]

C. N. Yang and C. P. Yang,One-dimensional chain of anisotropic spin-spin interactions. ii. properties of the ground-state energy per lattice site for an infinite system,Phys. Rev.150(Oct, 1966) 327–339

work page 1966

[23] [23]

M. Takahashi,One-dimensional electron gas with delta-function interaction at finite temperature,Progress of Theoretical Physics46(11, 1971) 1388–1406, [https://academic.oup.com/ptp/article-pdf/46/5/1388/5269149/46-5-1388.pdf]

work page 1971

[24] [24]

J. S. V. Dyke, G. S. Barron, N. J. Mayhall, E. Barnes, and S. E. Economou, Preparing Bethe Ansatz Eigenstates on a Quantum Computer,PRX Quantum2 (2021), no. 4 040329, [arXiv:2103.13388]

work page arXiv 2021

[25] [25]

J. S. Van Dyke, E. Barnes, S. E. Economou, and R. I. Nepomechie,Preparing exact eigenstates of the open XXZ chain on a quantum computer,J. Phys. A55(2022), no. 5 055301, [arXiv:2109.05607]

work page arXiv 2022

[26] [26]

W. Li, M. Okyay, and R. I. Nepomechie,Bethe states on a quantum computer: success probability and correlation functions,J. Phys. A55(2022), no. 35 355305, [arXiv:2201.03021]

work page arXiv 2022

[27] [27]

Raveh and R

D. Raveh and R. I. Nepomechie,Deterministic Bethe state preparation,Quantum8 (2024) 1510, [arXiv:2403.03283]

work page arXiv 2024

[28] [28]

Sopena, M

A. Sopena, M. H. Gordon, D. García-Martín, G. Sierra, and E. López,Algebraic Bethe Circuits,Quantum6(2022) 796, [arXiv:2202.04673]

work page arXiv 2022

[29] [29]

R. Ruiz, A. Sopena, M. H. Gordon, G. Sierra, and E. López,The Bethe Ansatz as a Quantum Circuit,Quantum8(2024) 1356, [arXiv:2309.14430]. – 16 –

work page arXiv 2024

[30] [30]

R. Ruiz, A. Sopena, E. López, G. Sierra, and B. Pozsgay,Bethe Ansatz, quantum circuits, and the F-basis,SciPost Phys.18(2025), no. 6 187, [arXiv:2411.02519]. – 17 –

work page arXiv 2025