Refined enumeration of symmetry classes of alternating sign matrices

Fischer, Ilse; Saikia, Manjil P.

doi:10.1016/j.jcta.2020.105350

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…The determinant expressions (3.30) and (3.31) for the spin-chain overlaps were conjectured in [12]. Using recent results by Fischer and Saikia [45], one can even compute the determinants explicitly in terms of integers enumerating alternating sign matrices and rhombus tilings. Indeed, using [45, (3.9) and (3.10)], we find…”

Section: The Spin-chain Overlapmentioning

confidence: 98%

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Hagendorf

Parez

2022

SciPost Phys.

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The open XXZ spin chain with the anisotropy \Delta=-\frac12Δ=−12 and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain’s ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state’s logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

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Section: The Spin-chain Overlapmentioning

confidence: 98%

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Hagendorf

Parez

2022

SciPost Phys.

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show abstract

“…The determinant expressions (3.30) and (3.31) for the spin-chain overlaps were conjectured in [12]. Using recent results by Fischer and Saikia [43], one can even compute the determinants explicitly in terms of integers enumerating alternating sign matrices and rhombus tilings. Indeed, using [43, (3.9) and (3.10)], we find…”

Section: The Spin-chain Overlapmentioning

confidence: 98%

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Hagendorf,

Parez

2021

Preprint

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The open XXZ spin chain with the anisotropy ∆ = − 1 2 and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

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“…We have carried out similar checks on classes of ASM with symmetries, in particular the one-refined partition functions A V (2m + 1, k) and A HT (2m, k), counting respectively the vertically symmetric ASM (VSASM) of order 2m + 1 with a 1 at position k m on the second row, and the half-turn symmetric ASM (HTSASM) of order 2m with a unique 1 on the first row in column k. Their exact expressions are both given in [38], from which the asymptotic behaviour can be determined analytically. In the case of VSASM, the arctic curve is the same [26] as for ordinary ASM and it is also expected to be the case for HTSASM.…”

Section: 13)mentioning

confidence: 99%

Factorization in the multirefined tangent method

Debin¹,

Ruelle²

2021

J. Stat. Mech.

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When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete by observing a factorization property: if Z n+k denotes a refined partition function of a system of n + k non-crossing paths, with the endpoints of the k most external paths possibly displaced, then at dominant order in n, it factorizes as where is the contribution of the k most external paths. Moreover if the shape of the arctic curve is known, we find that the asymptotic value of is fully computable in terms of the large deviation function L introduced in Debin et al (2019 J. Stat. Mech. 113107) (also called Lagrangean function). We present detailed verifications of the factorization in the Aztec diamond and for alternating sign matrices by using exact lattice results. Reversing the argument, we reformulate the tangent method in a way that no longer requires the extension of the domain, and which reveals the hidden role of the L function. As a by-product, the factorization property provides an efficient way to conjecture the asymptotics of multirefined partition functions.

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Refined enumeration of symmetry classes of alternating sign matrices

Cited by 3 publications

References 29 publications

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Factorization in the multirefined tangent method

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