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<p>Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the SO(6) spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian <i>Y</i> <sup>+</sup>(4) encode the information about one-point functions of the D3-D5 domain wall version of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25541_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 4 SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the SO(6) sector of the D3-D5 domain wall system.</p>

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On exact overlaps of integrable matrix product states: inhomogeneities, twists and dressing formulas

  • 期刊论文

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  • 发表日期：

    2025年2月18日

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  • Tamas Gombor,
  • Charlotte Kristjansen,
  • Vasileios Moustakis,
  • Xin Qian

摘要

Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the SO(6) spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian Y +(4) encode the information about one-point functions of the D3-D5 domain wall version of N \( \mathcal{N} \) = 4 SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the SO(6) sector of the D3-D5 domain wall system.