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A KK-theoretic note on the spectral localiser 光谱定位器的kk理论注释
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-06 DOI: 10.1007/s11005-026-02163-8
Koen van den Dungen
{"title":"A KK-theoretic note on the spectral localiser","authors":"Koen van den Dungen","doi":"10.1007/s11005-026-02163-8","DOIUrl":"10.1007/s11005-026-02163-8","url":null,"abstract":"<div><p>We review the construction of the spectral localiser (due to Loring and Schulz-Baldes) from a <i>KK</i>-theoretic perspective. We first give a <i>KK</i>-theoretic argument providing a spectral flow expression for the even or odd index pairing in terms of the “infinite volume” spectral localiser. Our approach towards this first step is more direct, treats the even and odd cases on an equal footing, and has the advantage that the construction of the spectral localiser becomes immediately apparent from the computation of the index pairing via a Kasparov product. In a second step of “spectral truncation”, we then describe how this spectral flow expression can be computed in terms of the signature of the “finite volume” spectral localiser. Throughout, we do not require invertibility of the operator representing the <i>K</i>-homology class, and the even index pairing then obtains an additional contribution coming from the Fredholm index.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02163-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical Heun observables and elliptic solvability 经典Heun观测值与椭圆可解性
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-06 DOI: 10.1007/s11005-026-02157-6
Luc Vinet, Alexei Zhedanov
{"title":"Classical Heun observables and elliptic solvability","authors":"Luc Vinet,&nbsp;Alexei Zhedanov","doi":"10.1007/s11005-026-02157-6","DOIUrl":"10.1007/s11005-026-02157-6","url":null,"abstract":"<div><p>We introduce a classical analog of the algebraic Heun operator associated with a classical Leonard pair. Given two observables <i>X</i> and <i>Y</i> satisfying the classical counterpart of the Askey–Wilson relations, we define a <i>classical Heun observable</i> <i>W</i> as the most general bilinear combination of <i>X</i>, <i>Y</i>, and their Poisson bracket. We prove that, when <i>W</i> is taken as Hamiltonian, the observables <i>X</i> and <i>Y</i> satisfy quartic differential equations whose generic solutions are elliptic functions of second order. This result provides a universal algebraic mechanism transforming the elementary dynamics associated with classical Leonard pairs into elliptic dynamics and yields an algebraic explanation of a classical observation of Manning on the connection between the Heun equation and elliptic solvability. The construction is illustrated on three examples: an extension of the Pöschl–Teller system, the Zhukovsky–Volterra gyrostat, and a relativistic <span>(A_1)</span> model related to the classical Askey–Wilson algebra.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local measurements and the entanglement transition in quantum spin chains 量子自旋链中的局部测量和纠缠跃迁
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-05 DOI: 10.1007/s11005-026-02171-8
Sven Bachmann, Mahsa Rahnama, Gabrielle Tournaire
{"title":"Local measurements and the entanglement transition in quantum spin chains","authors":"Sven Bachmann,&nbsp;Mahsa Rahnama,&nbsp;Gabrielle Tournaire","doi":"10.1007/s11005-026-02171-8","DOIUrl":"10.1007/s11005-026-02171-8","url":null,"abstract":"<div><p>We consider the transition between short-range entangled (SRE) and long-range entangled states of infinite quantum spin chains which is induced by local measurements. Specifically, we assume that the initial state is in a non-trivial symmetry-protected topological phase of a compact local symmetry group <span>(mathcal {G})</span>. We show that the on-site measurements of an appropriate local charge on intervals of increasing lengths transform the initial SRE state into a family of states with increasingly long-range correlations. In particular, the post-measurement states cannot be uniformly short-range entangled. In the case where the initial state is obtained from a product state using a quantum cellular automaton, we construct the infinite volume post-measurement state and exhibit almost-local observables that are maximally correlated.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp estimates for large N Weingarten functions 大N Weingarten函数的精确估计
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-03 DOI: 10.1007/s11005-026-02162-9
Ron Nissim
{"title":"Sharp estimates for large N Weingarten functions","authors":"Ron Nissim","doi":"10.1007/s11005-026-02162-9","DOIUrl":"10.1007/s11005-026-02162-9","url":null,"abstract":"<div><p>Weingarten functions provide a tool for computing Haar measure matrix integrals of polynomials in the matrix entries. An important property of Weingarten functions is their particularly simple large <i>N</i> limits. In 2017, Benoît Collins and Sho Matsumoto studied when this limit holds for Weingarten functions associated with integrals of products of 2<i>n</i> matrix entries, as <span>(n rightarrow infty )</span>, together with the matrix size <i>N</i> [11]. They showed that the large <i>N</i> limit is uniformly achieved as long as <span>(n=o(N^{4/7}))</span>, a result which already has applications to strong asymptotic freeness [2, 3]. However, their result is not optimal. They conjectured that their result should actually hold up to <span>(n=o(N^{2/3}))</span> which is optimal. We prove this conjecture for the matrix groups <span>(G in {textrm{U}(N))</span>, <span>(textrm{O}(N))</span>, <span>(textrm{Sp}(N)})</span>. The proof proceeds by introducing a Markov process on permutations (pairings) which we call the unitary (orthogonal) <i>Weingarten process</i>. We believe this process may have further applications to the theory of Weingarten functions. We also prove two new bounds regarding the large <i>N</i> limit of the Weingarten function in the regimes when <span>(n=o(N^{4/5}))</span>, and <span>(n=o(N))</span>.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An algebraic theory of gapped domain wall partons 间隙域壁部的代数理论
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-10-01 DOI: 10.1007/s11005-026-02166-5
Matthew Buican, Roman Geiko, Milo Moses, Bowen Shi
{"title":"An algebraic theory of gapped domain wall partons","authors":"Matthew Buican,&nbsp;Roman Geiko,&nbsp;Milo Moses,&nbsp;Bowen Shi","doi":"10.1007/s11005-026-02166-5","DOIUrl":"10.1007/s11005-026-02166-5","url":null,"abstract":"<div><p>The entanglement bootstrap program has generated new quantum numbers associated with degrees of freedom living on gapped domain walls between topological phases in two dimensions. Most fundamental among these are the so-called parton quantum numbers, which give rise to a zoo of composite sectors. In this note, we propose a categorical description of partons. Along the way, we make contact with ideas from generalized symmetries and SymTFT.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT Hodge CohFT的亚纯微分和扭曲DR层次
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-09-30 DOI: 10.1007/s11005-026-02150-z
Xavier Blot, Paolo Rossi, Adrien Sauvaget
{"title":"Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT","authors":"Xavier Blot,&nbsp;Paolo Rossi,&nbsp;Adrien Sauvaget","doi":"10.1007/s11005-026-02150-z","DOIUrl":"10.1007/s11005-026-02150-z","url":null,"abstract":"<div><p>In [4], two families of classical and quantum integrable hierarchies associated to arbitrary Cohomological Field Theories (CohFTs) were introduced: the meromorphic differential and twisted double ramification hierarchies. For trivial CohFT, the authors established a connection with the untwisted Double Ramification (DR) hierarchy. In this paper, we extend this study to the Hodge CohFT and prove an analogous correspondence with the untwisted DR hierarchy. This yields nontrivial identities between Hodge integrals over the DR cycle, the twisted DR cycle and the cycle of meromorphic differentials.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02150-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shape modes of (mathbb {C}P^1) vortices c1涡旋的形状模态。
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-09-29 DOI: 10.1007/s11005-026-02156-7
Nora Gavrea, Derek Harland, Martin Speight
{"title":"Shape modes of (mathbb {C}P^1) vortices","authors":"Nora Gavrea,&nbsp;Derek Harland,&nbsp;Martin Speight","doi":"10.1007/s11005-026-02156-7","DOIUrl":"10.1007/s11005-026-02156-7","url":null,"abstract":"<div><p>In this paper, we investigate the existence of internal modes of vortices in the gauged <span>(mathbb {C}P^1)</span> sigma model. We develop a clean geometric formalism that highlights the symmetries of the Jacobi operator, obtained from the second variation of the energy functional. The formalism and subsequent results fundamentally rely on the Bogomol’nyi decomposition of the energy functional and can therefore be extended to other models with such a decomposition. We prove the existence of at least one shape mode for a general <span>(mathbb {C}P^1)</span> vortex solution on <span>(mathbb {R}^2)</span> and find numerically the shape modes and corresponding frequencies of a radially symmetric vortex. A surprising result is that the shape mode eigenvalues are very close to the scattering threshold, suggesting weakly bound shape modes could be characteristic of the <span>(mathbb {C}P^1)</span> model.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13624056/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149102597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Affine webs of type Q Q型仿射网
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-09-29 DOI: 10.1007/s11005-026-02155-8
Linliang Song, Xingyu Wang
{"title":"Affine webs of type Q","authors":"Linliang Song,&nbsp;Xingyu Wang","doi":"10.1007/s11005-026-02155-8","DOIUrl":"10.1007/s11005-026-02155-8","url":null,"abstract":"<div><p>We introduce a new diagrammatic <span>(Bbbk )</span>-linear monoidal supercategory <img>, the affine web supercategory of type <i>Q</i>, where <span>(Bbbk )</span> is a commutative ring in which 2 is invertible. This category is the affinization of the web supercategory of type <i>Q</i>, originally introduced by Brown and Kujawa. It serves as the type <i>Q</i> analog of the affine web category (of type <i>A</i>) introduced by Davidson, Kujawa, Muth, and independently by Wang and the first named author. We obtain diagrammatic integral bases for the Hom-spaces of this category. We show that <img> provides a combinatorial model for a natural monoidal supercategory of endosuperfunctors for Lie superalgebras of type <i>Q</i>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A simple proof of exponential decay for the near-critical planar Ising model 近临界平面Ising模型的指数衰减的一个简单证明
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-09-29 DOI: 10.1007/s11005-026-02160-x
Jianping Jiang, Frederik Ravn Klausen
{"title":"A simple proof of exponential decay for the near-critical planar Ising model","authors":"Jianping Jiang,&nbsp;Frederik Ravn Klausen","doi":"10.1007/s11005-026-02160-x","DOIUrl":"10.1007/s11005-026-02160-x","url":null,"abstract":"<div><p>For the Ising model defined on <span>(amathbb {Z}^2)</span> at critical temperature with external field <span>(a^{15/8}h)</span>, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high-temperature expansion, random-cluster and random current representations. A new input in the proof is that, in the near-critical sourceless single current measure, there are many loops formed by a path on <span>(amathbb {Z}^2)</span> with diameter of order 1, together with two external edges that connect the path’s endpoints to the ghost.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometry of autonomous versions of discrete Painlevé equations related to the Weyl group (W(E_8^{(1)})) 与Weyl群相关的离散painlev<s:1>方程的自治版本的几何 (W(E_8^{(1)}))
IF 1.6 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2026-09-26 DOI: 10.1007/s11005-026-02167-4
Jaume Alonso, Yuri B. Suris
{"title":"Geometry of autonomous versions of discrete Painlevé equations related to the Weyl group (W(E_8^{(1)}))","authors":"Jaume Alonso,&nbsp;Yuri B. Suris","doi":"10.1007/s11005-026-02167-4","DOIUrl":"10.1007/s11005-026-02167-4","url":null,"abstract":"<div><p>Discrete Painlevé equations are integrable two-dimensional birational maps associated to a family of generalized Halphen surfaces. A generalized Halphen surface can be realized either as <span>({mathbb {P}}^2)</span> blown up at nine points or as <span>({mathbb {P}}^1times {mathbb {P}}^1)</span> blown up at eight points. These maps become autonomous if the blow-up points are in a special position (nine points in <span>({mathbb {P}}^2)</span> supporting a pencil of cubic curves, resp. eight points in <span>({mathbb {P}}^1times {mathbb {P}}^1)</span> supporting a pencil of biquadratic curves), so that a generalized Halphen surface becomes a rational elliptic surface. In the generic case, the symmetry of a discrete Painlevé equation is the Weyl group <span>(W(E_8^{(1)}))</span>. One has a system of commuting maps which correspond to translational elements of <span>(W(E_8^{(1)}))</span> associated to the roots of the lattice <span>(E_8^{(1)})</span>. In the present note, we give a geometric construction of these commuting maps. For this, we use some novel birational involutions based on the above mentioned pencils of curves.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02167-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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