Letters in Mathematical Physics最新文献

{"title":"Topological quantum color code model on infinite lattice","authors":"Shiyu Cao,&nbsp;Zhian Jia,&nbsp;Sheng Tan","doi":"10.1007/s11005-026-02158-5","DOIUrl":"10.1007/s11005-026-02158-5","url":null,"abstract":"<div><p>The color code model is a crucial instance of a Calderbank–Shor–Steane (CSS)-type topological quantum error-correcting code, which notably supports transversal implementation of the full Clifford group. Its robustness against local noise is rooted in the structure of its topological excitations. From the perspective of quantum phases of matter, it is essential to understand these excitations in the thermodynamic limit. In this work, we analyze the color code model on an infinite lattice within the quasi-local <span>(C^{*})</span>-algebra framework, using a cone-localized Doplicher–Haag–Roberts (DHR) analysis. We classify its irreducible anyon superselection sectors and construct explicit string operators that generate anyonic excitations from the ground state. We further examine the fusion and braiding properties of these excitations. Our results show that the topological order of the color code is described by <span>(textsf{Rep}(D(mathbb {Z}_2 times mathbb {Z}_2)) simeq textsf{Rep}(D(mathbb {Z}_2)) boxtimes textsf{Rep}(D(mathbb {Z}_2)))</span>, which is equivalent to a double layer of the toric code and consistent with established analyses on finite lattices. We also establish the existence and uniqueness of the KMS state at every finite inverse temperature and derive an explicit description of the corresponding thermal distribution of stabilizer excitations.\u0000</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":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132512","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}

{"title":"Spatial entanglement sudden death in spin chains at all temperatures","authors":"Samuel O. Scalet","doi":"10.1007/s11005-026-02169-2","DOIUrl":"10.1007/s11005-026-02169-2","url":null,"abstract":"<div><p>We prove a finite entanglement length for the Gibbs state of any local Hamiltonian on a spin chain at any finite temperature: After removing an interval of size at least equal to the entanglement length, the remaining left and right half-chains are in a separable state.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035325","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}

{"title":"Spatial localization of relativistic quantum systems: the commutativity requirement and the locality principle: part I—a general analysis","authors":"Valter Moretti","doi":"10.1007/s11005-026-02159-4","DOIUrl":"10.1007/s11005-026-02159-4","url":null,"abstract":"<div><p>We study the role of commutativity in the representation of relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A celebrated no-go theorem by Halvorson and Clifton shows that the commutativity of localization effects associated with causally separated regions is incompatible with other apparently natural assumptions about spatial localization. In particular, commutativity is assumed to provide the mathematical representation of locality in the Araki–Haag–Kastler formulation of quantum field theory. This raises the question of whether commutativity follows from more elementary locality principles of quantum theory. Adopting Busch’s operational analysis in terms of no-signaling and relativistic consistency, we argue that, for a particle-like system, the commutativity requirement does not follow from these principles. Under a natural local detectability principle, elementary localization observables are not localized in arbitrarily small spacetime neighborhoods of the corresponding spatial regions, but rather in regions containing the entire rest space (a Cauchy surface) on which the measurement is performed. This is a consequence of the very nature of a particle, which is assumed to be localized at a unique position on a rest space completely filled with ideal detectors. In this respect, there is no direct conflict with the Araki–Haag–Kastler formulation of local quantum physics. On the other hand, we also show that commutativity and localization may coexist when one refers to less idealized localization procedures. Indeed, we introduce conditional localization POVMs associated with bounded spatial regions interpreted as laboratories. Owing to a result in quantum information theory known as the gentle measurement lemma, these observables describe conditional localization probabilities. In principle, these observables satisfy commutativity when associated with causally separated laboratories. As a consequence, they could be represented by local observables in the sense of Araki–Haag–Kastler. Explicit examples of such local observables satisfying the commutativity requirement are presented in a second paper within the framework of local quantum field theory.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02159-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035326","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}

{"title":"On quivers, spectral networks and black holes","authors":"Paolo Arnaudo,&nbsp;Alba Grassi,&nbsp;Qianyu Hao","doi":"10.1007/s11005-026-02136-x","DOIUrl":"10.1007/s11005-026-02136-x","url":null,"abstract":"<div><p>It was recently found that connection coefficients of the Heun equation can be derived in a closed form using crossing symmetry in two-dimensional Liouville theory via the Nekrasov–Shatashvili functions. In this work, we systematize this approach to second-order linear ODEs of Fuchsian type, which arise in the description of <span>(mathcal {N}=2)</span>, four-dimensional quiver gauge theories. After presenting the general procedure, we focus on the specific case of Fuchsian equations with five regular singularities and present some applications to black-hole perturbation theory. First, we consider a massive scalar perturbation of the Schwarzschild black hole in AdS₇. Next, we analyze vector-type perturbations of the Reissner–Nordström-AdS₅ black hole. We also discuss the implications of our results in the context of the AdS/CFT correspondence and present explicit results in the large spin limit, where we make connection with the light-cone bootstrap. Furthermore, using the spectral network technology, we identify the region of the moduli space in Seiberg–Witten theory that is relevant for the study of black-hole quasinormal modes. Our results suggest that, in some cases, this region corresponds to the strong-coupling regime, highlighting the potential applicability of the conformal GMN TBA framework to address scenarios where the gravitational dictionary implies that the instanton counting parameters are not parametrically small.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02136-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986613","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}

{"title":"Spectral properties of the Dirichlet Laplacian in twisted and sheared waveguides","authors":"Diana Carolina Suarez Bello","doi":"10.1007/s11005-026-02153-w","DOIUrl":"10.1007/s11005-026-02153-w","url":null,"abstract":"<div><p>In this work, we analyze the Dirichlet Laplacian <span>(-Delta _{Omega }^D)</span> in an unbounded waveguide <span>(Omega subset mathbb {R}^3)</span>, where the cross section is translated in a constant direction and rotated along a spatial line. We focus on the effects of twisting on the spectrum, discussing conditions under which discrete eigenvalues emerge. Our results highlight the interplay between geometry and spectral properties, showing that shearing can induce a richer spectral structure even in straight waveguides.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02153-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986564","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}

{"title":"A Pontryagin class obstruction for purely electric and purely magnetic Weyl curvature tensors","authors":"Thijs de Kok","doi":"10.1007/s11005-026-02152-x","DOIUrl":"10.1007/s11005-026-02152-x","url":null,"abstract":"<div><p>Do all manifolds that admit Lorentzian metrics also admit such metrics that have a purely electric (PE) or purely magnetic (PM) Weyl curvature tensor? To (partially) answer this question, we show that for all algebraic curvature tensors on a 4<i>k</i>-dimensional scalar product space that are even or odd under the action of a orientation-reversing isometry, the products of Pontryagin forms that land in the top-degree exterior power of the dual vector space vanish. We use this to derive the vanishing of all products of Pontryagin classes that land in the top-degree de Rham cohomology of a 4<i>k</i>-dimensional pseudo-Riemannian manifold with a PE or PM Riemann or Weyl curvature tensor. For compact manifolds, this gives nontrivial cohomological obstructions to the existence of such pseudo-Riemannian metrics with globally PE or PM Riemann or Weyl curvature tensors. These obstructions can be linked to the existence of Lorentzian metrics of several Petrov subtypes, which play an important role in classifying exact solutions to the Einstein equations. Moreover, they can be applied to foliations by nondegenerate umbilic hypersurfaces, which may appear as time slices of spacetimes.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02152-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986961","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}

{"title":"Quantization as a categorical equivalence for Hilbert bimodules and Lagrangian relations","authors":"Benjamin H. Feintzeig","doi":"10.1007/s11005-026-02142-z","DOIUrl":"10.1007/s11005-026-02142-z","url":null,"abstract":"<div><p>I consider two categories: the first consists in Lagrangian relations between Poisson algebras as models of classical physics, and the second consists in Hilbert bimodules between C*-algebras as models of quantum physics. Strict deformation quantization and the classical limit each determine functors between these categories. I prove that the quantization and classical limit functors are “almost inverse” to each other, thus establishing a categorical equivalence.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926744","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}

{"title":"The sine-Gordon equation in light-cone coordinates on the half-lines revisited: a Riemann–Hilbert approach","authors":"Iryna Karpenko","doi":"10.1007/s11005-026-02147-8","DOIUrl":"10.1007/s11005-026-02147-8","url":null,"abstract":"<div><p>In this work, we study the initial-boundary value (IBV) problems for the sine-Gordon (sG) equation in the light-cone coordinates <span>(u_{xt}=sin u)</span> in the quarter-planes <span>(x&gt; 0, t &gt; 0)</span> and <span>(x &lt; 0, t &gt; 0)</span>, assuming a suitable decay as <span>(xrightarrow +infty )</span> or as <span>(xrightarrow -infty )</span>. Employing the Riemann–Hilbert (RH) problem framework, we demonstrate that these two IBV problems differ significantly with respect to the boundary data required for well-posedness. Specifically, the solution of the “right problem” (<span>(xge 0)</span>) is uniquely determined by the initial data <i>u</i>(<i>x</i>, 0), <span>(xge 0)</span> alone, whereas for the “left problem” (<span>(xle 0)</span>), the boundary data <i>u</i>(0, <i>t</i>) have to be prescribed in addition to the initial data in order to obtain a well-posed problem. The latter problem is solved using the unified transform method (also known as the Fokas method).</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13541954/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148896267","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}

{"title":"Reconstructing double-well potentials from transition layers in long-range phase coexistence models","authors":"Francesco De Pas,&nbsp;Serena Dipierro,&nbsp;Enrico Valdinoci","doi":"10.1007/s11005-026-02146-9","DOIUrl":"10.1007/s11005-026-02146-9","url":null,"abstract":"<div><p>In models of phase coexistence, the precise form of the double-well potential is of central importance, yet it cannot be derived from first principles. In this paper, we investigate an inverse problem: starting from a prescribed transition layer with power-type decay at infinity, we reconstruct the structural properties of the associated double-well potential. We focus on the case of long-range interactions, where the dependence of the potential on the layer and its derivatives is particularly delicate. Our analysis establishes a correspondence between the decay rate of the transition layer and the regularity of the potential, revealing the existence of specific patterns and the possible emergence of degeneracies.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926260","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}

{"title":"Resonance transformations for the ((2,2p+1)) minimal string via (x-y) swap: a proof of Artemev’s conjecture","authors":"Kornelis Dekinga,&nbsp;Sergey Shadrin,&nbsp;Erik Verlinde","doi":"10.1007/s11005-026-02140-1","DOIUrl":"10.1007/s11005-026-02140-1","url":null,"abstract":"<div><p>This paper contains a proof of a recent conjecture of Artemev that connected the resonance transformations for the <span>((2,2p+1))</span> minimal string to the <span>(x-y)</span> swap in the theory of topological recursion.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13529612/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878968","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}