Communications in Mathematical Physics最新文献

{"title":"Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus","authors":"Igor Burban,&nbsp;Semyon Klevtsov","doi":"10.1007/s00220-025-05267-9","DOIUrl":"10.1007/s00220-025-05267-9","url":null,"abstract":"<div><p>In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of a complex torus <i>E</i> and a symmetric positively definite matrix <i>K</i> of size <i>g</i> with non-negative integral coefficients, satisfying some further constraints. The space of the corresponding wave functions turns out to be <span>(delta )</span>-dimensional, where <span>(delta )</span> is the determinant of <i>K</i>. We construct a hermitian holomorphic bundle of rank <span>(delta )</span> on the abelian variety <i>A</i> (which is the <i>g</i>-fold product of the torus <i>E</i> with itself), whose fibres can be identified with the space of wave function of Keski-Vakkuri and Wen. A rigorous construction of this “magnetic bundle” involves the technique of Fourier–Mukai transforms on abelian varieties. The constructed bundle turns out to be simple and semi-homogeneous and it can be equipped with two different (and natural) hermitian metrics: the one coming from the center-of-mass dynamics and the one coming from the Hilbert space of the underlying many-body system. We prove that the canonical Bott–Chern connection of the first hermitian metric is always projectively flat and give sufficient conditions for this property for the second hermitian metric.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05267-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"The q-Immanants and Higher Quantum Capelli Identities","authors":"Naihuan Jing,&nbsp;Ming Liu,&nbsp;Alexander Molev","doi":"10.1007/s00220-025-05273-x","DOIUrl":"10.1007/s00220-025-05273-x","url":null,"abstract":"<div><p>We construct polynomials <span>(mathbb {S}_{mu }(z))</span> parameterized by Young diagrams <span>(mu )</span>, whose coefficients are central elements of the quantized enveloping algebra <span>(textrm{U}_q(mathfrak {gl}_n))</span>. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of <i>z</i>, we get <i>q</i>-analogues of Okounkov’s quantum immanants for <span>(mathfrak {gl}_n)</span>. We show that the Harish-Chandra image of <span>(mathbb {S}_{mu }(z))</span> is a factorial Schur polynomial. We derive quantum analogues of the higher Capelli identities by calculating the images of the <i>q</i>-immanants in the braided Weyl algebra. We also give a symmetric function interpretation and new proof of the Newton identities of Gurevich, Pyatov and Saponov.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05273-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Tensor K-Matrices for Quantum Symmetric Pairs","authors":"Andrea Appel,&nbsp;Bart Vlaar","doi":"10.1007/s00220-025-05241-5","DOIUrl":"10.1007/s00220-025-05241-5","url":null,"abstract":"<div><p>Let <span>({{mathfrak {g}}})</span> be a symmetrizable Kac–Moody algebra, <span>(U_q({{mathfrak {g}}}))</span> its quantum group, and <span>(U_q({mathfrak {k}})subset U_q({{mathfrak {g}}}))</span> a quantum symmetric pair subalgebra determined by a Lie algebra automorphism <span>(theta )</span>. We introduce a category <span>(mathcal {W}_{theta })</span> of <i>weight</i> <span>(U_q({mathfrak {k}}))</span>-modules, which is acted on by the category of weight <span>(U_q({{mathfrak {g}}}))</span>-modules via tensor products. We construct a universal tensor K-matrix <span>({{mathbb {K}}} )</span> (that is, a solution of a reflection equation) in a completion of <span>(U_q({mathfrak {k}})otimes U_q({{mathfrak {g}}}))</span>. This yields a natural operator on any tensor product <span>(Motimes V)</span>, where <span>(Min mathcal {W}_{theta })</span> and <span>(Vin {{mathcal {O}}}_theta )</span>, <i>i.e.</i>, <i>V</i> is a <span>(U_q({{mathfrak {g}}}))</span>-module in category <span>({{mathcal {O}}})</span> satisfying an integrability property determined by <span>(theta )</span>. Canonically, <span>(mathcal {W}_{theta })</span> is equipped with a structure of a bimodule category over <span>({{mathcal {O}}}_theta )</span> and the action of <span>({{mathbb {K}}} )</span> is encoded by a new categorical structure, which we call a <i>boundary</i> structure on <span>(mathcal {W}_{theta })</span>. This generalizes a result of Kolb which describes a braided module structure on finite-dimensional <span>(U_q({mathfrak {k}}))</span>-modules when <span>({{mathfrak {g}}})</span> is finite-dimensional. We also consider our construction in the case of the category <span>({{mathcal {C}}})</span> of finite-dimensional modules of a quantum affine algebra, providing the most comprehensive universal framework to date for large families of solutions of parameter-dependent reflection equations. In this case the tensor K-matrix gives rise to a formal Laurent series with a well-defined action on tensor products of any module in <span>(mathcal {W}_{theta })</span> and any module in <span>({{mathcal {C}}})</span>. This series can be normalized to an operator-valued rational function, which we call trigonometric tensor K-matrix, if both factors in the tensor product are in <span>({{mathcal {C}}})</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05241-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Large Deviations and Additivity Principle for the Open Harmonic Process","authors":"Gioia Carinci,&nbsp;Chiara Franceschini,&nbsp;Rouven Frassek,&nbsp;Cristian Giardinà,&nbsp;Frank Redig","doi":"10.1007/s00220-025-05271-z","DOIUrl":"10.1007/s00220-025-05271-z","url":null,"abstract":"<div><p>We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. We characterize its stationary measure as a mixture of product measures. For all spin values, we identify the law of the mixture in terms of the Dirichlet process. Next, by using the explicit knowledge of the non-equilibrium steady state we establish formulas predicted by Macroscopic Fluctuation Theory for several quantities of interest: the pressure (by Varadhan’s lemma), the density large deviation function (by contraction principle), the additivity principle (by using the Markov property of the mixing law). To our knowledge, the results presented in this paper constitute the first rigorous derivation of these macroscopic properties for models of energy transport with unbounded state space, starting from the microscopic structure of the non-equilibrium steady state.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05271-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Bekenstein-Type Bound in QFT","authors":"Roberto Longo","doi":"10.1007/s00220-025-05261-1","DOIUrl":"10.1007/s00220-025-05261-1","url":null,"abstract":"<div><p>Let <i>B</i> be a spacetime region of width <span>(2R &gt;0)</span>, and <span>(varphi )</span> a vector state localized in <i>B</i>. We show that the vacuum relative entropy of <span>(varphi )</span>, on the local von Neumann algebra of <i>B</i>, is bounded by <span>(2pi R)</span>-times the energy of the state <span>(varphi )</span> in <i>B</i>. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05261-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Associated Varieties of Simple Affine VOAs (L_k(sl_3)) and W-algebras (W_k(sl_3,f))","authors":"Cuipo Jiang,&nbsp;Jingtian Song","doi":"10.1007/s00220-025-05291-9","DOIUrl":"10.1007/s00220-025-05291-9","url":null,"abstract":"<div><p>In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra <span>(V^k(sl_n))</span> for <span>(k=-n+frac{n-1}{q})</span> is generated by two singular vectors of conformal weight 3<i>q</i> if <span>(n=3)</span>, and by one singular vector of conformal weight 2<i>q</i> if <span>(ngeqslant 4)</span>. We next determine the associated varieties of the simple vertex operator algebras <span>(L_k(sl_3))</span> for all the non-admissible levels <span>(k=-3+frac{2}{2m+1})</span>, <span>(mgeqslant 0)</span>. The varieties of the associated simple affine <i>W</i>-algebras <span>(W_k(sl_3,f))</span>, for nilpotent elements <i>f</i> of <span>(sl_3)</span>, are also determined.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Affine (imath )Quantum Groups and Twisted Yangians in Drinfeld Presentations","authors":"Kang Lu,&nbsp;Weiqiang Wang,&nbsp;Weinan Zhang","doi":"10.1007/s00220-025-05263-z","DOIUrl":"10.1007/s00220-025-05263-z","url":null,"abstract":"<div><p>We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine <span>(imath )</span>quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Phase Transitions for the XY Model in Non-uniformly Elliptic and Poisson-Voronoi Environments","authors":"Paul Dario,&nbsp;Christophe Garban","doi":"10.1007/s00220-025-05269-7","DOIUrl":"10.1007/s00220-025-05269-7","url":null,"abstract":"<div><p>The goal of this paper is to analyze how the celebrated phase transitions of the <i>XY</i> model are affected by the presence of a non-elliptic quenched disorder. In dimension <span>(d=2)</span>, we prove that if one considers an <i>XY</i> model on the infinite cluster of a supercritical percolation configuration, the Berezinskii–Kosterlitz–Thouless (BKT) phase transition still occurs despite the presence of quenched disorder. The proof works for all <span>(p&gt;p_c)</span> (site or edge). We also show that the <i>XY</i> model defined on a planar Poisson-Voronoi graph also undergoes a BKT phase transition. When <span>(dge 3)</span>, we show in a similar fashion that the continuous symmetry breaking of the <i>XY</i> model at low enough temperature is not affected by the presence of quenched disorder such as supercritical percolation (in <span>(mathbb {Z}^d)</span>) or Poisson-Voronoi (in <span>(mathbb {R}^d)</span>). Adapting either Fröhlich–Spencer’s proof of existence of a BKT phase transition (Fröhlich and Spencer in Commun Math Phys 81(4):527–602, 1981) or the more recent proofs (Lammers in Probab Theory Relat Fields 182(1–2):531–550, 2022; van Engelenburg and Lis in Commun Math Phys 399(1):85–104, 2023; Aizenman et al. in Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models, 2021. arXiv preprint arXiv:2110.09498; van Engelenburg and Lis in On the duality between height functions and continuous spin models, 2023. arXiv preprint arXiv:2303.08596) to such non-uniformly elliptic disorders appears to be non-trivial. Instead, our proofs rely on Wells’ correlation inequality (Wells in Some Moment Inequalities and a Result on Multivariable Unimodality. PhD thesis, Indiana University, 1977).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05269-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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":"Localization for Lipschitz Monotone Quasi-periodic Schrödinger Operators on (mathbb Z^d) via Rellich Functions Analysis","authors":"Hongyi Cao,&nbsp;Yunfeng Shi,&nbsp;Zhifei Zhang","doi":"10.1007/s00220-025-05288-4","DOIUrl":"10.1007/s00220-025-05288-4","url":null,"abstract":"<div><p>We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on <span>(mathbb Z^d)</span> with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on Rellich function analysis in the perturbative regime. We show that at each scale, the resonant Rellich function uniformly inherits the Lipschitz monotonicity property of the potential via a novel Schur complement argument.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Membership Problem for Constant-Sized Quantum Correlations is Undecidable","authors":"Honghao Fu,&nbsp;Carl A. Miller,&nbsp;William Slofstra","doi":"10.1007/s00220-024-05229-7","DOIUrl":"10.1007/s00220-024-05229-7","url":null,"abstract":"<div><p>When two spatially separated parties make measurements on an unknown entangled quantum state, what correlations can they achieve? How difficult is it to determine whether a given correlation is a quantum correlation? These questions are central to problems in quantum communication and computation. Previous work has shown that the general membership problem for quantum correlations is computationally undecidable. In the current work we show something stronger: there is a family of constant-sized correlations—that is, correlations for which the number of measurements and number of measurement outcomes are fixed—such that solving the quantum membership problem for this family is computationally impossible. Thus, the undecidability that arises in understanding Bell experiments is not dependent on varying the number of measurements in the experiment. This places strong constraints on the types of descriptions that can be given for quantum correlation sets. Our proof is based on a combination of techniques from quantum self-testing and undecidability results for linear system nonlocal games.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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}