329 research outputs found

    Super-diffusion in one-dimensional quantum lattice models

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    We identify a class of one-dimensional spin and fermionic lattice models which display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit super-diffusive transport at finite temperature and half filling.Comment: 4 pages + appendices, v2 as publishe

    Tight bounds on the convergence rate of generalized ratio consensus algorithms

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    Phylogenetic toric varieties on graphs

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    We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the pro- jective coordinate ring of the models of graphs with one cycle are explicitly described. The phylogenetic models of graphs with the same topological invariants are deforma- tion equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.Comment: 36 pages, improved expositio

    Author index for volumes 101–200

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    Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory

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    We analyze the classical and quantum vacua of 2d N=(8,8)\mathcal{N}=(8,8) supersymmetric Yang-Mills theory with SU(N)SU(N) and U(N)U(N) gauge group, describing the worldvolume interactions of NN parallel D1-branes with flat transverse directions R8\mathbb{R}^8. We claim that the IR limit of the SU(N)SU(N) theory in the superselection sector labeled M(modN)M \pmod{N} --- identified with the internal dynamics of (M,N)(M,N)-string bound states of Type IIB string theory --- is described by the symmetric orbifold N=(8,8)\mathcal{N}=(8,8) sigma model into (R8)D1/SD(\mathbb{R}^8)^{D-1}/\mathbb{S}_D when D=gcd(M,N)>1D=\gcd(M,N)>1, and by a single massive vacuum when D=1D=1, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the U(N)U(N) theory with an additional U(1)U(1) 2-form gauge field BB coming from the string theory Kalb-Ramond field. This U(N)+BU(N)+B theory has generalized field configurations, labeled by the Z\mathbb{Z}-valued generalized electric flux and an independent ZN\mathbb{Z}_N-valued 't Hooft flux. We argue that in the quantum mechanical theory, the (M,N)(M,N)-string sector with MM units of electric flux has a ZN\mathbb{Z}_N-valued discrete θ\theta angle specified by M(modN)M \pmod{N} dual to the 't Hooft flux. Adding the brane center-of-mass degrees of freedom to the SU(N)SU(N) theory, we claim that the IR limit of the U(N)+BU(N) + B theory in the sector with MM bound F-strings is described by the N=(8,8)\mathcal{N}=(8,8) sigma model into SymD(R8){\rm Sym}^{D} ( \mathbb{R}^8). We provide strong evidence for these claims by computing an N=(8,8)\mathcal{N}=(8,8) analog of the elliptic genus of the UV gauge theories and of their conjectured IR limit sigma models, and showing they agree. Agreement is established by noting that the elliptic genera are modular-invariant Abelian (multi-periodic and meromorphic) functions, which turns out to be very restrictive.Comment: 47 pages. Comments welcome

    Complexity Theory

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    Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
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