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    Disciplines / Research questions

    物理学

    691 个研究主题 · 2739 个问题

    CTM 反演关系3 个问题

    1. Rigorous derivation of the surface and corner free energies of the anisotropic triangular-lattice Ising model: Baxter's product-form conjectures and the corner-factor gauge ambiguity

    2. Rigorous foundation of the inversion-relation derivation of the bulk, surface and corner free energies of the square-lattice Ising model

    3. Conjectured inversion relations for thermalized interaction-round-a-face lattice models built from rational conformal field theories

    CTM 谱的指数结构3 个问题

    1. Algebraic and field-theoretic structure of the corner transfer matrix of the exact continuous matrix product state for the Lieb-Liniger model

    2. Lattice-level foundation and domain of validity of the entanglement-spectrum–corner-Hamiltonian correspondence in open quantum spin chains

    3. Analytic theory of the corner-transfer-matrix eigenvalue spectrum and its curvature-induced regularization at criticality for the Ising model on the hyperbolic plane

    CTM 算符乘积表示1 个问题

    1. Physical origin of flat corner transfer matrix spectra and the renormalizability–entanglement connection in the 2D kicked quantum Ising Floquet system

    CTM 星—三角关系2 个问题

    1. Exact spectrum of the Floquet evolution operator of star-triangle-derived integrable quantum circuits (Potts and ZQ\mathbb{Z}_Q circuits)

    2. Regularisation of continuous-spin extended Z-invariance and three-point Lagrangian systems as quasi-classical limits of Yang-Baxter lattice models

    CTM 与八顶点模型3 个问题

    1. Rigorous derivation of the corner free energy product formulae for integrable Potts and loop models, and the periodicity structure of their exponents

    2. Rigorous derivation of the electric critical exponents ηe=1−μ/π\eta_e=1-\mu/\pi and δe=(3π+μ)/(π−μ)\delta_e=(3\pi+\mu)/(\pi-\mu) of the symmetric eight-vertex model

    3. Rigorous foundation of the tail-operator construction of form factors in Belavin's (Z/nZ)(\mathbb{Z}/n\mathbb{Z})-symmetric model and the determinant/Riemann–Hilbert structure of eight-vertex form factors

    CTM 与密度矩阵2 个问题

    1. A priori characterization of exact entanglement equipartition and reconstruction of the entanglement Hamiltonian from symmetry-resolved entanglement in gapped quantum systems

    2. Microscopic foundation of the entanglement-spectrum-corner-Hamiltonian correspondence in integrable open spin chains

    CTM 与无限 PEPS 收缩1 个问题

    1. Conditioning and degeneracy of the environment-differentiation linear systems in CTM-based projected entangled-pair state optimization

    CTM 与序参量3 个问题

    1. Single-valued hyperelliptic representation of the automorphism-invariant order-parameter combination Lpq(r)L_{pq}(r) of the chiral Potts model for arbitrary rapidities

    2. Pair-correlation functions of the two-dimensional integrable N-state chiral Potts model

    3. Chiral Potts order parameters from finite-lattice determinant representations: homogeneous and thermodynamic limits in general ZpZ_p representations, and one-determinant form factors for the generators vnv_n

    CTM 与硬六边形模型1 个问题

    1. Foundations of the inversion-relation free energy of thermalized IRF lattice models and the identity of the coset factor G\mathcal{G}

    CTMRG3 个问题

    1. Kosterlitz–Thouless critical reduced field of the triangular Ising antiferromagnet in a field: controlled finite-bond-dimension extrapolation for C3C_3-symmetric CTMRG and the asymptotics of the three-state Potts critical line

    2. Robust lattice-tailored corner transfer matrix renormalization group for non-positive tensor networks on Archimedean lattices

    3. Symmetry-adapted subspace-iteration CTMRG for two-dimensional tensor networks

    density-matrix renormalization group（DMRG）2 个问题

    1. A priori prediction of the shared bond dimension of bundled matrix product states for many low-lying excitations

    2. Convergence theory and principled subspace enrichment for one-site DMRG-type alternating optimization in tensor train format with adaptive ranks

    diagonal 与 non-diagonal scattering3 个问题

    1. First-principles derivation of the boundary entropy for the current-perturbed SU(2)kSU(2)_k WZNW model: proving the diagonalize-and-normalize g-function procedure in a non-diagonal integrable quantum field theory

    2. Modified crossing in exact S-matrices of 1+1d QFTs with non-invertible symmetries: dynamical verification and completion of the categorical bootstrap

    3. Analytic characterization and field-theory realization of extremal charged S-matrices in 1+1 dimensions

    dichromatic polynomial2 个问题

    1. Arbitrary-width structure of the Potts partition-function-zero accumulation locus on self-dual square-lattice strips (the Chang–Shrock conjecture)

    2. The generalized Beraha conjecture for non-planar graphs: integer-Q eigenvalue cancellations, limiting curves, and density of flow roots for generalized Petersen graphs

    difference property1 个问题

    1. Prove or disprove that the boost condition [Q2,Q3]=0[Q_2,Q_3]=0 is equivalent to Yang–Baxter solvability for non-difference-form and non-diagonalizable nearest-neighbour spin chains

      未解决约 31 年
    dilogarithm identities2 个问题

    1. Removing the full-rank hypothesis from the cluster aa-variable periodicity derivation of higher-degree Rogers dilogarithm identities

    2. Nil-DAHA and quantum dilogarithm derivations of Rogers-Ramanujan type identities: the Cherednik-Feigin quantum lift and dilogarithm identities for untwisted nonsimply-laced affine types

    dilogarithm sum rules2 个问题

    1. Periodicity, Rogers dilogarithm sum rules and cluster-algebra status of the (N,p) crossed Y-systems from the low-energy AdS4 x CP3 string

    2. Precise generalized Nahm conjecture for half-indices of 3d Chern-Simons matter theories and the dynamical verification of the candidate modular Nahm sums

    DNA超拉伸形变的机理3 个问题

    1. Quantitative microscopic account of the DNA overstretching transition: coexistence force, S-state structure, and sequence-dependent cooperativity

      未解决约 12 年

    2. Structural organization and melting kinetics of overstretched DNA under defined topological constraint

      未解决约 16 年

    3. Sequence-dependent B-to-S kinetics, the B–S free-energy landscape, and hairpin-trapped reannealing among overstretched DNA structures

      未解决约 11 年
    Dolan–Grady 关系2 个问题

    1. A Lusztig-type quantum group structure for the q-Onsager algebra at roots of unity: presentation, cyclic tridiagonal pairs, and non-abelian symmetry sectors of the open XXZ chain

      未解决约 10 年

    2. Open directions in the charge-pump characterization of SPT phases: pivot loops, the Onsager algebra, representation-SPTs, and equivariant families

      未解决约 1 年
    domain-wall boundary condition2 个问题

    1. Completing the steepest-descent asymptotics of two-dimensional Ising interface partition functions: wetting-pole residues and uniform ordering of exponentially small corrections

      未解决约 1 年

    2. Arctic curves of the six-vertex model with partial domain-wall, reflecting-end, and half-turn boundary conditions: generic-weight determination and the domain-wall equivalence class

      未解决约 8 年
    dressed energy2 个问题

    1. Large-time asymptotics and finite-temperature spectral function of a mobile impurity in a one-dimensional gas

    2. Rigorous low-temperature expansions for the thermodynamic nonlinear integral equations of integrable models beyond the Lieb–Liniger gas, and rigorous 1/L finite-size corrections

    dressed velocity1 个问题

    1. An independent, fully classical derivation of the effective velocity and dressing equations of generalized hydrodynamics for classical integrable field theories with radiative modes (sinh-Gordon prototype)

    Drude weight3 个问题

    1. Sine-Gordon TBA and generalised hydrodynamics at generic coupling: Y-system equivalence, charge-conjugation-odd conserved quantities, and anomalous topological-charge transport beyond Euler scale

    2. Rigorous foundations of the finite-temperature spin Drude weight of the gapless XXZ chain: charge completeness, incommensurate anisotropies, and the fractal (popcorn) structure

    3. Open spin-transport problems for the integrable arbitrary-spin XXZ chain: low-temperature Drude weight, irrational anisotropy, the isotropic point, and Kohn-formula equivalence

    Duality and Star-Triangle Transformations of Planar Ising Models1 个问题

    1. The precise relation between Chang duality of the two-dimensional ϕ4\phi^4 theory and the continuum limit of Kramers-Wannier duality

      未解决约 5 年
    entanglement spectrum 与 CTM spectrum1 个问题

    1. Natural momentum labeling of corner-tensor entanglement spectra for infinite two-dimensional quantum systems

    entropy production in integrable systems2 个问题

    1. Hydrodynamic entropy production versus entanglement growth in a trapped one-dimensional Bose gas thermalising via diffusion

    2. Extensive entropy increase in isolated quantum systems: beyond the eigenstate thermalization hypothesis and beyond instantaneous quenches

    Euler-scale transport2 个问题

    1. Open problems of ballistic macroscopic fluctuation theory: rigorous foundations, shock selection, subleading corrections, full counting statistics, and the non-integrable, quantum, and experimental frontiers

    2. Well-definedness and shock-limited validity of the nonlinear projection formula for Euler-scale correlation functions

    excited-state TBA3 个问题

    1. TBA/NLIE equations for monster potentials: the excited-state sector of the ODE/IM correspondence

    2. TBA pseudo-energy reformulation of exact finite-volume expectation values and generalization to integrable quantum field theories with non-diagonal scattering beyond the sine-Gordon model

    3. Excited-state g-functions from analytic continuation of the Tracy-Widom TBA

    face-type Yang–Baxter 方程4 个问题

    1. Associative Yang-Baxter-type equation for fully dynamical (IRF-type) quantum R-matrices

    2. Classification of integrable interaction-round-a-face models of qubits and of their integrable unitary boundary processes

    3. Multiplicity-generalized conformal-field-theory construction of trigonometric RR-matrices and interaction-round-a-face weights (benchmark: the unrestricted su(3)k\mathfrak{su}(3)_k adjoint face model)

    4. Rigorous proof or refutation of the general-rank basic hypergeometric sum/integral identity and multi-spin IRF Yang-Baxter solution of Gahramanov and Jafarzade

    face–vertex correspondence4 个问题

    1. Universal vertex-IRF transformation for quantum affine algebras: realizing generalized Belavin-Drinfeld data, extending the Balog-Dabrowski-Feher classification, infinite-dimensional evaluation, and the Whittaker-module link

      未解决约 19 年

    2. Completing the 20-vertex to solid-on-solid correspondence: explicit evaluation of the Boltzmann weight constants

      未解决约 1 年

    3. Exact spectra and elliptic quantum-group structures for the q-deformed Inozemtsev and MZ' long-range spin chains

      未解决约 2 年

    4. Two-sided invertibility of cell maps and connecting-system hypotheses in the groupoid intertwiner-twist construction for the dynamical Yang-Baxter equation

      未解决约 2 年
    finite-entanglement scaling2 个问题

    1. Rigorous origin of the finite-bond-dimension scaling law ξ(D)∼Dκ\xi(D)\sim D^{\kappa} in tensor network renormalization

    2. Theory of the finite-entanglement perturbation and the encoding of conformal operator content in matrix product state transfer operators

    form factors 与关联函数表示2 个问题

    1. Consistent form factor programme and physical interpretation of the minimal form factor ambiguity for integrable QFTs deformed by finitely many generalized TTˉT\bar T perturbations

      未解决约 2 年

    2. Convergence of the form-factor expansion of correlation functions in the 1+1-dimensional sinh-Gordon model beyond the space-like vacuum two-point function, and the sharp large-N asymptotics of its summands

      未解决约 6 年
    form-factor bootstrap3 个问题

    1. Quantum energy inequalities in interacting integrable quantum field theories beyond one-particle level: stress-tensor prefactor freedom, parity breaking, and higher particle numbers

    2. Completing the form-factor bootstrap for TTˉT\bar T-deformed integrable quantum field theories: higher-particle form factors and the fate of the kinematic residue equation

    3. Thermodynamic form factor bootstrap for integrable quantum field theories with bound states and non-diagonal scattering

    Fredholm determinant1 个问题

    1. Completing the deformed Tracy–Widom theory for Fredholm determinants of Schrödinger-type kernels: general wave functions, multi-interval support, large-gap asymptotics, and the Schlesinger structure

    fusion hierarchy2 个问题

    1. Closure relations and complete separation-of-variables spectrum characterization for twisted glM∣Ngl_{\mathcal{M}|\mathcal{N}} and Hubbard models

      未解决约 7 年

    2. Trace conjectures and zero-pattern classification for the dilute A2(2)A_2^{(2)} loop model at λ=π/3λ=π/3: the conformal partition functions of critical site percolation on the triangular lattice

      未解决约 3 年
    Gaudin determinant1 个问题

    1. Rigorous proof of the universal MPS–Bethe-state overlap formula for orthogonal and symplectic rational spin chains

      未解决约 1 年
    Gaussian/c=1c=1 临界线2 个问题

    1. Stochastic-geometry description of critical Ashkin–Teller interfaces: the boundary-operator map, the four fractal dimensions, SLE4_4 traces, and FK–spin duality in the c=1c=1 extended conformal field theory

    2. Critical behaviour of the ferromagnetic square-lattice Ashkin–Teller model: rigorous verification of the predicted critical exponents and transition order along the transition curves

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