GEWU Magazine

CTM inversion relations3 questions

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
Rigorous foundation of the inversion-relation derivation of the bulk, surface and corner free energies of the square-lattice Ising model
Conjectured inversion relations for thermalized interaction-round-a-face lattice models built from rational conformal field theories

Exponential structure of the CTM spectrum3 questions

CTM operator product representation1 questions

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

CTM star-triangle relation2 questions

CTM and the eight-vertex model3 questions

CTM and the density matrix2 questions

CTM and infinite PEPS contraction1 questions

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

CTM and order parameter3 questions

CTM and hard-hexagon model1 questions

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

CTMRG3 questions

density-matrix renormalization group（DMRG）2 questions

diagonal and non-diagonal scattering3 questions

dichromatic polynomial2 questions

difference property1 questions

Prove or disprove that the boost condition $[Q_2,Q_3]=0$ is equivalent to Yang–Baxter solvability for non-difference-form and non-diagonalizable nearest-neighbour spin chains
Open for about 31 years

dilogarithm identities2 questions

dilogarithm sum rules2 questions

Mechanism of DNA overstretching deformation3 questions

Dolan–Grady relation2 questions

domain-wall boundary condition2 questions

dressed energy2 questions

dressed velocity1 questions

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 questions

Duality and Star-Triangle Transformations of Planar Ising Models1 questions

The precise relation between Chang duality of the two-dimensional $\phi^4$ theory and the continuum limit of Kramers-Wannier duality
Open for about 5 years

Entanglement spectrum and CTM spectrum1 questions

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

entropy production in integrable systems2 questions

Euler-scale transport2 questions

excited-state TBA3 questions

Face-type Yang–Baxter equation4 questions

face–vertex correspondence4 questions

finite-entanglement scaling2 questions

Form factors and correlation function representation2 questions

form-factor bootstrap3 questions

Fredholm determinant1 questions

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 questions

Gaudin determinant1 questions

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

Gaussian/

c=1

critical line2 questions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Chiral Potts order parameters from finite-lattice determinant representations: homogeneous and thermodynamic limits in general ZpZ_pZp​ representations, and one-determinant form factors for the generators vnv_nvn​

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

Kosterlitz–Thouless critical reduced field of the triangular Ising antiferromagnet in a field: controlled finite-bond-dimension extrapolation for C3C_3C3​-symmetric CTMRG and the asymptotics of the three-state Potts critical line

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stochastic-geometry description of critical Ashkin–Teller interfaces: the boundary-operator map, the four fractal dimensions, SLE4_44​ traces, and FK–spin duality in the c=1c=1c=1 extended conformal field theory

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

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

Rigorous derivation of the electric critical exponents $\eta_e=1-\mu/\pi$ and $\delta_e=(3\pi+\mu)/(\pi-\mu)$ of the symmetric eight-vertex model

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

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

Chiral Potts order parameters from finite-lattice determinant representations: homogeneous and thermodynamic limits in general $Z_p$ representations, and one-determinant form factors for the generators $v_n$

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

Kosterlitz–Thouless critical reduced field of the triangular Ising antiferromagnet in a field: controlled finite-bond-dimension extrapolation for $C_3$ -symmetric CTMRG and the asymptotics of the three-state Potts critical line

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

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

Removing the full-rank hypothesis from the cluster $a$ -variable periodicity derivation of higher-degree Rogers dilogarithm identities

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

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

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

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

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

Closure relations and complete separation-of-variables spectrum characterization for twisted $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models

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

Stochastic-geometry description of critical Ashkin–Teller interfaces: the boundary-operator map, the four fractal dimensions, SLE $_4$ traces, and FK–spin duality in the $c=1$ extended conformal field theory