Condensed Matter Physicist; PhD

Contribute to a public benchmark of research-level physics challenges designed to evaluate whether advanced AI systems can perform genuine physics research reasoning. Review the benchmark paper, arXiv:, before applying to assess your interest. Assignments are matched to your publication record and may involve creating, solving, reviewing, or auditing research-level problems. All work must include clear, complete written reasoning that another specialist can independently follow and verify.

Matching is narrow: applicants must have published on at least one specific phenomenon below, rather than condensed matter physics broadly. One-dimensional field theory:
Abelian bosonization;
Majorana and Ising-Luttinger sectors; scaling dimensions; one-loop RG; OPE; commensurate-incommensurate transitions. Parafermion zero modes and FQH-superconductor heterostructures: ZN algebra, non-Abelian braiding, fusion channels, fractional Josephson effects, Berry phases. Rational CFT and non-Abelian quantum Hall edge theories: torus CFT, Verlinde lines, modular S matrix, Verlinde formula, Moore-Read states, fusion categories, non-invertible symmetries, modular in variance. SPT and Haldane phases: AKLT models, string order, matrix product states, transfer matrices, Kraus channels, decoherence-induced mixed-state topological order.

Flat-band Hubbard models: checkerboard lattices, topological nearly flat bands, flat-band ferromagnetism, Hartree-Fock, Stoner instability, interaction-driven transitions, determinant QMC. SYK and disordered fermions: low-rank random couplings, Majorana fermions, quenched averaging, large-N melonic diagrams, Schwinger-Dyson equations, free energy, residual entropy. Correlated electron transport:
Hubbard models, Fermi liquids, Kubo response, interaction expansions, Matsubara Green''s functions, vertex corrections, momentum relaxation, lattice scattering, low-density expansions. Wigner crystallization: two-component Coulomb systems, electron-hole bilayers, critical mass ratios, Wigner-Seitz coupling, Lindemann melting, energy-scale analysis, QMC phase diagrams. Quantum geometry and Z2 topology: quantum metric, Wannier spread and obstruction, maximally localized Wannier functions, Kane-Mele in variants, Wilson loops, Rashba coupling, plane-wave continuum models.

Hatsugai-Kohmoto models and Mott physics:
Hubbard bands, quasi particle lifetimes, phase-space scattering constraints, RG stability. Schwinger-Keldysh EFT and fracton hydrodynamics: dissipative hydrodynamics, multipole symmetries, Goldstone and superfluid stiffness, derivative counting, mode dispersions. 2D electron-gas QMC: diffusion Monte Carlo, Slater-Jastrow states, finite-size corrections, thermodynamic extrapolation, long-range Coulomb boundary conditions, structure factors, RPA, Fermi liquids. Dirac-material transport: graphene Dirac fermions, charged-impurity disorder, nonlinear and Thomas-Fermi screening, electron-hole puddles, topological-insulator surfaces, Boltzmann transport.

Topological crystalline insulators: band representations, Wyckoff positions, rotation symmetry, disclinations, Frank angles, fractional charge, filling anomalies, discrete shift in variants. Kitaev honeycomb physics:
Majorana fermionization, Z2 gauge theory, flux sectors, spin liquids, parity projection, torus degeneracy, Bogoliubov-de Gennes methods, exact diagonalization. Semiclassical thermoelectric transport: relaxation-time Boltzmann theory, anisotropic masses, Seebeck response, bipolar transport, polarity, two-band models. Inelastic neutron scattering: multi phonon scattering laws, harmonic-oscillator response, incoherent dynamic structure factors, Debye-Waller factors, bound-atom cross sections, low-temperature limits. Magnetic space groups and magneto-optics:
Belov-Neronova-Smirnova notation, Wyckoff analysis, propagation vectors, multi-k structures, irreducible representations, Kerr effects. Modulated-structure crystallography: kinematic diffraction, structure factors, satellite reflections, reciprocal-space indexing, selection and extinction rules, super space symmetry, static strain waves.

PhD in condensed matter physics or a closely related field is required. Postdoctoral researchers, research scientists, and junior faculty are particularly strong fits. Senior PhD students with a strong first-author record may apply. Published work on the exact relevant phenomenon is required. General experience in an adjacent topic or method…