Condensed Matter Physicist (PhD)

Role Overview

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:2509.26574, 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.

Research Areas

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 invariance.
• 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 invariants, Wilson loops, Rashba coupling, plane-wave continuum models.
• Hatsugai-Kohmoto models and Mott physics: Hubbard bands, quasiparticle 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 invariants.
• 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: multiphonon 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, superspace symmetry, static strain waves.

Qualifications

• 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 alone does not satisfy this requirement.
• A verifiable record of three to five representative publications, preferably first-author papers from the past five years, with arXiv IDs or DOIs. Publications and authorship will be checked against public records.
• Your publications must demonstrate at least one method family: field theory, including bosonization, torus CFT, Schwinger-Keldysh EFT, or RG; many-body numerics, including diffusion or determinant QMC, exact diagonalization, MPS, or transfer matrices; band theory and topology, including Wannier functions, Berry phases, Wilson loops, Wyckoff positions, or band representations; response and transport, including Kubo methods, Matsubara Green''s functions, diagrammatic perturbation theory, or Boltzmann transport; or scattering and symmetry analysis, including neutron scattering, magnetic space groups, irreducible-representation analysis, or kinematic diffraction.
• Working proficiency with LaTeX, Python, SymPy, and Jupyter. Familiarity with an agentic coding extension in VS Code is useful; gaps are acceptable when stated honestly.
• English proficiency at B2 level or higher, including the ability to communicate rigorous written reasoning.

Work Terms

• Remote, asynchronous hourly engagement with no fixed working hours.
• Commitment of 10 hours per week for an 8 to 10 week period, beginning immediately.
• The specific research area and assignment are agreed after matching; candidates may be accepted directly or invited to a short live alignment call.

Compensation

$80 to $110 per hour, determined by the depth of the candidate''s subdomain match.

Application Process

• Complete the attached application with basic information, education, research experience, method self-attestation, and up to five best-fit research areas.
• For every selected area, provide an arXiv ID or DOI for your own paper, your author position, and the methods demonstrated. Selections without supporting publication evidence are not scored.
• Publication records and authorship are verified against the public record.
• A 30 to 45 minute assessment may be requested only when needed; most applicants will not be asked to complete one.