Condensed Matter Physicist (PhD)

## About the work

**CritPt** is a public benchmark of research-level physics challenges, built to test whether frontier AI models can carry out genuine physics research reasoning rather than textbook problem solving. The benchmark paper is **[arXiv:2509.26574](https://arxiv.org/abs/2509.26574)** and we recommend reading it before applying. It will tell you quickly whether this work interests you.

We are engaging physicists to work on research-level physics problems in their own subfield. Depending on where your publication record fits, that can mean creating problems, solving them, reviewing completed work, or auditing it. We agree the specific assignment with you once you are matched to an area.

This is research-grade work rather than volume work. Whatever you produce has to be complete enough for another specialist in your subfield to follow and verify independently, so written reasoning is part of every assignment.

## Research areas in this panel

Nineteen areas. We match narrowly: you need to have published on one of these specific phenomena, not in condensed matter broadly. Each area lists the methods it requires.

**1. One-dimensional field theory: bosonization, Majorana and Ising-Luttinger sectors, RG:** Abelian bosonization, Majorana fermion field theory in one dimension, coupled Ising and Luttinger-liquid sectors, scaling dimensions of vertex operators, one-loop renormalization-group flow equations, operator product expansion, commensurate-incommensurate transition.

**2. Parafermion zero modes, non-Abelian braiding, FQH-superconductor heterostructures:** Parafermion zero modes, ZN parafermion algebra, non-Abelian braiding statistics, fusion channels of topological defects, fractional Josephson effect, adiabatic evolution and Berry phases, fractional quantum Hall-superconductor heterostructures.

**3. Rational CFT, Verlinde lines, non-Abelian quantum Hall edge theories:** Rational conformal field theory on the torus, Verlinde lines as topological defect lines, modular S matrix and the Verlinde formula, Moore-Read non-Abelian quantum Hall state, chiral edge theories of quantum Hall states, fusion categories and non-invertible symmetries, modular invariance of the primary field spectrum.

**4. SPT and Haldane phase, matrix product states, decoherence of topological order:** AKLT valence-bond-solid model, Haldane phase and symmetry-protected topological order, string order parameters, matrix product states, transfer-matrix evaluation of correlation functions, Kraus-operator quantum channels, decoherence-induced mixed-state topological order.

**5. Flat-band Hubbard models, flat-band ferromagnetism, Hartree-Fock and DQMC:** Checkerboard-lattice Hubbard model, topological nearly flat bands, flat-band ferromagnetism, Hartree-Fock mean-field theory, Stoner ferromagnetic instability, interaction-driven quantum phase transitions, determinant quantum Monte Carlo.

**6. SYK model, large-N disordered fermions, Schwinger-Dyson thermodynamics:** Sachdev-Ye-Kitaev model, low-rank random couplings, Majorana fermions, quenched disorder averaging, large-N melonic diagrammatics, Schwinger-Dyson equations, thermodynamic free energy, residual zero-temperature entropy.

**7. Correlated electron transport: Hubbard model, Kubo formalism, diagrammatic perturbation theory:** Hubbard model, Fermi-liquid theory, Kubo linear-response formalism, perturbative diagrammatic expansion in the interaction, Matsubara Green's function technique, vertex corrections and momentum relaxation, electron-electron scattering on a lattice, low-density expansion near a band edge.

**8. Wigner crystallization, two-component Coulomb systems, quantum melting:** Wigner crystallization, two-component Coulomb crystallization, critical mass ratio for quantum crystals, electron-hole bilayers, Wigner-Seitz coupling parameter, Lindemann criterion for quantum melting, dimensional analysis of competing energy scales, quantum Monte Carlo phase diagrams.

**9. Quantum geomet