Condensed Matter Physics seminars

Tensor networks help describe the structures underlying two-dimensional topological phases and topological quantum computation. This talk develops an operator-algebra perspective on those connections and presents recent mathematical understanding of topological order. The introduction is designed to be accessible without prior training in operator algebras.

A polynomial-time algorithm samples the Sherrington–Kirkpatrick Gibbs distribution with negligible total-variation error for inverse temperatures below one half. The talk combines stochastic localization, Jarzynski's equality and rejection sampling with covariance and functional-inequality estimates. It also derives a weak Poincaré inequality that simplifies the construction and relates the guarantees to earlier Wasserstein results.

The superfluid fraction measures how much of a fluid supports frictionless motion. This seminar studies low-temperature systems in which external potentials tune that fraction and transport measurements quantify it. For an equilibrium, weakly interacting Bose condensate, the researchers also extract the fraction from a single density image. The approach offers a new measurement route for investigating recently realized supersolid phases.

Liang Kong reviews a unified mathematical treatment of gapped and gapless boundaries in topological orders in two spatial dimensions. It leads to topological Wick rotation, proposed as a broader organising principle for suitable quantum field theories. The talk examines generalisations and applications, including how familiar topological holography and sandwich constructions emerge as special cases.

Maarten Stroeks examines ground-energy optimisation for fermionic Hamiltonians whose interactions are classical in a suitable basis, a setting motivated by electronic structure in chemistry and condensed matter. Despite QMA hardness, fermionic Gaussian states achieve an approximation ratio of at least one third independent of sparsity. Semidefinite algorithms handle several traceless and positive-semidefinite families, including fixed particle number. A construction that mixes covariance matrices, called a Gaussian blend, provides the technical foundation.

Carolina Paiva develops exact matrix product states for strongly interacting electrons in lattice bands. Conformal-field-theory correlation functions already provide exact representations of fractional quantum Hall trial wavefunctions, including Laughlin states. Extending the construction to fractional Chern insulators is obstructed by the lattice length scale. The talk shows how ideal Chern bands overcome that obstruction and derives an exact representation of Laughlin model states in a hybrid Wannier basis on a torus.