Two-dimensional Conformal Field Theories (CFT) have been very successful as effective theories for classical statistical models at a critical point (like the critical 2d Ising model), or for quantum critical points in one spatial dimension. The results obtained from the CFT approach include, for instance, exact scaling exponents, solutions of the Kondo and other quantum impurity problems, and the many results on entanglement measures and quantum quenches obtained in the past decade. Yet, in spite of the many successes of CFT, there is a large class of one-dimensional systems that seems out of reach: inhomogeneous systems. For instance, a quantum gas in a trapping potential is inhomogeneous, because the density usually varies with position. The same is true about various out-of-equilibrium situations, for example if particles are released from a trap. I will sketch how the standard CFT framework can be adapted to accomodate such situations, by relying on a few elementary, yet illustrative, examples based on free fermions.
Joint ICTP/SISSA Statistical Physics Seminar: "Inhomogeneous Quantum Systems in 1D: How does one Describe them with Conformal Field Theory?"
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