Condensed Matter Seminar: Eslam Khalaf, Harvard University
Bootstrapping the Quantum Many-Body Problem
Event Details:
- Date: Monday, April 13, 2026
- Time: 10:00 - 11:00 AM
- Location: 1080 Physics Research Building
Abstract
Predicting the properties of strongly correlated quantum phases from microscopic Hamiltonians remains a central challenge in condensed matter theory. I will present a recently developed quantum many-body bootstrap framework that reformulates the ground-state problem as a convex optimization over correlation functions, imposing positivity and symmetry constraints without constructing the exponentially large many-body wavefunction. I will first describe how this approach yields tight rigorous lower bounds on the ground-state energy, complementary to conventional variational upper bounds. This will be demonstrated on two problems: (i) interactions in the lowest Landau level, where the energy bounds lie within less than 1% of the exact ground-state energy and capture key properties of Laughlin and composite Fermi liquid correlation functions, and (ii) flat-band superconductors, where for frustration-free Hamiltonians the framework provides rigorous lower bounds on the superfluid stiffness — a genuinely many-body quantity inaccessible to variational methods. In the second half of the talk, I will discuss how this approach generalizes to produce rigorous two-sided bounds on ground-state correlators directly in the thermodynamic limit. I will show how physically motivated choices of operator sets — including defect and string operators that target nonlocal excitations in symmetry-broken phases — yield tight bounds on energies and correlation functions in 1D and 2D lattice models. I will close with an outlook on the broader potential of this framework and its various generalizations.
Bio
Short Bio from Harvard's Department of Physics