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# Quantum Many-Body Days – S. Sachdev & M. Metlitski

## September 28, 2021 @ 10:00 am - 12:00 pm

The conference on **Recent Progress in Many-Body Theories (RPMBT) **will take place here at UNC in September 2022.

As a bridge program, this year we are hosting a series of virtual talks in September 2021: the **Quantum Many-Body Days.
**The format of these talks will be 45 minutes for presentation and 15 minutes for questions and discussion. Please see below links for more information.

More information here: https://tarheels.live/rpmbt21/schedule/

Zoom link: https://unc.zoom.us/j/94760934546, p/w: 314159

YouTube live link: https://www.youtube.com/channel/UCOUN5aVy-vUWgwm4CxloGTw

Local organizing committee

J. Drut (Chair), G. Basar, A. Nicholson, S. Chandrasekharan, L. Mitas, and T. Papenbrock

**September 28th, 2021: Universal behavior and strongly coupled theories
**

**“Fermi surfaces large and small: unifying theories of the Kondo lattice and Hubbard models”**

S. Sachdev – 10am

Fermi surfaces which obey the Luttinger theorem are often referred to as “large”. However, it is possible to have “small” Fermi surfaces with electron-like quasiparticles, in certain metallic states (sometimes called FL*) which evade the Luttinger theorem using emergent gauge fields. It is relatively easy to construct FL* states in Kondo lattice models, but much harder in a single band Hubbard model. I will describe a new approach which yields a variational wavefunction for FL* in the Hubbard model, and also a theory for the transition between small and large Fermi surfaces. The key idea is to avoid fractionalizing the electron, and to instead fractionalize a paramagnon into a pair of ancilla qubits. I will note applications to the phase diagram of the cuprates.

**“Boundary criticality of the O(N) model in d = 3 critically revisited”**

M. Metlitski – 11am

Session chair: Basar

It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.