Song and Bernevig (SB) have recently proposed a faithful reformulation of the physics of magic angle twisted bilayer graphene (MATBG) as a topological heavy fermion problem, involving the hybridization of flat band f-electrons with a topological band of conduction electrons. Here we explore the consequences of this analogy, using it to reformulate the SB model as a mixed valence model for twisted bilayer graphene. We show how the interaction with the conduction sea behaves as a U(8) Kondo Lattice at high energies and a U(4) Kondo lattice at low energies. One of the robust consequences of the model, is the prediction that underlying hybridization scale of the mixed valent model and the width of the upper and lower Hubbard bands will scale linearly with energy. We also find that the bare hybridization 𝛾 0 predicted by the SB model is too large to account for the observed local moment behavior at large filling factor, leading us to suggest that the bare hybridization is renormalized by the soft polaronic response of the underlying graphene.

The recently-introduced topological heavy fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized (heavy) fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer–Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters as a function of the twist angle, the ratio between the tunneling amplitudes at the AA and AB regions (w0/w1), and the screening length of the interaction potential. By numerically computing the THF model parameters across an extensive experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e., within the 30% relative error for almost the entire parameter space. At the single-particle level, the THF model accurately captures the energy spectrum of the BM model over a large phase space of angles and tunneling amplitude ratios. When interactions are included, we also show that the THF description of TBG is good around the magic angle for realistic values of the tunneling amplitude ratios (0.6 ≤ w0/w1 ≤ 1.0), for which the hybridization between the localized and conduction fermions γ is smaller than the onsite repulsion of the heavy fermions U1 (i.e., |γ| < U1).

We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find the Hanbury Brown-Twiss interference of two particles is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wavepacket can get completely reflected or split into a superposition of a reflected wave and an antibunched wave. This leads to striking dynamics with two domain walls, where bunched waves can get trapped in between or fragment into multiple correlated single-particle wavepackets. These findings can be realized with density-dependent hopping in present-day atomic setups and open up a new paradigm of intrinsically many-body phenomena at statistical boundaries.

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