arXiv subjects

Liam L. H. Lau

Publications and source records attributed to Liam L. H. Lau.

6 recordsLinked to original sources

arXiv2026

Particle-hole Symmetric Slave Boson Method for the Mixed Valence Problem

We introduce an analytic slave boson method for treating the finite $U$ Anderson impurity model. Our approach introduces two bosons to track both $Q\rightleftharpoons Q\pm1$ valence fluctuations and reduces to a single symmetric $s$-boson in the effective action, encoding all the high energy atomic physics information in the boson's kinematics, while the low energy part of the action remains unchanged across finite $U$, infinite $U$, and Kondo limits. We recover the infinite $U$ and Kondo limit actions from our approach and show that the Kondo resonance already develops in the normal state when the slave boson has yet to condense. We show that the slave rotor and $s$-boson have the same algebraic structure, and we establish a unified functional integral framework connecting the $s$-boson and slave rotor representations for the single impurity Anderson model.

cond-mat.str-el↗

arXiv2025

Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems

We examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency $ω_0 \ll U/2$, the onsite Coulomb scale $U/2$), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a novel frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling $α^*$ when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast ($ω_0 \gtrsim U/2$), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively $U_{\text{eff}}$ due to phonon mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group (NRG) calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

cond-mat.str-el↗

arXiv2025

Topological Mixed Valence Model for Twisted Bilayer Graphene

Song and Bernevig (SB) have recently proposed a topological heavy fermion description of the physics of magic angle twisted bilayer graphene (MATBG), involving the hybridization of flat band electrons with a relativistic conduction sea. We explore the consequences of this model, seeking a synthesis of understanding drawn from heavy fermion physics and MATBG experiments. We identify a key discrepancy between measured and calculated onsite Coulomb interactions, implicating renormalization effects that are not contained in the current model. With these considerations in mind, we consider an SB model with a single, renormalized onsite interaction between the f-electrons, containing a phenomenological heavy fermion binding potential on the moiré AA-sites. This feature allows the simplified model to capture the periodic reset of the chemical potential with filling and the observed stability of local moment behavior. We argue that a two stage Kondo effect will develop in MATBG as a consequence of the relativistic conduction band: Kondo I occurs at high temperatures, establishing a coherent hybridization at the $Γ$ points and a non-Fermi liquid of incoherent fermions at the moiré K-points; at much low temperatures Kondo II leads to a Fermi liquid in the flat band. Utilizing an auxiliary-rotor approach, we formulate a mean-field treatment of MATBG that captures this physics, describing the evolution of the normal state across a full range of filling factors. By contrasting the relative time-scales of phonons and valence fluctuations in bulk heavy fermion materials with that of MATBG we propose a valley-polaron origin to the Coulomb renormalization and the heavy fermion binding potential identified from experiment. We also discuss the possibility that the two-fluid, non-Fermi liquid physics of the relativistic Kondo lattice is responsible for the strange metal physics observed in MATBG.

cond-mat.str-el↗

arXiv2023

TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters

The recently-introduced Topological Heavy Fermion (THF) model [Phys. Rev. Lett. 129, 047601] 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 [Phys. Rev. Lett. 129, 047601]. 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 ($w_0 / w_1$), 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 ($0.6 \leq w_0/w_1 \leq 1.0$), for which the hybridization between the localized and conduction fermions $γ$ is smaller than the onsite repulsion of the heavy fermions $U_1$ (i.e. $|γ| < U_1$).

cond-mat.str-el↗

arXiv2021

Quantum walk of two anyons across a statistical boundary

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 that the two-particle interference 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.

cond-mat.quant-gas↗

arXiv2020

ODEN: A Framework to Solve Ordinary Differential Equations using Artificial Neural Networks

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to evaluate neural networks' performance. Neural networks are shown to be proficient at approximating continuous solutions within their training domains. We illustrate neural networks' ability to outperform traditional standard numerical techniques. Training is thoroughly examined and three universal phases are found: (i) a prior tangent adjustment, (ii) a curvature fitting, and (iii) a fine-tuning stage. The main limitation of the method is the nontrivial task of finding the appropriate neural network architecture and the choice of neural network hyperparameters for efficient optimization. However, we observe an optimal architecture that matches the complexity of the differential equation. A user-friendly and adaptable open-source code (ODE$\mathcal{N}$) is provided on GitHub.

physics.comp-ph↗