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In this talk, I will report our recent progress on Kagome superconductor AV3Sb5 (A=K, Rb, and Cs). As the first-step toward understanding of their largely unconventional natures, we conducted systematic analyses based on density functional theory calculation. Tight-binding parameters computed by maximally localized Wannier functions technique demonstrates that the out-of-plane Sb out -p orbital is a key element for the description of Van Hove singularity structures known in this material near Fermi level. Correlation strengths are also found to be largely determined by Sb out -p states. Based on constrained random phase approximation, we found that on- site and inter-site interaction parameter are both significantly affected by Sb out -p screenings. The chemical effect on the van Hove singularity structure and the possible suggestion of detecting time reversal symmetry breaking phase will be presented and discussed.

We derive a minimal low-energy model for Bernal bilayer graphene and related rhombohedral graphene multilayers at low electronic densities by constructing Wannier orbitals defined in real-space supercells of the original primitive cell. Starting from an ab-initio electronic structure theory comprising the atomic carbon $p_z$-orbitals, momentum locality of the Fermi surface pockets around $K,K'$ is circumvented by backfolding the $\pi$-bands to the concomitant mini-Brillouin zone of the supercell, reminiscent of their (twisted) moiré counterparts. The supercell Wannier functions reproduce the spectral weight and Berry curvature of the microscopic model and offer an intuitive real-space picture of the emergent physics at low electronic densities being shaped by flavor-polarized wave packets with mesoscopic extent. By projecting an orbital-resolved, dual-gated Coulomb interaction to the effective Wannier basis, we find that the low-energy physics of Bernal bilayer graphene is governed by ...

This talk explores the connections between quantum error correction (QEC) and the renormalization group (RG) in three parts:

First, we review the operator algebraic formulation of QEC.
Second, we apply this formalism to demonstrate that real-space RG flow prepares approximate local QEC codes in the infrared.
Third, we make this connection explicit by showing that the exact RG flow of density matrices is described by a Lindblad master equation.

van Hove singularities (vHS) -- momenta for which the group velocity of a Bloch state vanishes, and the density of states diverges -- have a dramatic impact on interaction effects when located near the Fermi level, resulting in a rich competition between superconductivity and charge order. While the presence of vHS near the Fermi level is typically unusual, it appears to be a ubiquitous feature of many recently discovered kagome metals. In this talk I will relate the novel properties of many of these materials to the nature of their vHS. Firstly I will discuss AV3Sb5, in which ARPES identifies twofold vHS near the Fermi level with opposite concavity. The opposite concavity of the vHS results in a weak-coupling instabilitly towards excitonic order, hybridising the two bands. Landau theory predicts the coexistence of charge density wave and excitonic order, offering a possible explanation of many of the unconventional responses seen in AV3Sb5. Second, I will discuss ScV6Sn6. Recent STM e...

I will discuss recent theoretical investigations of disorder response and the spin susceptibility of unconventional superconductivity on the kagome lattice. Despite the existence of a sign-changing gap structure, which sums to zero over the Fermi surface, such unconventional pairing states remain robust to disorder and exhibit a Hebel-Slichter peak in the temperature-dependent spin-relaxation rate. It originates from destructive interference effects peculiar to the kagome lattice. For the same reason, unconventional pairing states on the kagome lattice do not exhibit a neutron resonance peak. These results build on previous theoretical studies of the surprising robustness of unconventional pairing states to disorder on the kagome lattice. Taken together these results imply that unconventional superconductivity on the kagome lattice is deceptive in the sense that its properties may appear similar to conventional non-sign-changing superconductivity. These results may be of relevance to t...

In this talk, I will discuss new progress in understanding electronic loop current states in correlated electron systems. A brief review of this type states will be given for cuprates and Kagome lattice superconductors. We will develop correlated electron models where the loop current states are ground states and discuss the physics behind it.

In this talk, I will discuss the charge correlations in two different classes of kagome metals, each with electron fillings near saddle points in their band structures. In the first compound, CsV3Sb5, a dominant breathing mode of the kagome network drives the formation of a metastable charge density state. Charge correlations in this state undergo an unusual evolution upon tuning the carrier filling, suggesting the presence of a nearby nematic instability. In the second compound, ScV6Sn6, charge order is driven by an out-of-plane instability of the Sc-Sn chains that thread through the kagome planes. This drives a form of frustrated charge order likely responsible for the pseudogap and anomalous electronic properties reported in this material. The differing routes to charge order across multiple families of kagome metals will be discussed.

Recently, a new interpretation of gravitational spacetime in terms of quantum entanglement has been developed. The idea of holography in string theory provides a simple geometric computation of entanglement entropy. This generalizes the well-known Bekenstein-Hawking formula of black hole entropy and strongly suggests that a gravitational spacetime consists of many qubits with quantum entanglement. Also a new progress on black hole information problem has been made recently by applying this idea. A new insight on holography for de Sitter spaces have also been obtained from quantum information viewpoints. I will explain these developments in this lecture.

In low dimensional superconductors, disorder and many body interactions leads to a veritable zoo of intriguing phases and phase transitions. A exemplar of the same is for instance the highly debated anomalous metallic phase which exists circumventing the celebrated Anderson localisation. On the other hand, disorder itself triggers a host of very intriguing and exotic effects such as the Quantum Griffiths Phase (QGP) that stems from the associated Infinite Randomness Fixed Point (IRFP). In this talk we provide incontrovertible proof of emergence of a QGP in the 2D electron gas formed in the LaScO_3 /SrTiO_2 heterostructure. The signatures of the QGP are embedded in the magneto-resistance exhibited by the sample. In particular, we show that in the Griffiths phase (that obtains at higher temperatures), the effective dynamical exponent diverges as a function of the magnetic field. Further, at lower temperatures we argue that the divergence signalling the QGP is cut-off by interplay of diso...

In this talk, I will discuss recent results for charge density wave (CDW) and pair density wave (PDW) instabilities on the kagome lattice near a van Hove singularity. I then discuss the relevance of these results to experimental observations in kagome metals such as CsV_3Sb_5.