Thanks to the classical work of Bekenstein and Hawking we have learnt that gravity is holographic. This means that the quantum degrees of freedom of gravity are connected to surfaces, and not to volumes enclosed by such surfaces. Based on this idea the term Holographic Principle has been coined. The first mathematically precise implementation of this principle was inside string theory. This is the famous AdS/CFT correspondence. Later the idea of holography separated from string theory. This was due to the striking results of quantum information theory which is  is based on the phenomenon of entanglement regarded as a new resource. Soon entanglement based articulation of  ideas provided new insight on considerations of the nature of gravity. The first step was the combination of the idea of holography with the idea of entanglement. In this context it was realized that even classical spacetime geometry is an emergent concept, inherently of quantum origin.

 

In this talk in the simplest holographic scenario we put strings back into the mix [1]. We show that the world sheets of classical strings regarded as objects testing classical spacetime geometry encode quantum information geometric data. Data which is not necessarily directly related to entanglement.

 

[1]: Bercel Boldis and Péter Lévay: "Segmented strings and holography", Phys. Rev. D 109, 046002 – Published 5 February 2024

In quantum mechanics, the Schrieffer-Wolff transformation (SW, also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. In the talk a geometric interpretation of the SW is presented [1] as a local coordinate chart in the space of hermitian matrices near the degeneracy stratum. Inspired by this approach, the splitting of the eigenvalues of a perturbation is interpreted in terms of the distancing from the degeneracy stratum. The physical examples range widely, including problems from condensed matter physics and quantum error correction.

 

[1] Joint work with György Frank, Dániel Varjas, András Pályi

Moiré systems have recently attracted a lot of attention in condensed-matter physics following the experimental discovery of superconductivity in twisted bilayer graphene [1]. A whole plethora of other unique quantum phases of matter have been since explored, with most theoretical investigations focusing on the emergence of flat bands and correlated electronics [2]. Scanning tunneling microscopy (STM) simulations of moiré systems have however been overlooked, despite moiré patterns almost always arising from the pairing of two-dimensional (2D) materials and the potential assistance that simulations could provide for scientists investigating van der Waals heterostructures. Indeed, moiré patterns can sometimes lead to complex STM images, especially true in the case of mixed symmetry coupling, i.e., hexagonal-rectangular symmetry pairing [3, 4]. In these systems, the moiré unit cell can be very large and even infinite for the incommensurate case, excluding the application of methods based on periodic cells, e.g., density functional theory. Other approaches are thus required; in this talk, I will introduce a new method, the moiré plane wave expansion model (MPWEM), to simulate STM images, which simply requires a priori knowledge of the non-interacting STM images and a small set of intuitive parameters [5].

 

[1] Y. Cao et al., Nature 556, 43-50 (2018)

[2] D. M. Kennes et al., Nat. Phys. 17, 155-163 (2021)

[3] M. Le Ster et al., Phys. Rev. B 99, 075422 (2019)

[4] M. Le Ster et al., 2D Mater. 7, 011005 (2019)

[5] M. Le Ster et al., submitted.

One dimensional chains of free fermions belong to the simplest many body systems, where many physical quantities can be computed with ease. In quantum information theory free fermionic circuits are also distinguished: they lead to classical simulability of quantum states. Recently a new class of models was discovered[1,2], which have a hidden free fermionic structure, despite being apparently interacting. The hidden free fermions are obtained with a construction that is distinct from the well known Jordan-Wigner transformation. We review the progress in this topic, focusing on selected models and their properties.

 

[1]: B Pozsgay, arXiv:2402.02984

[2]: P Fendley, B Pozsgay, SciPost Phys. 16, 102 (2024)