Publications

Order by: publication date number of citations

• Transport in one-dimensional integrable quantum systems

  Jesko Sirker

  SciPost Phys. Lect. Notes 17 (2020) · published 20 August 2020 | Toggle abstract · pdf

  These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/2 XXZ spin chain.

  14 citations

• On model selection in cosmology

  Martin Kerscher, Jochen Weller

  SciPost Phys. Lect. Notes 9 (2019) · published 19 June 2019 | Toggle abstract · pdf

  We review some of the common methods for model selection: the goodness of fit, the likelihood ratio test, Bayesian model selection using Bayes factors, and the classical as well as the Bayesian information theoretic approaches. We illustrate these different approaches by comparing models for the expansion history of the Universe. In the discussion we highlight the premises and objectives entering these different approaches to model selection and finally recommend the information theoretic approach.

  14 citations

• Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes

  Aashish A. Clerk

  SciPost Phys. Lect. Notes 44 (2022) · published 21 March 2022 | Toggle abstract · pdf

  These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches and concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, quantum master equations, and non-Hermitian Hamiltonians. The importance of having both non-trivial synthetic gauge fields and dissipation for obtaining non-reciprocal interactions is stressed. Connections to broader topics such as quantum reservoir engineering and the quantum theory of continuous-measurement based feedforward are also discussed.

  13 citations

• A beginner's guide to non-abelian iPEPS for correlated fermions

  Benedikt Bruognolo, Jheng-Wei Li, Jan von Delft, Andreas Weichselbaum

  SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021 | Toggle abstract · pdf

  Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

  13 citations

• An introduction to axions and their detection

  Igor García Irastorza

  SciPost Phys. Lect. Notes 45 (2022) · published 29 March 2022 | Toggle abstract · pdf

  In these notes I try to introduce the reader to the topic of axions: their theoretical motivation and expected phenomenology, their role in astrophysics and as dark matter candidate, and the experimental techniques to detect them. Special emphasis is made in this last point, for which a relatively updated review of worldwide efforts and future prospects is made. The material is intended as an introduction to the topic, and it was prepared as lecture notes for Les Houches summer school 2021. Abundant references are included to direct the reader to deeper insight on the different aspects of axion physics.

  13 citations

• Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

  Patrick Emonts, Erez Zohar

  SciPost Phys. Lect. Notes 12 (2020) · published 17 January 2020 | Toggle abstract · pdf

  In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

  12 citations

• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

  Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi

  SciPost Phys. Lect. Notes 63 (2022) · published 22 September 2022 | Toggle abstract · pdf

  This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

  12 citations

• Useful relations among the generators in the defining and adjoint representations of SU(N)

  Howard E. Haber

  SciPost Phys. Lect. Notes 21 (2021) · published 20 January 2021 | Toggle abstract · pdf

  There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric tensor $d_{abc}$ that arises in the study of the SU(N) Lie algebra, one can also consider relations that involve the adjoint representation matrix, $(D^a)_{bc}=d_{abc}$. In this review, we summarize many useful relations satisfied by the defining and adjoint representation matrices of SU(N). A few relations special to the case of N=3 are highlighted.

  11 citations

• Phase transitions above the upper critical dimension

  Bertrand Berche, Tim Ellis, Yurij Holovatch, Ralph Kenna

  SciPost Phys. Lect. Notes 60 (2022) · published 12 August 2022 | Toggle abstract · pdf

  These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous phase transitions, we discuss the apparent failure of the Gaussian fixed point to capture scaling for Landau mean-field theory, which should hold in the thermodynamic limit above $d_{\rm uc}$. We recount how Fisher's dangerous-irrelevant-variable formalism applied to thermodynamic functions partially repairs the situation but at the expense of hyperscaling and finite-size scaling, both of which were, until recently, believed not to apply above $d_{\rm uc}$. We recall limitations of various attempts to match the RG with analytical and numerical results for Ising systems. We explain how the extension of dangerous irrelevancy to the correlation sector is key to marrying the above concepts into a comprehensive RG scaling picture that renders hyperscaling and finite-size scaling valid in all dimensions. We collect what we believe is the current status of the theory, including some new insights and results. This paper is in grateful memory of Michael Fisher who introduced many of the concepts discussed and who, half a century later, contributed to their advancement.

  11 citations

• Dark matter in astrophysics/cosmology

  Anne M. Green

  SciPost Phys. Lect. Notes 37 (2022) · published 25 January 2022 | Toggle abstract · pdf

  These lecture notes aim to provide an introduction to dark matter from the perspective of astrophysics/cosmology. We start with a rapid overview of cosmology, including the evolution of the Universe, its thermal history and structure formation. Then we look at the observational evidence for dark matter, from observations of galaxies, galaxy clusters, the anisotropies in the cosmic microwave background radiation and large scale structure. To detect dark matter we need to know how it's distributed, in particular in the Milky Way, so next we overview relevant results from numerical simulations and observations. Finally, we conclude by looking at what astrophysical and cosmological observations can tell us about the nature of dark matter, focusing on two particular cases: warm and self-interacting dark matter.

  10 citations