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SciPost Physics Lecture Notes

A brief tutorial on information theory

Tarek Tohme, William Bialek

SciPost Phys. Lect. Notes 87 (2024) · published 23 September 2024 | · pdf

At the 2023 Les Houches Summer School on Theoretical Biological Physics, several students asked for some background on information theory, and so we added a tutorial to the scheduled lectures. This is largely a transcript of that tutorial, lightly edited. It covers basic definitions and context rather than detailed calculations. We hope to have maintained the informality of the presentation, including exchanges with the students, while still being useful.
An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation

Jan Naumann, Erik Lennart Weerda, Matteo Rizzi, Jens Eisert, Philipp Schmoll

SciPost Phys. Lect. Notes 86 (2024) · published 10 September 2024 | · pdf

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.
Field theory of collinear and noncollinear magnetic order

Oleg Tchernyshyov

SciPost Phys. Lect. Notes 85 (2024) · published 5 September 2024 | · pdf

These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.
Ambitions for theory in the physics of life

William Bialek

SciPost Phys. Lect. Notes 84 (2024) · published 15 August 2024 | · pdf

Theoretical physicists have been fascinated by the phenomena of life for more than a century. As we engage with more realistic descriptions of living systems, however, things get complicated. After reviewing different reactions to this complexity, I explore the optimization of information flow as a potentially general theoretical principle. The primary example is a genetic network guiding development of the fly embryo, but each idea also is illustrated by examples from neural systems. In each case, optimization makes detailed, largely parameter-free predictions that connect quantitatively with experiment.
Normative approaches to neural coding and behavior

Ann Hermundstad

SciPost Phys. Lect. Notes 83 (2024) · published 13 August 2024 | · pdf

These are a brief set of lectures notes for lectures given at the Les Houches Summer School in Theoretical Biological Physics in July 2023. In these notes, I provide an introduction to some of the theoretical frameworks that are used to understand how the brain makes sense of incoming signals from the environment to ultimately guide effective behavior. I then discuss how we can apply these frameworks to understand the structure and function of real brains.

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Physics: High-Energy Physics - Theory

The Higgs Mechanism with Diagrams: a didactic approach

by Jochem Kip, Ronald Kleiss

Version 1 (latest version)
Submitted 2024-09-11 11:51 to SciPost Physics Lecture Notes · latest activity: 2024-09-30 09:03
Physics: Biophysics • Statistical and Soft Matter Physics

Population genetics: an introduction for physicists

by Andrea Iglesias-Ramas, Samuele Pio Lipani, Rosalind Allen

Version 1 (latest version)
Submitted 2024-08-12 15:52 to SciPost Physics Lecture Notes · latest activity: 2024-10-03 09:43

Series contained in this Journal

Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

Johannes Hauschild, Frank Pollmann

SciPost Phys. Lect. Notes 5 (2018) · published 8 October 2018 | · pdf

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [https://github.com/tenpy/tenpy]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

272 citations
Lecture notes on Generalised Hydrodynamics

Benjamin Doyon

SciPost Phys. Lect. Notes 18 (2020) · published 28 August 2020 | · pdf

These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.

127 citations
Tangent-space methods for uniform matrix product states

Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete

SciPost Phys. Lect. Notes 7 (2019) · published 15 January 2019 | · pdf

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to variationally optimize ground-state approximations, implement real-time evolution and describe elementary excitations for a given model Hamiltonian. Also, we explain how matrix product states approximate fixed points of one-dimensional transfer matrices. We show how all these methods can be translated to the language of continuous matrix product states for one-dimensional field theories. We conclude with some extensions of the tangent-space formalism and with an outlook to new applications.

125 citations
Phase transitions in the early universe

Mark Hindmarsh, Marvin Lüben, Johannes Lumma, Martin Pauly

SciPost Phys. Lect. Notes 24 (2021) · published 15 February 2021 | · pdf

These lecture notes are based on a course given by Mark Hindmarsh at the 24th Saalburg Summer School 2018 and written up by Marvin L\"uben, Johannes Lumma and Martin Pauly. The aim is to provide the necessary basics to understand first-order phase transitions in the early universe, to outline how they leave imprints in gravitational waves, and advertise how those gravitational waves could be detected in the future. A first-order phase transition at the electroweak scale is a prediction of many theories beyond the Standard Model, and is also motivated as an ingredient of some theories attempting to provide an explanation for the matter-antimatter asymmetry in our Universe. Starting from bosonic and fermionic statistics, we derive Boltzmann's equation and generalise to a fluid of particles with field dependent mass. We introduce the thermal effective potential for the field in its lowest order approximation, discuss the transition to the Higgs phase in the Standard Model and beyond, and compute the probability for the field to cross a potential barrier. After these preliminaries, we provide a hydrodynamical description of first-order phase transitions as it is appropriate for describing the early Universe. We thereby discuss the key quantities characterising a phase transition, and how they are imprinted in the gravitational wave power spectrum that might be detectable by the space-based gravitational wave detector LISA in the 2030s.

83 citations
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

Pietro Silvi, Ferdinand Tschirsich, Matthias Gerster, Johannes Jünemann, Daniel Jaschke, Matteo Rizzi, Simone Montangero

SciPost Phys. Lect. Notes 8 (2019) · published 18 March 2019 | · pdf

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.

80 citations

Physics: High-Energy Physics - Theory

Physics: Biophysics • Statistical and Soft Matter Physics

Series contained in this Journal

272 citations

127 citations

125 citations

83 citations

80 citations