Course Identification

Computational Condensed Matter (a two-week summer course)

Lecturers and Teaching Assistants

Prof. Eran Bouchbinder, Prof. Natalia Chepiga , Prof. Edan Lerner

Course Schedule and Location

Second Semester
09:00 - 17:00, FGS, Rm B

Field of Study, Course Type and Credit Points

Physical Sciences: 2.00 points
Chemical Sciences: 2.00 points


A condensed two-week summer course:

July 28th - August 8th, 2024 (Sunday-Thursday + Sunday-Thursday, 09:00-17:00 every day). The course will be structured so that frontal lectures are given in the mornings, followed by practical, hands-on sessions after lunch. The course will host 26 participants, priority will be given to early-stage PhD students, though everyone is encouraged to apply.


Prof. Edan Lerner (classical part, University of Amsterdam, see
Prof. Natalia Chepiga (quantum part, Delft University of Technology, see

Coordinator: Prof. Eran Bouchbinder (Ben May Center,

See additional details below


A graduate-level course in Quantum Mechanics, A graduate-level course in Statistical Physics/Thermodynamics, Knowledge of a low-level programming language such as C or Fortran is preferable (for the classical part), Basic knowledge of Matlab (for the quantum part)



Language of Instruction


Attendance and participation


Grade Type

Pass / Fail

Grade Breakdown (in %)

Depending on 100% attendance (which is obligatory) and completion of all hands-on assignments

Evaluation Type

No final exam or assignment

Scheduled date 1


Estimated Weekly Independent Workload (in hours)



Detailed plan

Classical condensed matter (July 28th until and including Sunday, August 4th): In this module, we will focus on the atomistic-micromechanical world: we will ask and answer how systems of discrete interacting particles — representing bubbles, droplets or any other discrete mesoscopic entities — flow, jam, form solids and yield. In addition to delving into the physics of soft condensed matter, we will aim at constructing a broadly applicable computational platform that will be used to study the behavior of simple computer models for soft matter systems.

Day 1

Lecture 1:

  • Overview: emergent phenomena in soft condensed matter
  • The role of computer experiments in soft matter research
  • Course overview – what are we going to learn this week?
  • Introduction to molecular dynamics: complexity, integrators, thermostats and boundary conditions
  • Quick and dirty thermostats and barostats

Exercise 1:

  • Simple computer models of soft matter: inverse power law and harmonic interactions
  • ‘My first MD’
  • Is my code working? Tests via conservation laws

Day 2

Lecture 2:

  • Equilibrium statistical physics and liquid state theory
  • Metropolis Monte Carlo
  • Diffusivity, viscosity and the Stokes-Einstein relation
  • Supercooled liquids and the glass transition

Exercise 2:

  • Cell-lists – reducing the computational complexity
  • Measuring a liquid’s viscosity and diffusivity
  • Equation-of-state and heat capacity
  • Liquid structure and dynamics

Day 3

Lecture 3:

  • Disordered solids: overview and open questions
  • Continuum elasticity and Debye’s vibrational density of states
  • Atomistic elasticity at finite temperature
  • Athermal atomistic elasticity
  • Viscoelasticity

Exercise 3:

  • Thermal and athermal elasticity of disordered solids

Day 4

Lecture 4:

  • Elastoplasticity – overview and open questions
  • Theory of plastic instabilities in the zero-temperature limit
  • Computational approaches to soft matter deformation and flow

Exercise 4:

  • Lees-Edwards boundary conditions
  • Stress-strain curves at finite temperatures
  • Herschel-Bulkley rheology

Day 5

Lecture 5:

  • ‘Jamming’ and ‘unjamming’, mean-field treatments
  • Strain-stiffening
  • Divergent viscosity of non-Brownian suspensions

Exercise 5:

  • Elastic moduli across jamming
  • The coordination-pressure relation
  • The vibrational density of states near unjamming
  • Finite-size scaling near the jamming point
  • Memory formation, absorbing states

Day 6

  • Research projects

Exercise 6:

  • Oscillatory shear above and below jamming
  • Computational projects


Quantum condensed matter (August 5th until August 8th): In this module, we will focus on collective phenomena in quantum many-body systems, whose modern understanding relies to a large extent on computational approaches. An overview of numerical tools for strongly correlated quantum systems, with a focus on Hilbert-space approaches, will be given. The module will provide a technical overview of main existing algorithms, hands-on tutorial on implementation of basic exact diagonalization and tensor network codes, and theoretical lectures on applications.

Day 7

Lecture 7 (Introduction):

  • Quantum many-body problems
  • Exact diagonalization
  • Complexity
  • Quantum-Classical correspondence
  • Corner Transfer Matrix Renormalization Group (CTMRG) for classical 2D systems
  • Entanglement
  • Schmidt decomposition
  • Area law

Exercise 7:

  • Exact diagonalization (Ising + Heisenberg chains)
  • Area law

Day 8

Lecture 8 (Basic Density-Matrix-Renormalization-Group – DMRG – algorithm):

  • Matrix Product States (MPS) – tensor network representation of quantum state
  • Matrix Product Operator (MPO) – tensor network representation of many-body Hamiltonian
  • Variational optimization of networks
  • Infinite-size DMRG
  • Observables – how to make measurements with tensor networks
  • Periodic boundary conditions

Exercise 8:

  • Exact MPS
  • Expressing a quantum state obtained with ED as a tensor network
  • Constructing MPO for the simplest models (Ising, Heisenberg, ...)

Day 9

Lecture 9 (Applications):

  • Study of quantum phase transitions:

powerful combination of DMRG and boundary conformal field theory

  • Topological phases and entanglement spectra
  • Time evolution/finite-temperature calculations

Exercise 9:

  • Implementation of a finite-size DMRG (part-2)
  • Contracting the network

Day 10

Lecture 10 (Beyond DMRG):

  • MERA – tensor network ansatz for critical systems
  • Sliced-DMRG – tensor networks for non-lattice Hamiltonians
  • Tree- and comb-tensor networks
  • iPEPS – tensor networks in 2D: Introduction + Applications
  • Current developments of tensor networks in 3D

Exercise 10:

  • Implementation of a finite-size DMRG (part-3)
  • Variational optimization of the network

Learning Outcomes

Students will acquire basic and hands-on computational skills in the fields of classical and quantum condensed matter.  In addition, they will become familiar with outstanding open questions related to emergent phenomena in hard and soft condensed matter.

Reading List

  • “Computer simulation of liquids”, M.P. Allen and D.J. Tildesley,

Oxford university press (2017)

  • “The density-matrix renormalization group in the age of matrix product states”,

U. Schollwoeck, Annals of Physics 326, 96 (2011)

  • Additional teaching materials will be distributed in due time