Condensed-Matter Physics

Fundamental and challenging problems in condensed-matter physics can be investigated with quantum simulators. Because it is a very specialized and technical topic, and I have no in-depth knowledge of the field, I simply refer to three review papers about the topic, and provide a basic list of selected applications.

> Quantum simulation [R8]

  • Hubbard model (the simplest model of interacting particles on a lattice)

  • Spin models

  • Quantum phase transitions

  • Disordered and frustrated systems

  • Superconductivity


  • “quantum phase transition from a superfluid to a Mott insulator using a cold atomic gas in an optical lattice”

  • “simulation of an antiferro-magnetically coupled spin chain in an external magnetic field”

  • “simulation of artificial gauge fields”

  • “the high-temperature superconductivity of compounds containing copper-oxide planes is still a puzzlethat might be solved using large-scale simulations.”

> Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond [R12]

  • “provide an efficient way to calculate ground state properties and dynamical evolution of many condensed matter system”

  • “superfluid – Mott insulator (SF–MI) quantum phase transition”

  • “ultracold disordered Bose-Fermi mixtures in optical lattices may serve as a paradigm fermionic system to study a variety of disordered phases and phenomena: from Fermi glass to quantum glass and quantum percolation”

  • “frustrated models: antiferromagnetic models” 1

  • etc.

> Quantum simulations with ultracold quantum gases [R5]

  • quantum simulation of ultracold Fermi gases with attractive interactions: e.g. BEC–BCS crossover 2

  • In a typical condensed-matter system, electrons can be modelled as moving on a lattice generated by the periodic array of atom cores. Such a general setting can be simulated with ultracold atoms using the concept of an “optical lattice”.

  • Artificial gauge fields: Can one use atomic gases to simulate charged quantum many-body systems, such as an electron fluid in an external magnetic field?

And additional topics for research from I. Bloch’s guest lecture [L1]:

  • Motion of a single hole in a quantum antiferromagnet [70]: an elementary, simple problem definition by three renown physicists.

  • High-temperature superconductivity in copper oxides [71].

See also:

  • Quantum simulations of materials on near-term quantum computers [85]:
    “ground and excited state properties of several spin-defects in solids including the negatively charged nitrogen-vacancy (NV) center, the neutral silicon-vacancy (SiV) center in diamond, and the Cr impurity (4+) in 4H-SiC


” Frustration appears when all the constraints imposed by the Hamiltonian cannot be simultaneously fullfilled and it is an inherent property of some strongly correlated systems. ” [R12].


” Bardeen–Cooper–Schrieffer (BCS) superfluidity originates from the weak pairing of particles into Cooper pairs, which are made of two particles of opposite spin and velocity. […] In the other limit of interaction strength […] as these molecules are made of two fermions, they behave as bosonic particles and form a Bose–Einstein condensate (BEC) at low temperature. ” [R5].

Further reading:

  • About BEC: Making, probing and understanding Bose-Einstein condensates [R14]

Complements: An Introduction » Quantum Simulation » Applications