# 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

Examples:

“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

- 1
” 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].

- 2
” 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