Invited contribution to the “Annalen der Physik” topical issue “Quantum Simulation”, guest editors: R. Blatt, I. Bloch, J. I. Cirac, and P. Zoller.
Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories†
Article first published online: 22 JUL 2013
© 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Special Issue: Quantum Simulations
Volume 525, Issue 10-11, pages 777–796, November 2013
How to Cite
Wiese, U.-J. (2013), Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories. Ann. Phys., 525: 777–796. doi: 10.1002/andp.201300104
- Issue published online: 4 NOV 2013
- Article first published online: 22 JUL 2013
- Manuscript Accepted: 20 JUN 2013
- Manuscript Revised: 11 JUN 2013
- Manuscript Received: 6 MAY 2013
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.