Condensed matter physics

Condensed matter physics constructs and studies the behavior of simplified models designed to capture the universal physics of material systems. Phenomena of interest include: magnetism, phase transitions, superconductivity, frustrated systems, topological phases, and the interplay of thermalization and many-body localization in closed systems. While many seminal models can be studied analytically in certain limits (for example the 1D and 2D classical Ising model), a number of seemingly innocuous models have proven exceedingly difficult to solve. This has led to some models, such as the Fermi–Hubbard model, becoming a proving ground for classical numerical methods. While there has been significant progress in recent decades in understanding the physics of these models through numerical simulation, it is still a challenging problem for many models and parameter regimes. As observed by Feynman [1], quantum computers have a natural advantage over their classical counterparts for simulating the simple Hamiltonians studied in condensed matter physics. While Feynman's proposal was more focused on analog simulation, digital quantum simulation of condensed matter systems has evolved into a major research direction. In this section, we focus on models whose end-to-end complexities have been well studied in the literature: the Fermi–Hubbard model, the Sachdev–Ye–Kitaev (SYK) model, and spin models.

Bibliography

1. Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6-7):467–488, 1982. doi:10.1007/BF02650179.