What is condensed matter physics?

What do condensed matter physicists study?

High school students are often taught there are three states of matter: solids, liquids, and gases. However, this is misleading as there are many more states of matter. Liquid crystals, superconductors, and ferromagnets are distinct states of matter that do not fit in the high school classification. Condensed matter physics (CMP) is concerned with practically any material system that involves a large number (say at least a million) of interacting atoms or molecules. We can consider this to be a complex system because there are many different ways of arranging the constituents (atoms or molecules) of the system.

What approaches and techniques do condensed matter physicists use to study and understand these systems?

CMP provides a coherent intellectual framework for a multi-faceted approach to investigate and understand complex material systems.
First, one can look at the material at many different scales ranging from the microscopic level (scale of individual atoms and molecules) to the mesoscopic (roughly thousands of atoms or molecules, micrometer scale) to the macroscopic (what can be seen with the naked eye). The different scales can be different system sizes, length scales, energy scales, and time scales.
At every scale one can use different tools and approaches, which fall into three broad categories: experimental, theoretical, and computational. All three are intellectually and technically challenging. All are important.

Experiment
There are several distinct parts to this.
Synthesis and fabrication: one has to make a sample of the material. This involves chemistry. Making large clean samples is an art in itself.
Characterisation: this concerns testing that one actually has a sample of chemical composition and purity desired.
Property measurement: this concerns determining what the physical properties (for example, crystal structure or electrical resistance) of the sample are. Often one varies external conditions such as temperature, magnetic field, and pressure, and determines how the properties of interest vary with these parameters. Some of the most interesting condensed matter physics happens under extreme conditions: low temperatures, high magnetic fields, or high pressures.

Theory and model building
The fundamental question that one is trying to answer is: How do the material properties emerge from the chemical composition and atomic structure of the material? In particular, what are the physical mechanisms responsible for the different states of matter found in the material? In CMP it is found that these questions are best understood in terms of deciding on the essential system components and  physical interactions between them that occur at different length and energy scales. Constructing (or dreaming up!) the simplest possible model for these interactions is a real art.

Computation
This has several aspects often requiring the use of state-of-the-art supercomputers and algorithms. One is broadly known as quantum chemistry and concerns starting with a knowledge of the basic chemical composition and calculating from quantum theory the properties of the system. In spite of massive advances in computational power and algorithms over the past 60 years, one is still confined to relatively small numbers of atoms and/or unreliable approximation schemes.
The second computational side is calculating properties of the theoretical models that can be compared to experiment. Even for "simple" models usually requires either massive computational power on small systems or unreliable approximation schemes.

Finally, an important challenge is that of intellectual synthesis and critical evaluation. Here, one tries to bring together the results of all these complementary investigations to gain a coherent picture of the material and its properties. Inevitably, there are inconsistencies, sometimes minor and sometimes major. Investigators then have to decide in which element the problem lies.

I think CMP is more complex, challenging, and full of surprises than other areas of physics, such as atomic physics, elementary particle physics, fluid mechanics, and optics. There is a lot more that is unknown in CMP and a lot more that can go wrong.