Absolute zero

Abstract: It is shown that certain analytical properties of the propagators of many-fermion systems lead rigorously to the existence of sharp discontinuities of the momentum distribution at absolute zero. This discontinuity in the momentum distribution is used to define a Fermi surface for a system of interacting fermions. It is shown that the volume of this surface in momentum space is unaffected by the interaction. The same analytic properties are shown to lead, by direct statistical mechanical arguments, to simple expressions for the low-temperature heat capacity, the spin paramagnetism, and the compressibility of the system. These expressions are very analogous to the corresponding expressions for noninteracting particles. Finally, it is shown how the whole formalism may be generalized when an external periodic potential is present (band case).

Abstract: In Statistical Physics one mostly deals with thermal motion of a system of particles at nonzero temperatures. For example, in a classical ideal gas of point-like molecules each particle has an average kinetic energy equal to dk B T/2 in d dimensions. Here T is the absolute temperature and k B = 1.6 × 1023 Joule per Kelvin is Boltzmann’s constant. Statistical Physics is used try to explain such laws and to predict the properties of materials consisting of many such particles; therefore, in this example the specific heat is 3Nk B /2 in three dimensions if the gas consists of N particles. In most applications, the number N of particles is very large, and they influence each other by their intermolecular forces. For example, a glass of beer contains about 1025 water molecules, and if these molecules did not interact with each other, the beer would vanish by evaporation, not by drinking. These interactions are also unhealthy for theoretical physics since with interactions usually one cannot solve exactly the problem of how the molecules move and what their average energy is, because even on a computer it is not possible to store the positions and velocities of 1025 point-like molecules. (The Cray-2 supercomputer has only two Gigabytes of main memory.) Instead, one is forced to work with a much smaller number of molecules, below 106, and solve numerically the equations of motion arising from Newton’s law: force equals mass times acceleration. This method is called molecular dynamics and has already been used in the first chapter of this book by Zabolitzky. We will not deal with this technique here; readers who want to know more are referred to the book of D.W.Heermann [1].

Abstract: The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on the heavy-electron material YbRh2Si2 found that near a field-induced QCP electrons move ever more slowly and scatter off one another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and scattering cross-section. But these studies could not shed light on whether these properties were an artefact of the applied field, or a more general feature of field-free QCPs. Here we report that, when germanium-doped YbRh2Si2 is tuned away from a chemically induced QCP by magnetic fields, there is a universal behaviour in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current-carrying motions of the electron fluid.