A Look at Zero-Temperature Quantum Phase Transitions
Understanding Quantum Phase Transitions: Absolute Zero Physics
Quantum Phase Changes
At absolute zero temperature, quantum phase transitions (QPTs) only occur between separate quantum phases of matter. QPTs are abrupt shifts in the ground state of a many-body system triggered exclusively by quantum fluctuations, unlike standard transitions. Access these transitions by changing a non-thermal control parameter like magnetic field, pressure, or chemical composition. Condensed matter physicists and theorists are interested in QPTs because they can affect electronic systems across wide portions of the phase diagram.
Thermal Energy Drives Classical Transitions Comparing QPTs to classical phase transitions (CPTs), also known as thermal phase transitions, clarifies their unique properties.
A CPT signifies particle rearrangement and an abrupt thermodynamic property shift, or cusp. Water freezing is a common illustration. The system's energy and thermal fluctuations' entropy compete to induce classical phase alterations. The first discontinuous derivative of a thermodynamic potential defines CPT order. The first-order transition from water to ice includes latent heat, a discontinuity of internal energy. The continuous, second-order transition from ferromagnet to paramagnet is considered.
The critical behavior of CPTs at non-zero temperatures is explained by classical thermodynamics, not quantum physics, even though superconductivity requires a quantum mechanical description. A classical system has no entropy at absolute zero temperatures, hence a CPT cannot exist.
The Quantum Critical Point (QPT) occurs at zero temperature, making it inexplicable by thermal fluctuations. The typical order loss is caused by quantum fluctuations from Heisenberg's uncertainty principle.
QPTs center on the quantum critical point (QCP). The QCP is the precise point where the non-thermal control parameter suppresses a transition temperature like Curie or Néel to zero Kelvin. At the QCP, quantum fluctuations diverge and become scale invariant in time and space, driving the transition.
Even if absolute zero is not conceivable, the system's behavior at low, non-zero temperatures near to the QCP shows the transition's essential characteristics. At this stage, quantum fluctuations (whose energy scale is connected with quantum oscillation frequency) compete with classical fluctuations (whose energy scale is correlated with temperature).
The quantum critical region, where quantum fluctuations dominate system behavior, is particularly attractive for investigation. This dominance often manifests as non-Fermi liquid phases or other unexpected physical states.
System Diversity and Foundational Theory Quantum phase transitions distinguish an ordered phase from a “quantum” disordered phase in the phase diagram. Quantum materials near these critical regions exhibit long-range many-body quantum entanglement.
The primary textbook on quantum phases, transitions, and observable characteristics is Subir Sachdev's Quantum Phase Transitions. Its second edition includes an introduction to quantum field theory, making it suitable for beginners. The basic course material covers:
Classical phase changes. Renormalization group. Examples include the quantum Ising and quantum rotor models. Boson Hubbard model. Quantum critical point, correlations, susceptibilities. The second edition covers contemporary theoretical developments including the Fermi gas approaches unitarity, Dirac fermions, Fermi liquids and related phase transitions, quantum magnetism, and string theory-derived solvable models.
QPT research examines complex systems such Cuprate superconductors can switch from Mott insulating to d-wave superconducting via carrier doping. Several tests show that these materials have a zero-temperature phase transition beneath the superconducting area, which may explain high-temperature superconductivity.
At a zero-temperature transition in heavy-fermion metals, “weird states” fluctuations between two ordered states can cause unexpected physics and quantum critical behavior.
Superconductor-insulator quantum phase transitions exist.
The topological fermion condensation quantum phase transition is a rapid shift in a Fermi liquid's topological charge that may constitute a first-order phase transition. A two-dimensional Fermi surface can become a three-dimensional volume through this transition. Light phase change in Cavity Quantum Electrodynamics Lattices and quantum interface unbinding transitions have also been studied.
