A quantum critical point is a continuous zero-temperature quantum phase transition reached by tuning a nonthermal parameter of a Hamiltonian, such as interaction strength or magnetic field. The ground state changes its long-distance structure, its correlation length diverges, and its characteristic excitation energy tends to zero in the thermodynamic limit.
For the Transverse-field Ising model, exchange favors aligned spins while the transverse field favors a competing orientation. At the critical ratio the gap closes; the dynamical critical exponent relates the diverging time and length scales. A finite sample rounds the singular behavior. Experiments at nonzero temperature can access a nearby quantum-critical regime, but a finite-temperature anomaly alone does not locate or prove a zero-temperature critical point.
The quantum-critical regime is the finite-temperature region in which temperature exceeds the energy scale generated by detuning from a quantum critical point. Temperature then controls leading masses, relaxation rates, and correlation lengths.
Quantum critical scaling expresses observables as powers of temperature or detuning times universal functions of dimensionless ratios such as , , and .
The dynamical critical exponent relates critical frequency and wavenumber scales by . Relativistic critical theories have .
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A quantum critical point (QCP) is a theoretical concept in condensed matter physics that denotes a point at zero temperature where a continuous phase transition occurs due to quantum fluctuations. Unlike classical phase transitions that can be influenced by temperature and external parameters (like pressure or magnetic field), quantum critical points are affected primarily by quantum mechanical effects, specifically as they relate to changes in certain control parameters like magnetic field, doping level, or pressure.