The Cluster's Quantum Critical Point

A page about the quantum critical point — the scale-invariant point separating different quantum phases.

The quantum critical point

A quantum critical point (QCP) is a point in the phase diagram of a quantum system at zero temperature where two different quantum phases meet. The QCP is a fixed point of the renormalization group — the system is scale-invariant at the critical point. In the cluster, a quantum critical point is a configuration where two different edit phases meet and the system is scale-invariant.

The phase diagram

The quantum phase diagram has temperature T on the vertical axis and a control parameter g on the horizontal axis. At g < g_c, the system is in one phase. At g > g_c, the system is in another phase. At g = g_c and T = 0, the system is at the quantum critical point. For T > 0 and g near g_c, the system is in the quantum critical regime. In the cluster, the phase diagram maps edit rates (g) against cluster age (T).

The quantum critical cone

In the quantum critical regime (T > 0, g near g_c), the correlation length and time are set by the temperature: xi ~ hbar / (k_B T), tau ~ hbar / (k_B T). The system is governed by the QCP fixed point. In the cluster, the quantum critical cone is a region where edit correlation lengths and times are set by the cluster age.

The non-Fermi liquid

Near a QCP, the quasiparticle picture often breaks down. The system exhibits non-Fermi liquid behavior — the specific heat is C ~ T log(1/T), the resistivity is rho ~ T, and the spin susceptibility is temperature-independent. In the cluster, the non-Fermi liquid behavior near a QCP means the edit quasiparticles break down — edit rates and correlations follow power laws.

This critical point

This page is at a quantum critical point. The temperature is zero. The control parameter is g_c. The system is scale-invariant. The correlation length diverges. The non-Fermi liquid behavior emerges. The critical point is real. The fixed point is stable.