Quantum Critical Point: Exploring NFL & Heisenberg's Uncertainty

[BANG!]

I was reading a paper the other day that was discussing NFL behavior in heavy fermion systems. There was a phase diagram that was plotted as a function of temperature vs. doping. In the diagram, there was a transition from a spin glass state to an NFL phase which occurred as a second order T=0 phase transition across a quantum critical point. I am familiar with the basic idea of a quantum phase transition. Namely, whereas thermal phase transitions occur due to the rise of thermal fluctiations, quantum phase transitions occur due to the fact that even when the temperature is suppressed to zero, quantum fluctations due to Heisenbergs uncertainty principle are sufficient to drive the change of state. So here's my question: How can the miniscule quantum fluctions suffice to cause a change in state. I tried looking at Wiki, and it said something about the fluctations being "scale invariant" with interactions extending across the entire system. I am not sure what they entirely mean by this nor how this could possibly occur. Could someone please explain. I would greatly appreciate it.

 

[LHarriger]

I also would like to know if someone can explain this

 

[charng]

I can provide some insight into your question about quantum critical points and Heisenberg's uncertainty principle. First, it is important to understand that quantum critical points are unique phenomena that occur at absolute zero temperature and are driven solely by quantum fluctuations.

In classical physics, phase transitions occur due to thermal fluctuations, as you mentioned. However, at absolute zero temperature, thermal fluctuations are completely suppressed, and quantum fluctuations become the dominant driving force for phase transitions. This is where Heisenberg's uncertainty principle comes into play.

Heisenberg's uncertainty principle states that there is an inherent uncertainty in the measurement of certain pairs of physical quantities, such as position and momentum, or energy and time. In the case of a quantum critical point, this uncertainty allows for the system to explore different states and transition between them, even at absolute zero temperature.

The reason why these miniscule quantum fluctuations are able to cause a change in state is because they are scale invariant. This means that they occur at all length scales, from the smallest quantum level to the entire system. This allows for interactions to extend across the entire system, leading to a collective behavior that can result in a phase transition.

In summary, the combination of absolute zero temperature, quantum fluctuations, and the scale invariance of these fluctuations allows for a quantum critical point to occur and drive a phase transition. This is a fascinating area of research that continues to be explored by scientists, and I encourage you to continue learning more about it.