The Spectral Gap and Quantum Vacuum Fluctuations

[Cerenkov]

Hello.

Recently Scientific American magazine carried an article about the work of the authors of this paper.
https://arxiv.org/abs/1502.04573 The Undecidability of the Spectral Gap. The SciAm article is linked to here - https://www.scientificamerican.com/...ons/2018/special-editions-volume-27-issue-5s/ - under the heading of, The Unsolvable Problem.

Here is a short extract from that article.

How can a material go through a phase transition at a temperature of absolute zero (- 273.15 degrees Celsius) , at which there is no heat at all to provide energy? It comes down to the spectral gap. When the spectral gap disappears – when a material is gapless – the energy needed to reach an excited state becomes zero. The tiniest amount of energy will be enough to push the material through a phase transition. In fact, thanks to the weird quantum effects that dominate that dominate physics at these very low temperatures, the material can “borrow” this energy from nowhere, go through a phase transition and “give” the energy back.

To my laypersons eye it seems as if the authors use of the word 'nowhere' is a reference to the quantum vacuum. Now to my questions.

1.
Am I on the right track? Is this 'nowhere' the quantum vacuum that is believed to permeate the universe?

2.
Are the authors speculating about these gapless quantum transitions or has such a phenomenon actually been observed?

3.
Assuming that the answer to the above is affirmative, could I please be directed to any relevant links about these observations?

Thank you in advance.

Please note that my level of understanding is Basic and so your replies would be of most help to me if they were pitched at that level.

Thanks again.

Cerenkov.

 

[king vitamin]

In fact, thanks to the weird quantum effects that dominate that dominate physics at these very low temperatures, the material can “borrow” this energy from nowhere, go through a phase transition and “give” the energy back.

1.
Am I on the right track? Is this 'nowhere' the quantum vacuum that is believed to permeate the universe?

Unfortunately, the quote you've given from the article is just misleading. At a quantum phase transition, there is no energy difference between the different ground states, and as one tunes from one phase to the other, one or the other phase becomes energetically favorable. No "borrowing" of energy needs to take place.

This is all talking about ideal zero temperature ground states at equilibrium. Even if we could manipulate quantum states directly at zero temperature, if one adiabatically tunes through a quantum phase transition in some finite amount of time one does not actually end up in the ground state because of the energy you've input. (And the third law of thermodynamics prohibits actually getting to a ground state in a macroscopic system anyways.)

2.
Are the authors speculating about these gapless quantum transitions or has such a phenomenon actually been observed?

3.
Assuming that the answer to the above is affirmative, could I please be directed to any relevant links about these observations?

Yes, there are an enormous number of known quantum phase transitions! The standard reference is the textbook, Quantum Phase Transitions, by Subir Sachdev. Generically, a system at zero temperature can go through different phases as you tune various macroscopic parameters (besides temperature), and any such transition is in the class you ask about. One example you may be familiar with is Helium-4, which is normally a superfluid at 0K but it solidifies under pressure. One very well-controlled system with a quantum phase transition is the superfluid-insulator transition seen in ultracooled Rubidium atoms in optical lattices, see this famous paper: https://www.nature.com/articles/415039a.

Note that we cannot reach zero Kelvin in experiments (due to the third law of thermo), but the presence of a zero temperature phase transition has a lot of experimentally observable effects at finite temperature which we can measure. (Sachdev's textbook goes into this at length.)

 

[Cerenkov]

Thanks for the reply, king vitamin.

I'll make some time to read that nature article.

Cerenkov.