Journal of High Energy Physics
May 2017, 2017:136
Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling
Pramod Padmanabhan, Soo-Jong Rey, Daniel Teixeira, Diego Trancanelli Email author
Open AccessRegular Article – Theoretical Physics
First Online: 25 May 2017
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.
Keywords: Discrete Symmetries Extended Supersymmetry Lattice Integrable Models Random Systems
PDF (public access)
Reluctant Student is heartfelt sorry for skipping so many classes and begs to know anyhow: Are they saying that information, in their model, isn’t lost in black holes? If so, could it apply to data storage in quantum computers? That’s a big topic these days.
Rob Sheldon replied:
I don’t think physics classes would help with this stuff. You have to assume the lotus position and meditate for weeks to be able to understand this.
Briefly, super-symmetry has been taught to theoretical particle physics grad students for about 30 years, as the best way to explain “the Standard Model”. The SM has 18 free parameters, including the mass of each of the quarks that make up nuclei that make up atoms that make up the universe. A theory with fewer free parameters would be a step forward, and SUSY was the logical extension.
This over-confidence of particle physicists led to the construction of CERN LHC and roughly $15 bn in funding to find these SUSY particles at ~100 GeV energies. But excepting the Higgs boson, nothing was found despite two upgrades all the way to 15,000 GeV. Nothing has been more discouraging to particle physicists than the fact that the SM of 1974 has never been improved.
With the latest CERN upgrades, most particle physicists have acknowledged that SUSY is dead. Think epicycles. Was there modifications to Ptolemy that worked better than the Kepler ellipses in the Copernicus model? Indeed there were. Why did the theory fall from favor? Because it was so much harder to justify, much less use. Unfortunately, 30 years is a scientific lifetime. The tools they learned for 30 years are useless, dead, and non-transferable to other areas of physics.
What is the information angle doing in this paper?
There’s a sexy new theory out there that claims gravity is just a result of entropy (information) conservation at the particle level. Instead of A + B –> C, we have -A + C –> B. Plugging in their skills for A, it allows them to get a little more mileage from their investment. They are tenured profs, so it isn’t like they need to learn another skill. So they keep pumping out papers until retirement. It staves off boredom and depression, and maybe they can snag a grad student…
In short, skipping classes is bad in principle. Tsk. Tsk. Not always lethal.
See also: Could traversable wormholes that allow information to escape black holes really exist?
Post-modern physics: String theory gets over the need for evidence
Cosmic inflation theory loses hangups about the scientific methodWhat if naturalism changes the role of a science program? Perhaps stubbornly contrary evidence merely shows the need for more drive and zeal in generating new naturalist theories, not more reflection and evaluation of that direction.