Effects of interactions on the topological classification of free fermion systems

By Lukasz Fidkowski, Alexei Y. Kitaev. 2009

388 citations recorded by the source corpus.

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one-dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification lies in Z, but with the introduction of interactions the Z is broken to Z_8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field-theory interpretation of this phenomenon. There is a second-order phase transition between the two phases in the free theory, which can be avoided by going through the strongly interacting region. We show that this transition is in the two-dimensional Ising universality class, where a first-order phase transition line, terminating at a second-order transition, can be avoided by going through the analog of a high-temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e., the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first-order Peierls transition region, a second-order transition region, and a region with no transition.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f4078e0c027bf03066e86e4bf382f5b4bce55f59

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. E. Witten
2. D. Stanford
3. D. Else
4. Bela Bauer
5. Romain Vasseur
6. C. Nayak
7. D. Parker
8. Thomas Scaffidi

In Condensed Matter Physics

1. E. Witten
2. D. Parker
3. Romain Vasseur
4. Bela Bauer
5. D. Stanford
6. C. Nayak
7. D. Else
8. Thomas Scaffidi

Citations in the corpus

• Gapless Symmetry-Protected Topological Order (2017, background): “[35] Lukasz Fidkowski and Alexei Kitaev, “Effects of interactions on the topological classification of free fermion”
• JT gravity and the ensembles of random matrix theory (2019, background): “The extension to include time-reversal also has various applications; for instance, see [73] for a time-reversal invariant version of the Kitaev chain with T2 = 1 and [74] for a version with T2 = (−1)F.”