# A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems

### Submission summary

 As Contributors: Tanmoy Das Preprint link: scipost_202011_00005v1 Date submitted: 2020-11-05 09:49 Submitted by: Das, Tanmoy Submitted to: SciPost Physics Academic field: Physics Specialties: General Topology Atomic, Molecular and Optical Physics - Theory Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian quantum theory is envisioned to have far-reaching implications in basic science and applications. It is known that the PT-inner product is defined with respect to a non-canonical, system generated dynamical symmetry, namely the C symmetry. Here, we show that the PT invariant equation of motion is defined by the simultaneous time evolution of the state $\psi(t)$ and the operator C(t) to manifest unitarity. The dynamical C operator lends itself into a new term in the Berry phase. The PT symmetric theory is not generally applicable for spin-1/2 fermions, since here PT inner product becomes undefined due to Kramer's theory. We consider a spin-1/2 non-Hermitian setup which acquires the combined (PT)^2=+1 symmetry, despite T^2=-1 and P^2=+1. The Hamiltonian inherits a non-Abelian adiabatic transporter and topological degeneracy via the combined evolution of the state as well as the C operator. The putative dynamical C symmetry can be a novel springboard for many other exotic quantum and topological phases.

###### Current status:
Editor-in-charge assigned

The authors' response file is uploaded along with the preprint file in a pdf format. Because the response includes equations that cannot be typed here.

### List of changes

Only a few typographical changes are there as indicated in the authors' response file.

### Submission & Refereeing History

Resubmission scipost_202011_00005v1 on 5 November 2020
Submission 1907.07333v2 on 21 July 2020

## Reports on this Submission

### Report

The authors have addressed my minor comments in a satisfactory way. (My comment #5 was indeed referring to the list of parameters at the end of Section III.A, which is now Section 3.1.)

However, my main comments have not been addressed at all. It seems that none of them has lead to any change in the manuscript. The authors answer my comments essentially by stating the oposite and claiming that I am a beginner in the field. It seems that they cannot explain the relevance of their findings on the basis of a simple example.

After such response, I share now the opinion of the referee #2 that "the extensive mathematical manipulations done via C and Q matrices do not have much physical bearing."

I am also rather disappointed that my recommendation to add the explicit form of some matrices is answered by "...direct product algebra is a textbook stuff, and one usually does not waste journal paper’s pages with such stuff." As commented by referee #2 the authors try to get published the manuscript for about one year. The authors justify this by biased editors. However, their conceited way to answer referee reports may also contribute to this problem.

The authors cite my report in their response to referee #2 incorrectly. I wrote that the introduction is well structured and did not evaluate the whole manuscript.

At all, I do not recommend to publish the current version of the manuscript in SciPost.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Strengths

Interesting topic

### Weaknesses

Presentation and coherence

### Report

Some minor improvements are done. I re-iterate my recommendation that this work is not suitable for SciPost Physics. I would, after a slight hesitation, however recommend publication in SciPost Physics Core.

• validity: ok
• significance: ok
• originality: ok
• clarity: ok
• formatting: reasonable
• grammar: reasonable