Reply to the Comment on "Berezinskii-Kosterlitz-Thouless Transition in Two-Dimensional Dipolar Stripes"

TL;DR

This paper defends the original findings on the superfluidity of the stripe phase in a 2D dipolar system, clarifying the contributions to superfluid fraction and addressing criticisms about their previous analysis.

Contribution

It provides a detailed analysis of the spatial contributions to superfluidity in the stripe phase, confirming superfluidity persists in the thermodynamic limit, and clarifies discrepancies with prior commentaries.

Findings

Superfluid fraction from the stripe direction remains finite in the thermodynamic limit.

Stripe phase exhibits superfluidity at low temperatures.

Differences with previous results are explained through analysis of spatial contributions.

Abstract

This is a Reply to the Comment from F. Cinti and M. Boninsegni on our recent work on the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in a two-dimensional dipolar system [R.Bomb\'in, F. Mazzanti and J. Boronat, Physical Review A 100, 063614 (2019)]. The main criticism about our work, expressed in that Comment, is that we did not explicitly report the two spatial contributions to the total superfluid fraction. Here, we analyze our results for a point of the phase diagram corresponding to the stripe phase, close to the gas to stripe transition line, and for a temperature below the BKT critical temperature. The scaling with the system size of the contribution to the superfluid fraction, coming from the direction in which spatial order appears, shows that it remains finite in the thermodynamic limit, as we already stated in our original work. This allow us to state that the stripe phase is superfluid at low temperatures. Furthermore, we offer some comments that help to understand where the differences between the results of Cinti and Boninsegni and ours comes from.