From 7c75479e374836f292475a8a1b9364661a11fc7a Mon Sep 17 00:00:00 2001
From: mfm94 <mfm94@cornell.edu>
Date: Tue, 16 Jun 2020 20:29:07 +0000
Subject: Update on Overleaf.

---
 ref_response.tex | 34 +++++++++++++++++++---------------
 1 file changed, 19 insertions(+), 15 deletions(-)

(limited to 'ref_response.tex')

diff --git a/ref_response.tex b/ref_response.tex
index 9df15f7..f02cbc3 100644
--- a/ref_response.tex
+++ b/ref_response.tex
@@ -109,23 +109,27 @@ The behaviour of c/a is indeed interesting, but our model only considers the cou
     fit the present proposal?
 }\\
 
-We thank the referee for bringing up this point. We have added a discussion of possible physical 
+We thank the referee for bringing up this point. We have added a statement about possible physical 
 realizations to the conclusion section of our manuscript, which we believe broadens the appeal of our
 work by connecting it to the large body of research concerning microscopic theories of hidden order.
-The U-5f electrons in URu$_2$Si$_2$ exhibit a moderate degree of localization [cite], which is
-reflected in partial occupancy of many electronic states. Motivated by the results of refs [cite],
-we assume that the dominant U state consists of $j = 5/2$ electrons in the U-5f2 configuration, which has 
-total angular momentum $J = 4$. Within the $J=4$ multiplet, the precise energetic ordering
-of the $D_{4h}$ crystal field states still remains a matter of debate [cite]. In a simple
-framework of localized $j = 5/2$ electrons in the 5f2 configuration, our phenomenological theory
-is consistent with the ground state being the B$_{1g}$ crystal field state with
-order parameter 
-\[
-    H = \eta (J_x^2 - J_y^2)
-\]
-corresponding to hexadecapolar orbital order,
-where here $\eta$ is taken to be modulated at $\vec{Q} = (0, 0, 1)$. 
-The result of non-zero $\eta$ is a nematic distortion of the B1g orbitals, alternating along the c-axis.\\
+As we now say in the manuscript, physically, our phenomenological order parameter could correspond 
+to B$_{1g}$ multipolar ordering originating from the localized component of the U-5f electrons. 
+For the crystal field states of URu$_2$Si$_2$, this could correspond either to electric quadropolar or
+hexadecapolar order based on the available multipolar operators.
+% The U-5f electrons in URu$_2$Si$_2$ exhibit a moderate degree of localization [cite], which is
+% reflected in partial occupancy of many electronic states. Motivated by the results of refs [cite],
+% we assume that the dominant U state consists of $j = 5/2$ electrons in the U-5f2 configuration, which has 
+% total angular momentum $J = 4$. Within the $J=4$ multiplet, the precise energetic ordering
+% of the $D_{4h}$ crystal field states still remains a matter of debate [cite]. In a simple
+% framework of localized $j = 5/2$ electrons in the 5f2 configuration, our phenomenological theory
+% is consistent with the ground state being the B$_{1g}$ crystal field state with
+% order parameter 
+% \[
+%     H = \eta (J_x^2 - J_y^2)
+% \]
+% corresponding to hexadecapolar orbital order,
+% where here $\eta$ is taken to be modulated at $\vec{Q} = (0, 0, 1)$. 
+% The result of non-zero $\eta$ is a nematic distortion of the B1g orbitals, alternating along the c-axis.\\
 
 \ruleline{Report of the Second Referee -- BN13654/Kent-Dobias}\\
 
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