DOI: 10.57903/uj/qbtnzo
title: Topological quantum floating phase of dipolar bosons in an optical ladder - replication data

description: &lt;p&gt;The dataset consists of two files:&lt;/p&gt;
&lt;ul&gt;
 &lt;li&gt;Paper_Figures_Data.pkl&lt;/li&gt;
 &lt;li&gt;Paper_Figures_Data_Resubmission.pkl&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;These files contain the numerical data used to generate the figures in both the main text and supplementary materials of the associated research article. All data were obtained using Density Matrix Renormalization Group (DMRG) calculations for a bosonic ladder model with varying parameters.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Contents:&lt;/strong&gt;&lt;/p&gt;
&lt;ul&gt;
 &lt;li&gt;&lt;strong&gt;Paper_Figures_Data.pkl&lt;/strong&gt; contains the replication data for the figures presented in the &lt;em&gt;main text&lt;/em&gt;:
 &lt;ul&gt;
 &lt;li&gt;&lt;strong&gt;Figure 2:&lt;/strong&gt; (a) Entanglement entropy SvN, (b) P, and (c) the maximum of the structure factor S(k) for k ≠ 0, computed for a ladder with L = 96 rungs.&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Figure 3:&lt;/strong&gt; Structure factor S(k) for t/V = 0.05 as a function of Δ/V, calculated for L = 12, 24, 48, and 96. Peaks at incommensurate k values that become continuous with increasing L illustrate the floating phase.&lt;/li&gt;
&lt;li&gt;&lt;strong&gt;Figure 4:&lt;/strong&gt; (a) P and (b) the central charge c, both obtained via finite-size scaling ∼1/L for t/V = 0.05 using DMRG. Calculations were performed with χ = 600 for L ∈ {60, 72, 84, 96}. Error bars are shown for each data point.&lt;/li&gt;

 &lt;/ul&gt;
 &lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Paper_Figures_Data_Resubmission.pkl&lt;/strong&gt; contains the replication data for the &lt;em&gt;supplementary material&lt;/em&gt;:
 &lt;ul&gt;
 &lt;li&gt;&lt;strong&gt;Figure S3:&lt;/strong&gt; Structure factor S(k) for t/V = 0.05, as a function of Δ/V, for L = 12, 24, 48, and 96.&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Figure S4:&lt;/strong&gt; Structure factor S(k) for t/V = 0.3 and t⊥/t = 0.1, as a function of Δ/V, for L = 12, 24, 48, and 96.&lt;/li&gt;
 &lt;/ul&gt;
 &lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;File format:&lt;/strong&gt; The data are stored as Python pickle (.pkl) files and can be read using Python’s &lt;code&gt;pickle&lt;/code&gt; module. A sample script (&lt;code&gt;tree.py&lt;/code&gt;) is included to browse the file contents.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Data fields (file Paper_Figures_Data.pkl):&lt;/strong&gt;&lt;/p&gt;
&lt;ul&gt;
 &lt;li&gt;&lt;strong&gt;Common:&lt;/strong&gt; 'DeltaV_list' (Δ/V values), 'tV_list' (t/V values)&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Figure 2:&lt;/strong&gt; 'EntEntrs', 'PLams', 'Skmax'. These arrays have dimensions corresponding to the number of items in 'DeltaV_list' and 'tV_list', and they represent panels (a), (b), and (c) of Figure 2 in the main text, respectively.&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Figure 3:&lt;/strong&gt; 'Skcuts'. &lt;/strong&gt; Array of shape (5, 200, 51). The first dimension corresponds to four system sizes L and an extrapolation to L → ∞. The other two axes represent Δ/V (51 values) and k between -π and π (200 values),
&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;Figure 4:&lt;/strong&gt; 'PLamcut', 'ccut', 'OScut'. These contain lists of (value, error) pairs and correspond to quantities shown in Figure 4: P and the central charge c, obtained via finite-size scaling for t/V = 0.05, using DMRG data for L ∈ {60, 72, 84, 96}. 'Oscut' shows a similar string order (not shown in Fig 4) fit&lt;/li&gt;
&lt;/ul&gt;


&lt;p&gt;&lt;strong&gt;Data fields (file Paper_Figures_Data_Resubmission.pkl):&lt;/strong&gt;&lt;/p&gt;
&lt;ul&gt;
 &lt;li&gt;&lt;strong&gt;'SkcutsNNN':&lt;/strong&gt; Structure factor data corresponding to Figure S3. Array of shape (5, 200, 81), where the first dimension spans four system sizes L and an extrapolation to L → ∞. The second and third dimensions correspond to momentum k (sampled between –π and π) and Δ/V (sampled uniformly between 3 and 5), respectively.&lt;/li&gt;
 &lt;li&gt;&lt;strong&gt;'Skcutsty':&lt;/strong&gt; Structure factor data corresponding to Figure S4. Same array shape and axis meaning as above: (5, 200, 81) = (L, k, Δ/V).&lt;/li&gt;
&lt;/ul&gt;


&lt;p&gt;All arrays are stored in NumPy format within the pickle files and are structured for direct plotting and analysis.&lt;/p&gt;