# This file contains the data used for Fig. 6

---
# Values of g/h for the plot in Fig. 6(a)
g_values:
- 0.0
- 0.002006688963210702
- 0.004013377926421404
- 0.006020066889632107
- 0.008026755852842809
- 0.01003344481605351
- 0.012040133779264214
- 0.014046822742474915
- 0.016053511705685617
- 0.01806020066889632
- 0.02006688963210702
- 0.022073578595317722
- 0.024080267558528427
- 0.02608695652173913
- 0.02809364548494983
- 0.030100334448160532
- 0.032107023411371234
- 0.03411371237458194
- 0.03612040133779264
- 0.03812709030100334
- 0.04013377926421404
- 0.042140468227424746
- 0.044147157190635444
- 0.04615384615384615
- 0.048160535117056855
- 0.05016722408026755
- 0.05217391304347826
- 0.054180602006688956
- 0.05618729096989966
- 0.05819397993311036
- 0.060200668896321065
- 0.06220735785953176
- 0.06421404682274247
- 0.06622073578595317
- 0.06822742474916388
- 0.07023411371237458
- 0.07224080267558528
- 0.07424749163879597
- 0.07625418060200669
- 0.07826086956521738
- 0.08026755852842808
- 0.0822742474916388
- 0.08428093645484949
- 0.08628762541806019
- 0.08829431438127089
- 0.0903010033444816
- 0.0923076923076923
- 0.094314381270903
- 0.09632107023411371
- 0.09832775919732441
- 0.1003344481605351
- 0.1023411371237458
- 0.10434782608695652
- 0.10635451505016721
- 0.10836120401337791
- 0.11036789297658861
- 0.11237458193979932
- 0.11438127090301002
- 0.11638795986622072
- 0.11839464882943143
- 0.12040133779264213
- 0.12240802675585283
- 0.12441471571906353
- 0.12642140468227422
- 0.12842809364548494
- 0.13043478260869565
- 0.13244147157190633
- 0.13444816053511705
- 0.13645484949832776
- 0.13846153846153844
- 0.14046822742474915
- 0.14247491638795984
- 0.14448160535117055
- 0.14648829431438126
- 0.14849498327759195
- 0.15050167224080266
- 0.15250836120401337
- 0.15451505016722406
- 0.15652173913043477
- 0.15852842809364548
- 0.16053511705685616
- 0.16254180602006688
- 0.1645484949832776
- 0.16655518394648827
- 0.16856187290969898
- 0.17056856187290967
- 0.17257525083612038
- 0.1745819397993311
- 0.17658862876254178
- 0.1785953177257525
- 0.1806020066889632
- 0.18260869565217389
- 0.1846153846153846
- 0.1866220735785953
- 0.188628762541806
- 0.1906354515050167
- 0.19264214046822742
- 0.1946488294314381
- 0.19665551839464882
- 0.1986622073578595
- 0.2006688963210702
- 0.20267558528428092
- 0.2046822742474916
- 0.20668896321070232
- 0.20869565217391303
- 0.21070234113712372
- 0.21270903010033443
- 0.21471571906354514
- 0.21672240802675583
- 0.21872909698996654
- 0.22073578595317722
- 0.22274247491638793
- 0.22474916387959865
- 0.22675585284280933
- 0.22876254180602004
- 0.23076923076923075
- 0.23277591973244144
- 0.23478260869565215
- 0.23678929765886286
- 0.23879598662207355
- 0.24080267558528426
- 0.24280936454849497
- 0.24481605351170566
- 0.24682274247491637
- 0.24882943143812705
- 0.2508361204013378
- 0.25284280936454845
- 0.25484949832775916
- 0.2568561872909699
- 0.2588628762541806
- 0.2608695652173913
- 0.26287625418060195
- 0.26488294314381267
- 0.2668896321070234
- 0.2688963210702341
- 0.2709030100334448
- 0.2729096989966555
- 0.27491638795986617
- 0.2769230769230769
- 0.2789297658862876
- 0.2809364548494983
- 0.282943143812709
- 0.2849498327759197
- 0.2869565217391304
- 0.2889632107023411
- 0.2909698996655518
- 0.2929765886287625
- 0.29498327759197324
- 0.2969899665551839
- 0.2989966555183946
- 0.3010033444816053
- 0.30301003344481603
- 0.30501672240802674
- 0.30702341137123745
- 0.3090301003344481
- 0.3110367892976588
- 0.31304347826086953
- 0.31505016722408025
- 0.31705685618729096
- 0.3190635451505016
- 0.3210702341137123
- 0.32307692307692304
- 0.32508361204013375
- 0.32709030100334446
- 0.3290969899665552
- 0.33110367892976583
- 0.33311036789297654
- 0.33511705685618726
- 0.33712374581939797
- 0.3391304347826087
- 0.34113712374581934
- 0.34314381270903005
- 0.34515050167224076
- 0.3471571906354515
- 0.3491638795986622
- 0.3511705685618729
- 0.35317725752508355
- 0.35518394648829427
- 0.357190635451505
- 0.3591973244147157
- 0.3612040133779264
- 0.36321070234113706
- 0.36521739130434777
- 0.3672240802675585
- 0.3692307692307692
- 0.3712374581939799
- 0.3732441471571906
- 0.3752508361204013
- 0.377257525083612
- 0.3792642140468227
- 0.3812709030100334
- 0.3832775919732441
- 0.38528428093645484
- 0.3872909698996655
- 0.3892976588628762
- 0.3913043478260869
- 0.39331103678929763
- 0.39531772575250834
- 0.397324414715719
- 0.3993311036789297
- 0.4013377926421404
- 0.40334448160535114
- 0.40535117056856185
- 0.40735785953177256
- 0.4093645484949832
- 0.41137123745819393
- 0.41337792642140464
- 0.41538461538461535
- 0.41739130434782606
- 0.4193979933110367
- 0.42140468227424743
- 0.42341137123745815
- 0.42541806020066886
- 0.42742474916387957
- 0.4294314381270903
- 0.43143812709030094
- 0.43344481605351165
- 0.43545150501672236
- 0.4374581939799331
- 0.4394648829431438
- 0.44147157190635444
- 0.44347826086956516
- 0.44548494983277587
- 0.4474916387959866
- 0.4494983277591973
- 0.451505016722408
- 0.45351170568561866
- 0.4555183946488294
- 0.4575250836120401
- 0.4595317725752508
- 0.4615384615384615
- 0.46354515050167217
- 0.4655518394648829
- 0.4675585284280936
- 0.4695652173913043
- 0.471571906354515
- 0.4735785953177257
- 0.4755852842809364
- 0.4775919732441471
- 0.4795986622073578
- 0.4816053511705685
- 0.48361204013377923
- 0.48561872909698994
- 0.4876254180602006
- 0.4896321070234113
- 0.491638795986622
- 0.49364548494983274
- 0.49565217391304345
- 0.4976588628762541
- 0.4996655518394648
- 0.5016722408026756
- 0.5036789297658862
- 0.5056856187290969
- 0.5076923076923077
- 0.5096989966555183
- 0.5117056856187291
- 0.5137123745819397
- 0.5157190635451504
- 0.5177257525083612
- 0.5197324414715718
- 0.5217391304347826
- 0.5237458193979933
- 0.5257525083612039
- 0.5277591973244147
- 0.5297658862876253
- 0.5317725752508361
- 0.5337792642140468
- 0.5357859531772575
- 0.5377926421404682
- 0.5397993311036788
- 0.5418060200668896
- 0.5438127090301003
- 0.545819397993311
- 0.5478260869565217
- 0.5498327759197323
- 0.5518394648829431
- 0.5538461538461538
- 0.5558528428093645
- 0.5578595317725752
- 0.5598662207357858
- 0.5618729096989966
- 0.5638795986622073
- 0.565886287625418
- 0.5678929765886287
- 0.5698996655518394
- 0.5719063545150501
- 0.5739130434782608
- 0.5759197324414715
- 0.5779264214046822
- 0.579933110367893
- 0.5819397993311036
- 0.5839464882943143
- 0.585953177257525
- 0.5879598662207357
- 0.5899665551839465
- 0.5919732441471571
- 0.5939799331103678
- 0.5959866220735786
- 0.5979933110367892
- 0.6

# Chosen parameters for the Dicke-Ising model
J: -0.05
h: 1.0
omega: 1.125

# Critical g-value for the closing of the gap.
g_crit analytical: sqrt(\omega)*sqrt(\omega_0)/2
g_crit numerical: 0.5303300858899106

# --1QP--
# Hybridized one-magnon state (analytical and numerical result)
# for the effective model
one-magnon analytical: sqrt(\omega**2/2 + \omega_0**2/2 - sqrt(\omega**4 - 2*\omega**2*\omega_0**2
  + 16*\omega*\omega_0*g**2 + \omega_0**4)/2)
one-magnon numerical:
- 1.0
- 0.9999658988043985
- 0.9998636931053909
- 0.9996936750605048
- 0.9994563266329104
- 0.9991523123262311
- 0.9987824693691445
- 0.9983477956790979
- 0.9978494359935087
- 0.9972886665941691
- 0.9966668790657592
- 0.9959855635235785
- 0.9952462917214441
- 0.9944507004117318
- 0.9936004752798651
- 0.9926973357193773
- 0.9917430206549288
- 0.9907392755627598
- 0.9896878407837227
- 0.9885904411752372
- 0.987448777106483
- 0.9862645167664722
- 0.985039289727373
- 0.9837746816852122
- 0.9824722302862173
- 0.9811334219387333
- 0.9797596895069807
- 0.9783524107829797
- 0.9769129076359199
- 0.9754424457433257
- 0.9739422348148844
- 0.9724134292272231
- 0.9708571289957801
- 0.9692743810178661
- 0.9676661805287985
- 0.9660334727204154
- 0.9643771544782185
- 0.9626980761997731
- 0.9609970436627824
- 0.9592748199164253
- 0.9575321271741384
- 0.9557696486900433
- 0.9539880306047163
- 0.9521878837490131
- 0.9503697853972366
- 0.9485342809631204
- 0.9466818856339427
- 0.9448130859396162
- 0.9429283412548728
- 0.9410280852336989
- 0.9391127271760239
- 0.9371826533273372
- 0.935238228112442
- 0.9332797953049677
- 0.931307679134573
- 0.9293221853339989
- 0.9273236021282908
- 0.9253122011686065
- 0.9232882384130867
- 0.9212519549572747
- 0.9192035778165661
- 0.9171433206631284
- 0.9150713845196767
- 0.912987958412426
- 0.9108932199854578
- 0.9087873360786549
- 0.9066704632712704
- 0.904542748393097
- 0.9024043290051171
- 0.9002553338514121
- 0.8980958832840202
- 0.8959260896623411
- 0.8937460577285953
- 0.8915558849607612
- 0.8893556619043308
- 0.8871454724841441
- 0.8849253942974903
- 0.8826954988895865
- 0.8804558520124819
- 0.8782065138683677
- 0.8759475393382113
- 0.8736789781965781
- 0.8714008753134463
- 0.8691132708437723
- 0.8668162004055131
- 0.8645096952467676
- 0.8621937824026581
- 0.8598684848425285
- 0.8575338216080041
- 0.855189807942415
- 0.8528364554120633
- 0.8504737720197695
- 0.848101762311115
- 0.8457204274737681
- 0.8433297654302494
- 0.8409297709244787
- 0.8385204356024133
- 0.8361017480870723
- 0.8336736940482212
- 0.8312362562669697
- 0.828789414695521
- 0.826333146512294
- 0.8238674261726221
- 0.8213922254552228
- 0.8189075135046123
- 0.8164132568696311
- 0.8139094195382335
- 0.8113959629686822
- 0.8088728461172756
- 0.8063400254627319
- 0.8037974550273363
- 0.8012450863949556
- 0.798682868726009
- 0.7961107487694831
- 0.7935286708720635
- 0.7909365769844522
- 0.7883344066649344
- 0.7857220970802442
- 0.7830995830037801
- 0.7804667968112096
- 0.777823668473497
- 0.775170125547384
- 0.7725060931633428
- 0.7698314940110217
- 0.7671462483221899
- 0.7644502738511915
- 0.7617434858529022
- 0.7590257970581883
- 0.7562971176468531
- 0.7535573552180552
- 0.7508064147581757
- 0.7480441986061065
- 0.7452706064159278
- 0.7424855351169318
- 0.7396888788709536
- 0.7368805290269529
- 0.7340603740727947
- 0.7312282995841634
- 0.7283841881705431
- 0.7255279194181887
- 0.7226593698300051
- 0.7197784127622462
- 0.7168849183579379
- 0.713978753476921
- 0.7110597816224037
- 0.708127862863903
- 0.7051828537564467
- 0.7022246072559023
- 0.69925297263028
- 0.6962677953668596
- 0.693268917074971
- 0.6902561753842494
- 0.687229403838178
- 0.684188431782713
- 0.6811330842497767
- 0.6780631818353877
- 0.6749785405721854
- 0.6718789717960852
- 0.6687642820067885
- 0.6656342727218516
- 0.6624887403239961
- 0.6593274759013278
- 0.6561502650801031
- 0.6529568878496622
- 0.6497471183791206
- 0.6465207248253854
- 0.6432774691320309
- 0.6400171068185376
- 0.636739386759366
- 0.6334440509522961
- 0.6301308342754302
- 0.6267994642322071
- 0.6234496606837363
- 0.620081135567704
- 0.616693592603058
- 0.6132867269796107
- 0.609860225031645
- 0.6064137638945308
- 0.6029470111432961
- 0.5994596244120044
- 0.5959512509927122
- 0.5924215274126773
- 0.5888700789883892
- 0.585296519354878
- 0.5817004499686316
- 0.5780814595823168
- 0.5744391236893531
- 0.570773003936221
- 0.5670826475002095
- 0.5633675864301123
- 0.559627336947162
- 0.5558613987032596
- 0.5520692539932865
- 0.5482503669180032
- 0.5444041824937126
- 0.5405301257045173
- 0.5366276004925996
- 0.5326959886815212
- 0.5287346488270552
- 0.524742914989514
- 0.520720095420945
- 0.5166654711598837
- 0.5125782945256009
- 0.5084577875029419
- 0.5043031400078963
- 0.5001135080229788
- 0.4958880115902939
- 0.49162573264879633
- 0.4873257127007266
- 0.48298695029045463
- 0.47860839827698237
- 0.4741889608791037
- 0.46972749046964024
- 0.4652227840922287
- 0.46067357967075273
- 0.4560785518776281
- 0.4514363076226644
- 0.4467453811190512
- 0.44200422847700116
- 0.43721122176859967
- 0.43236464249925816
- 0.4274626744116239
- 0.42250339553659966
- 0.41748476939291396
- 0.41240463522106896
- 0.4072606971189386
- 0.402050511924179
- 0.396771475662127
- 0.3914208083460255
- 0.3859955368779248
- 0.38049247575189005
- 0.37490820520411433
- 0.36923904638454197
- 0.3634810330382166
- 0.35762987907727073
- 0.3516809412903524
- 0.3456291762674831
- 0.33946909040430695
- 0.33319468157621407
- 0.3267993707204271
- 0.3202759211060106
- 0.31361634247043135
- 0.30681177640379004
- 0.29985235829236084
- 0.29272704968137914
- 0.28542343292060784
- 0.2779274571710381
- 0.2702231209043031
- 0.2622920703362477
- 0.25411308487484846
- 0.2456614081135016
- 0.23690786361452487
- 0.22781766428629283
- 0.21834877463030505
- 0.20844960170774457
- 0.19805564437514037
- 0.18708446137400037
- 0.17542779574394482
- 0.16293860356961373
- 0.14940826434622018
- 0.13452299792238684
- 0.11777017331764443
- 0.09819858613966212
- 0.07359269886295078
- 0.03447586503045729
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan
- .nan

# Hybridized one-photon state (analytical and numerical result)
# for the effective model
one-photon analytical: sqrt(\omega**2/2 + \omega_0**2/2 + sqrt(\omega**4 - 2*\omega**2*\omega_0**2
  + 16*\omega*\omega_0*g**2 + \omega_0**4)/2)
one-photon numerical:
- 1.125
- 1.1250303112486844
- 1.1251211469035896
- 1.1252722141970901
- 1.125483030149033
- 1.1257529288316976
- 1.1260810711848743
- 1.126466457051734
- 1.126907939047124
- 1.1274042378325637
- 1.127953958357042
- 1.1285556066284992
- 1.129207606605054
- 1.129908316833988
- 1.1306560465161923
- 1.1314490707299423
- 1.1322856446066236
- 1.133164016308927
- 1.1340824387163628
- 1.13503917977176
- 1.136032531484425
- 1.1370608176203227
- 1.1381224001369066
- 1.139215684440466
- 1.1403391235577363
- 1.141491221321825
- 1.1426705346761965
- 1.143875675200383
- 1.145105309958142
- 1.1463581617637129
- 1.1476330089552969
- 1.1489286847574798
- 1.1502440763064468
- 1.1515781234038933
- 1.1529298170577456
- 1.154298197860386
- 1.1556823542481274
- 1.1570814206793123
- 1.158494575762611
- 1.1599210403619333
- 1.1613600756997675
- 1.162810981476745
- 1.1642730940217312
- 1.1657457844837253
- 1.1672284570742828
- 1.1687205473669813
- 1.1702215206586155
- 1.171730870395271
- 1.1732481166651554
- 1.1747728047590302
- 1.1763045037982345
- 1.1778428054296262
- 1.179387322586223
- 1.180937688311927
- 1.182493554648386
- 1.184054591581841
- 1.1856204860476272
- 1.1871909409899102
- 1.188765674474183
- 1.1903444188500232
- 1.1919269199616325
- 1.1935129364037116
- 1.1951022388202786
- 1.1966946092441089
- 1.1982898404745508
- 1.1998877354915591
- 1.201488106903876
- 1.2030907764293859
- 1.2046955744057601
- 1.206302339329607
- 1.2079109174224296
- 1.2095211622217887
- 1.2111329341961576
- 1.2127461003820355
- 1.2143605340419745
- 1.2159761143422534
- 1.2175927260489983
- 1.2192102592416387
- 1.2208286090426348
- 1.2224476753624953
- 1.2240673626591523
- 1.2256875797108262
- 1.227308239401561
- 1.2289292585186666
- 1.23055055756135
- 1.232172060559864
- 1.2337936949045403
- 1.2354153911841208
- 1.2370370830328297
- 1.2386587069856714
- 1.2402802023414659
- 1.2419015110331677
- 1.2435225775050411
- 1.245143348596292
- 1.2467637734307813
- 1.2483838033124683
- 1.2500033916262543
- 1.251622493743917
- 1.2532410669348466
- 1.2548590702813096
- 1.2564764645979867
- 1.258093212355544
- 1.2597092776080119
- 1.2613246259237614
- 1.2629392243198772
- 1.264553041199744
- 1.2661660462936668
- 1.2677782106023612
- 1.2693895063431626
- 1.270999906898801
- 1.27260938676861
- 1.274217921522037
- 1.2758254877543374
- 1.2774320630443299
- 1.2790376259141154
- 1.2806421557906478
- 1.2822456329690681
- 1.2838480385777062
- 1.2854493545446688
- 1.2870495635659298
- 1.2886486490748483
- 1.2902465952130442
- 1.29184338680256
- 1.2934390093192483
- 1.2950334488673212
- 1.2966266921550083
- 1.2982187264712635
- 1.2998095396634777
- 1.3013991201161395
- 1.3029874567304052
- 1.3045745389045327
- 1.3061603565151363
- 1.3077448998992256
- 1.309328159836992
- 1.310910127535306
- 1.3124907946118929
- 1.3140701530801575
- 1.315648195334624
- 1.3172249141369665
- 1.3188003026026018
- 1.3203743541878188
- 1.321947062677421
- 1.3235184221728584
- 1.3250884270808279
- 1.3266570721023196
- 1.3282243522220942
- 1.3297902626985632
- 1.3313547990540664
- 1.332917957065519
- 1.3344797327554183
- 1.3360401223831928
- 1.3375991224368788
- 1.339156729625111
- 1.3407129408694136
- 1.3422677532967804
- 1.343821164232529
- 1.3453731711934211
- 1.3469237718810354
- 1.3484729641753832
- 1.3500207461287592
- 1.3515671159598124
- 1.3531120720478345
- 1.3546556129272527
- 1.3561977372823197
- 1.3577384439419946
- 1.3592777318750051
- 1.3608156001850835
- 1.362352048106373
- 1.3638870749989922
- 1.365420680344759
- 1.3669528637430592
- 1.3684836249068595
- 1.3700129636588605
- 1.3715408799277793
- 1.3730673737447605
- 1.3745924452399105
- 1.3761160946389486
- 1.3776383222599713
- 1.3791591285103275
- 1.3806785138835973
- 1.3821964789566719
- 1.383713024386932
- 1.3852281509095201
- 1.3867418593347014
- 1.388254150545314
- 1.3897650254943021
- 1.3912744852023298
- 1.392782530755474
- 1.3942891633029904
- 1.3957943840551552
- 1.3972981942811733
- 1.3988005953071567
- 1.4003015885141659
- 1.4018011753363153
- 1.4032993572589394
- 1.4047961358168162
- 1.4062915125924478
- 1.4077854892143962
- 1.4092780673556695
- 1.4107692487321617
- 1.4122590351011397
- 1.4137474282597777
- 1.415234430043739
- 1.4167200423257988
- 1.4182042670145145
- 1.4196871060529324
- 1.4211685614173375
- 1.422648635116041
- 1.4241273291882046
- 1.4256046457027018
- 1.4270805867570133
- 1.4285551544761568
- 1.4300283510116483
- 1.4315001785404973
- 1.4329706392642296
- 1.4344397354079417
- 1.4359074692193836
- 1.4373738429680685
- 1.4388388589444099
- 1.4403025194588839
- 1.4417648268412184
- 1.4432257834396052
- 1.4446853916199345
- 1.4461436537650556
- 1.447600572274057
- 1.4490561495615677
- 1.4505103880570815
- 1.4519632902043007
- 1.453414858460496
- 1.4548650952958913
- 1.4563140031930606
- 1.4577615846463472
- 1.4592078421612988
- 1.460652778254117
- 1.4620963954511264
- 1.4635386962882573
- 1.4649796833105437
- 1.4664193590716377
- 1.4678577261333352
- 1.4692947870651187
- 1.4707305444437115
- 1.4721650008526452
- 1.4735981588818408
- 1.4750300211272007
- 1.4764605901902141
- 1.4778898686775734
- 1.479317859200801
- 1.480744564375888
- 1.4821699868229437
- 1.4835941291658539
- 1.485016994031951
- 1.486438584051693
- 1.487858901858351
- 1.4892779500877076
- 1.4906957313777625
- 1.4921122483684488
- 1.4935275037013547
- 1.494941500019456
- 1.496354239966855
- 1.4977657261885284
- 1.4991759613300815
- 1.5005849480375084
- 1.5019926889569641
- 1.503399186734537
- 1.5048044440160329
- 1.5062084634467634
- 1.5076112476713408
- 1.5090127993334799
- 1.510413121075804
- 1.5118122155396592
- 1.5132100853649317
- 1.5146067331898718
- 1.5160021616509243
- 1.517396373382562
- 1.5187893710171245
- 1.5201811571846644
- 1.5215717345127946
- 1.5229611056265429
- 1.5243492731482096
- 1.5257362396972303
- 1.5271220078900427
- 1.5285065803399576
- 1.529889959657033
- 1.5312721484479541
- 1.5326531493159152
- 1.534032964860506
- 1.535411597677602
- 1.5367890503592565
- 1.5381653254935999
- 1.5395404256647374
- 1.5409143534526535
- 1.5422871114331187
- 1.5436587021775983
- 1.5450291282531656
- 1.546398392222417
- 1.5477664966433893
- 1.549133444069483
- 1.550499237049384
- 1.55186387812699
- 1.5532273698413404

# --ED RESULTS--
# System sizes N for which the ED was performed
# Values of g/h for the ED results
g_values_ED:
- 0.0
- 0.07071067811865475
- 0.1414213562373095
- 0.21213203435596426
- 0.282842712474619
- 0.35355339059327373
- 0.4242640687119285
- 0.4949747468305833
- 0.565685424949238
- 0.6363961030678927

# Hybridized one-magnon energy for different Ns
one-magnon ED:
- - 0.9999999999999748
  - 0.9664668918698512
  - 0.9002515440874926
  - 0.8224482891830875
  - 0.7364126709937631
  - 0.642272292623967
  - 0.5396194652482713
  - 0.4287239463500898
  - 0.31241553975713643
  - 0.1993897675561187
- - 0.999999999999952
  - 0.9661923721532477
  - 0.8991968065173901
  - 0.8198887172480185
  - 0.7311424372244533
  - 0.6322281249538566
  - 0.5212874580987648
  - 0.3965659038461129
  - 0.2601469556120293
  - 0.1294010852431784
- - 0.9999999999999929
  - 0.9660549731602939
  - 0.8986668327134124
  - 0.8185916180622068
  - 0.7284254943947266
  - 0.626879036432253
  - 0.5109509043623843
  - 0.3767527016471832
  - 0.22459919347080382
  - 0.08366607673447213
- - 0.9999999999999494
  - 0.9659724893738963
  - 0.8983480182207457
  - 0.817807777971292
  - 0.7267679660155424
  - 0.62355164063234
  - 0.5042693022260094
  - 0.36302642468068225
  - 0.1977747053276957
  - 0.052905824048194106
- - 0.9999999999999512
  - 0.9659174817170015
  - 0.8981351301608358
  - 0.8172828852243228
  - 0.7256512710432883
  - 0.6212806225862932
  - 0.4995802020963449
  - 0.35283226253406585
  - 0.17628086349288896
  - 0.03257895013431611
- - 0.9999999999999538
  - 0.965878181498554
  - 0.8979828985409872
  - 0.8169068174321632
  - 0.7248478272770349
  - 0.619631379804181
  - 0.4961019578501418
  - 0.3449019308887671
  - 0.1583767894083934
  - 0.019585531291239633
- - 0.9999999999997975
  - 0.9658487013975527
  - 0.8978686326748715
  - 0.8166241401642358
  - 0.724242037794979
  - 0.6183791263105594
  - 0.4934164449240592
  - 0.3385239197989991
  - 0.14305689190337478
  - 0.011551121808610176

# Hybridized one-photon energy for different Ns
one-photon ED:
- - 1.1249999999999805
  - 1.1547496393656567
  - 1.209499417638125
  - 1.2678098343475779
  - 1.3257515396283504
  - 1.3823679310955024
  - 1.4365540571940558
  - 1.4803414666519823
  - 1.440965197098881
  - 1.688759374858246
- - 1.1250000000000184
  - 1.1547081670131976
  - 1.2092234433526283
  - 1.2671026885780006
  - 1.3244495780554943
  - 1.3803813001467622
  - 1.4339862755194355
  - 1.4632924851766422
  - 1.5638889835065142
  - 1.6084954276243282
- - 1.1250000000002056
  - 1.1546874683702764
  - 1.2090859511529217
  - 1.2667506811063323
  - 1.3238003795649047
  - 1.3793850218189379
  - 1.432722175663172
  - 1.4986837164455666
  - 1.511481515469987
  - 1.6125471896207482
- - 1.1250000000000386
  - 1.1546750612151886
  - 1.2090036185412916
  - 1.266540041342728
  - 1.3234117746509293
  - 1.3787868464194153
  - 1.4319747339974094
  - 1.489660067092752
  - 1.5218126557274942
  - 1.584857152363968
- - 1.1249999999999805
  - 1.1546667947956477
  - 1.2089487989423295
  - 1.266399866227478
  - 1.3231531853660874
  - 1.378388090957519
  - 1.4314827103276917
  - 1.4865732460393106
  - 1.538386423975843
  - 1.5364901366364858
- - 1.1249999999999813
  - 1.15466089266907
  - 1.208909676115467
  - 1.2662998696945316
  - 1.3229687507456722
  - 1.3781033662762567
  - 1.431135040210167
  - 1.456916710706035
  - 1.3684413935177897
  - 1.3829330823565371
- - 1.125000000000071
  - 1.154656467419441
  - 1.2088803527326402
  - 1.2662249447632306
  - 1.3228305890539165
  - 1.377889919632179
  - 1.430876677964509
  - 1.4840168100862057
  - 1.532697105968638
  - 1.6641373822384926

# Absolute energy differences between the ED results and the effective theory
# Absolute energy differences for hybridized one-magnon energy
one-magnon diff:
- - 2.5202062658991053e-14
  - 4.796163466380676e-14
  - 7.105427357601002e-15
  - 5.062616992290714e-14
  - 4.884981308350689e-14
  - 4.618527782440651e-14
  - 2.0250467969162855e-13
- - 0.0008246694754122652
  - 0.0005501497588087378
  - 0.0004127507658548968
  - 0.00033026697945737205
  - 0.0002752593225625599
  - 0.0002359591041150022
  - 0.00020647900311376866
- - 0.003184977342733264
  - 0.0021302397726307154
  - 0.0016002659686530363
  - 0.0012814514759863505
  - 0.001068563416076418
  - 0.0009163317962278539
  - 0.0008020659301121169
- - 0.007817942188797056
  - 0.005258370253727995
  - 0.003961271067916328
  - 0.0031774309770015163
  - 0.0026525382300323086
  - 0.002276470437872713
  - 0.0019937931699453015
- - 0.016489774335028407
  - 0.011219540565718611
  - 0.008502597735991935
  - 0.006845069356807731
  - 0.005728374384553647
  - 0.004924930618300238
  - 0.00431914113624432
- - 0.03305654120694812
  - 0.023012373536837716
  - 0.017663285015234065
  - 0.01433588921532114
  - 0.01206487116927435
  - 0.010415628387162146
  - 0.009163374893540466
- - 0.06732110198306623
  - 0.04898909483355968
  - 0.03865254109717925
  - 0.03197093896080433
  - 0.027281838831139826
  - 0.023803594584936694
  - 0.02111808165885415
- - 0.1558755807284426
  - 0.12371753822446568
  - 0.103904336025536
  - 0.09017805905903503
  - 0.07998389691241864
  - 0.07205356526711987
  - 0.06567555417735188
- - 0.4148713645444566
  - 0.3770825084135349
  - 0.35349621970393413
  - 0.3370899193163352
  - 0.3249457223461098
  - 0.31559148762371125
  - 0.3081883416975574
- - 0.513284589848015
  - 0.4903564332518482
  - 0.480317398358107
  - 0.4759241714680821
  - 0.47409511573229285
  - 0.4733797458756786
  - 0.473115439596299

# Absolute energy differences for hybridized one-photon energy
one-photon diff:
- - 1.9539925233402755e-14
  - 1.84297022087776e-14
  - 2.05613304160579e-13
  - 3.863576125695545e-14
  - 1.9539925233402755e-14
  - 1.865174681370263e-14
  - 7.105427357601002e-14
- - 0.00012411638033449357
  - 8.264402787538927e-05
  - 6.194538495418733e-05
  - 4.9538229866419314e-05
  - 4.127181032553828e-05
  - 3.536968374784344e-05
  - 3.09444341188847e-05
- - 0.0008238719151341112
  - 0.0005478976296373617
  - 0.00041040542993076023
  - 0.00032807281830060653
  - 0.00027325321933857616
  - 0.0002341303924759952
  - 0.0002048070096491994
- - 0.0021075005597468444
  - 0.0014003547901695335
  - 0.0010483473185012304
  - 0.0008377075548968715
  - 0.0006975324396469862
  - 0.0005975359067005304
  - 0.0005226109753995178
- - 0.0038831562911525452
  - 0.0025811947182965422
  - 0.0019319962277069003
  - 0.0015433913137314903
  - 0.0012848020288895867
  - 0.001100367408474412
  - 0.0009622057167186782
- - 0.005966402389072423
  - 0.003979771440332236
  - 0.0029834931125078956
  - 0.0023853177129853353
  - 0.0019865622510890635
  - 0.0017018375698267807
  - 0.001488390925749039
- - 0.007372733478618887
  - 0.004804951803998536
  - 0.003540851947735124
  - 0.0027934102819724416
  - 0.0023013866122547633
  - 0.0019537164947300845
  - 0.0016953542490720785
- - 7.839227040595809e-05
  - 0.016970589204934106
  - 0.0184206420639903
  - 0.009396992711175667
  - 0.006310171657734287
  - 0.023346363675541326
  - 0.003753735704629335
- - 0.08878634470038649
  - 0.03413744170724664
  - 0.018270026329280542
  - 0.007938886071773288
  - 0.008634882176575376
  - 0.16131014828147783
  - 0.0029455641693705292
- - 0.11099836926539575
  - 0.030734422031478026
  - 0.034786184027898015
  - 0.007096146771117917
  - 0.04127086895636434
  - 0.19482792323631304
  - 0.08637637664564246

# Exponent alpha of the energy difference scaling factor N^alpha for different g-values
# Exponent alpha for hybridized one-magnon energy
one-magnon exponent:
- -1.0867889871748866
- 0.9989355864541837
- 0.9948679718828625
- 0.9859656492614566
- 0.9670764550864593
- 0.9267042052045594
- 0.8378170761137653
- 0.6243283688163429
- 0.2147981947553487
- 0.056654072343188915

# Exponent alpha for hybridized one-photon energy
one-photon exponent:
- -0.33995994982341615
- 1.001926424623454
- 1.003994354230619
- 1.005784003783242
- 1.006437607152672
- 1.0017437518537904
- 1.0606947081980551
- -2.3122538347362886
- 1.3312676682328988
- -0.1725239346755452
...