回転するバリオン物質の相構造：
非可換カイラルソリトン格子、反強磁性
アイソスピン鎖とフェロ・フェリ磁性
西村健太郎(KEK)共同研究者：衛藤稔（山形大学）、新田宗土（慶應義塾大学）

熱場の量子論2022 2022年9月22日@京大基研
JHEP 08 (2022) 305 (arXiv: 2112.01381)

カイラルソリトン格子
パリティ対称性が破れた

ソリトンが並ぶ結晶状態• カイラル磁性体 Togawa et al., PRL (2012)• 強磁性相互作用→隣り合ったスピンをそろえる
FIG.
1 (color). Schematic diagram of crystalline and magnetic• ゼーマン効果→スピンは磁場の方向を向く
structures of Cr1=3 NbS2 . (a) A unit cell of the crystal. Spinmagnetic moments of localized electrons rotate in theabplane along the helical c axis because of DM interaction,• Dzyaloshinskii・Moriya相互作用→隣り合ったスピンを捻る
giving rise to CHM. A part of left-handed CHM is schematicallydrawn in ten unit cells in (b), whereas a whole left-handed CHM
in (c). (d) In magnetic fields perpendicular to the helical c axis,

by
an
fir
#
CS
wh
mo
1.
at
H
H
we

wh
Lð
H=

QCDにおけるCSL
T• 非中心衝突

クォーク・グルーオン・プラズマ相

200 MeV<latexit sha1_base64="IqB2mTwypoap8+huuW4aXNkWoi8=">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</latexit>

ハドロン相
カラー超伝導相vµB<latexit sha1_base64="CgWEca/41wyNLuDclDtNWEIj6vs=">AAACbnichVHLSsNAFD2N7/qqCiKIWCyKqzIRUXFVdOPSV6vQlpLEUQfzIo+Chv6Ae3EhKAoi4me48Qdc+AniRqjgxoU3aUC0qDdM5syZe+6cuaPaunA9xp4SUktrW3tHZ1eyu6e3rz81MFhwLd/ReF6zdMvZVhWX68LkeU94Ot+2Ha4Yqs631IPlcH+ryh1XWOamd2jzsqHsmWJXaIpHVLFk+JWg5BjppVollWFZFkW6GcgxyCCOVSt1gxJ2YEGDDwMcJjzCOhS49BUhg8EmroyAOIeQiPY5akiS1qcsThkKsQf036NVMWZNWoc13Uit0Sk6DYeUaUyyR3bL6uyB3bFn9vFrrSCqEXo5pFltaLld6T8e2Xj/V2XQ7GH/S/WnZw+7WIi8CvJuR0x4C62hrx6d1jcW1yeDKXbFXsj/JXti93QDs/qmXa/x9TMk6QHkn+1uBoWZrDyXnV2bzeSW4qfoxCgmME39nkcOK1hFPurYCc5xkXiVhqUxabyRKiVizRC+hTT9CfnIjh8=</latexit>

1 GeV<latexit sha1_base64="ChB6/euQ5r7mUt4iYKMzL+kYf8M=">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</latexit>

The STAR Collaboration, Nature (2017)• マグネター⌦<latexit sha1_base64="tyFqVA/aRQgCaum4DJ/yPVaqirc=">AAACaXichVG7TgJBFD2sb3wA2hBtiARjRQZD1FgZbexEkUcChOyuA67sK7sLCRJ/wMrOqJUmxhg/w8YfsOATDCUmNhZelk2MEvVOZubMmXvunJmRTFWxHcbaPmFoeGR0bHzCPzk1PRMIhmaztlG3ZJ6RDdWw8pJoc1XRecZRHJXnTYuLmqTynFTb7u3nGtyyFUM/cJomL2liVVcqiiw6RGWLuxqviuVglMWZG5FBkPBAFF6kjOA9ijiEARl1aODQ4RBWIcKmVkACDCZxJbSIswgp7j7HKfykrVMWpwyR2BqNVVoVPFanda+m7aplOkWlbpEyghh7YQ+sy57ZI3tlH7/Wark1el6aNEt9LTfLgbNw+v1flUazg6Mv1Z+eHVSw7npVyLvpMr1byH194+Sim97Yj7WW2C3rkP8b1mZPdAO98Sbf7fH9a/jpAxI/n3sQZFfiidV4ci8Z3dzyvmIcC1jEMr33GjaxgxQydO4xznGJK19HCAlhYb6fKvg8zRy+hRD9BFP5jAA=</latexit>

https://www.riken.jp/press/2020/20201005̲2/index.html

Brauner and Yamamoto, JHEP (2017)？

• 周期電磁場系
https://academist-cf.com/journal/?p=14730

Yamada and Yamamoto, PRD (2021)

CSLの普遍性
NG粒子

あらわな破れ（周期ポテンシャル）

表面項（ソリトンを安定化）

カイラル磁性体 [1]

マグノン

磁場

ジャロシンスキー・守谷
相互作用

回転する（磁場中の）QCD物質 [2,3]

ηʼ(π)
中間子

クォーク質量項

トポロジカル項

ソリトン[1] Togawa et al., PRL (2012)[2] Son and Stephanov, PRD (2008); Brauner and Yamamoto, JHEP (2017)[3] Huang, Nishimura and Yamamoto, JHEP (2018); Nishimura and Yamamoto, JHEP (2020)

非可換CSL
可換CSL

NG粒子

あらわな破れ

表面項

崩壊定数比

U(1)A

クォーク質量+QCD anomaly

トポロジカル項❌

クォーク質量+QCD anomaly

U 2 U(2)<latexit sha1_base64="64qCeOeB+lIEwxZWqUvCEfMH/A0=">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</latexit>

非可換CSL<latexit sha1_base64="a6IlgNT5jkd0E5k4H/jXbyGmqyc=">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</latexit>• 2フレーバの中間子： U = exp

✓

i⌘
f⌘

◆

⌃,

<latexit sha1_base64="2CM4tFBX2t44sOm7OD9e30/E5Ts=">AAACnXichVFNS9xQFD3GWnVq69huBBcNHRS76PgyiBVXggguSvFrHMHYIYl39GEmicmbQRvyB/wDLgqFFkop/Rntwo3uXPgTxKWCGxfeZAKllbY35N3zzrvnvvPeswNXRkqI8y6t+0HPw96+/sKjgcdPBotDT9civxU6VHV81w/XbSsiV3pUVVK5tB6EZDVtl2r27ly6XmtTGEnfW1UHAW02rW1PNqRjKabqxWlT0b7K+sQhbSWxSUEkXd/TTdprybZuvNLHG/XYDGQykWZSVvLyXSWpF0uiLLLQ7wMjByXksegXv8LEFnw4aKEJggfF2IWFiL8NGBAImNtEzFzISGbrhAQF1ra4irjCYnaXx22ebeSsx/O0Z5SpHd7F5T9kpY5RcSa+iStxLL6LC3H7115x1iP1csDZ7mgpqA8eDq/c/FfV5Kyw80v1T88KDUxnXiV7DzImPYXT0bffH12tzCyPxmPis7hk/5/EufjBJ/Da186XJVr+gAI/gPHndd8Ha5WyMVWuLE2WZmfyp+jDCF5gnO/7NWaxgEVUed+P+IkTnGrPtXntjfa2U6p15Zpn+C202h2YsKAx</latexit>

トポロジカル項✏⌘1⌃ 2 SU(2)• 非可換CSL=S2の自由度を持つ、パリティを破るソリトンによる結晶状態
自発的対称性の破れ： SU(2) ! U(1)<latexit sha1_base64="/H3HY90Wlg+nSs/zcBmBMZSPnDY=">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</latexit>(f⇡ /f⌘ )2カイラル摂動論
f⇡2 µ⌫
1 µ⌫†
Lkin =g tr(@µ ⌃@⌫ ⌃ ) + g @µ ⌘@⌫ ⌘42<latexit sha1_base64="ajsuWnd62F02LNA0eeTftgGSLfc=">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</latexit>

• 運動項

B
Lmass = tr(M U + M U † )2<latexit sha1_base64="+Favl53lzXGJ4GqXBSoXTfJs2GQ=">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</latexit>• クォーク質量項- Mが対角的なとき、SU(2)V対称
A
Lanom = (detU + detU † )2<latexit sha1_base64="DWrstgD7JEuKJ0uEPVM+TamROKM=">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</latexit>• QCDアノマリー項µ2B
Ltopo =
⌦ · r⌘
2
2⇡ f⌘<latexit sha1_base64="B3iAlR38H7rY7Xznd0MyB3z5EPo=">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</latexit>• トポロジカル項- CVEを中間子の自由度でマッチングした有効作用
Huang, Nishimura and Yamamoto, JHEP (2018); Nishimura and Yamamoto, JHEP (2020)- Cf) カイラルアノマリーを中性パイ中間子でマッチングした有効作用（π0→2γ）
Wess and Zumino, Phys. Lett. B (1971); Witten, Nucl. Phys. B (1983)

カイラル渦効果

⌦
スピン

⌦

運動量

スピン

jL =

運動量

µ2L
⌦
2
4⇡

µ2R
jR =
⌦
2
4⇡

左巻き

右巻き
<latexit sha1_base64="laf+UXso3ODhggvNsaEvRSubniY=">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</latexit>• 軸性カレント： j5 ⌘ jR

1 2
jL =
µ ⌦,
2
2⇡

Vilenkin, PRD (1979)(µR = µL = µ)• カイラル渦効果の輸送係数はカイラルアノマリーで決定される：
Son and Yamamoto, PRL (2012); Stephanov and Yin, PRL (2012)

1
2µ• 軸性カレント(アップ・ダウンクォーク)： j5 =
B⌦
2
Nc ⇡
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Landsteiner, Megias and Pena-Benitez, PRL (2011)

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S ：無次元化した角速度<latexit sha1_base64="S0rm6jvDtqMJ2WtlQ0XG3mIuQ3U=">AAACZHichVHLSsNAFD2Nr1qrrRZBEKRYKq7KRIqKq4Ibl33YB9RSkjjV0DQJSVqoxR/QreLClYKI+Blu/AEX/QFBXFZw48LbNCBa1DvMzJkz99w5MyObmmo7jHV9wsjo2PiEfzIwFZyeCYVn5wq20bQUnlcMzbBKsmRzTdV53lEdjZdMi0sNWeNFub7d3y+2uGWrhr7rtE1eaUgHulpTFckhKpOrhmMswdyIDgPRAzF4kTbCt9jDPgwoaKIBDh0OYQ0SbGpliGAwiaugQ5xFSHX3OY4RIG2TsjhlSMTWaTygVdljdVr3a9quWqFTNOoWKaOIsyd2x3rskd2zF/bxa62OW6PvpU2zPNBysxo6Wci9/6tq0Ozg8Ev1p2cHNWy6XlXybrpM/xbKQN86uujltrLxzgq7Zq/k/4p12QPdQG+9KTcZnr1EgD5A/Pncw6CwlhDXE8lMMpZKeV/hxyKWsUrvvYEUdpBGns7lOMUZzn3PQlCICPODVMHnaSL4FsLSJ66gido=</latexit>•先行研究Nishimura and Yamamoto (2020)との違い：ε 0✏hadron ⇠ 0.17<latexit sha1_base64="+s+pYvl/EOhm/P+jSPLoLgsONzY=">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</latexit>

Donogue, Golowich and Holstein (1992)✏CFL ⇠ 0.24
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Son and Stephanov PRD (2000)

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0<latexit sha1_base64="PFam5Coas2gloPo2ZU+mTatOe7I=">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</latexit>⌘ ソリトン<latexit sha1_base64="48UOsP05bg0ROr1G1zzxyVCS7uI=">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</latexit>

ダウンソリトン<latexit sha1_base64="3OuDDbHbpReBN3FySC/MhVabXVY=">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</latexit>⇡⇡<latexit sha1_base64="OXwHuTtSz3FhPOQXwfNLPe9vWA0=">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</latexit>

2⇡<latexit sha1_base64="vCvyKX+WiDhQdNZqMZbK5wbNcs0=">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</latexit>

0非可換ソリトン
3
SU(2)
⇥
U(1)
S
⇥ U(1)i 0⇠⇠=• 中間子場 U = ⌃e の配位空間： U(2) =Z2Z2<latexit sha1_base64="1f2ydOg10PymSxesLtJyQDPtsGE=">AAAC2XichVHLLgRBFL3d3u012EhsOiaEzaR6CGIlsbHEGMQ0k+5SM1PRr3TXTEKnF3Zia2FhRSIiPsPGD1jwB2JJYmPhTk+LV3A7XXXq3HtunaoyPYsHgpA7SW5qbmlta+9QOru6e3pTff2rgVv1KctT13L9ddMImMUdlhdcWGzd85lhmxZbM3fm6/m1GvMD7jorYtdjm7ZRdniJU0MgVUyJUPdtNR+NZcdVnbpOWdVLvkHDmM7FvC64zQL1vVAbjzBrG6JimupGVMxGymdhbmviX0ExlSYZEof6E2gJSEMSi27qAnTYBhcoVMEGBg4IxBYYEOBXAA0IeMhtQoicj4jHeQYRKKitYhXDCgPZHRzLuCokrIPres8gVlPcxcLfR6UKI+SWXJInckOuyAN5/bVXGPeoe9nF2WxomVfsPRzMvfyrsnEWUPlQ/elZQAlmYq8cvXsxUz8Fbehre8dPudnlkXCUnJFH9H9K7sg1nsCpPdPzJbZ8Ago+gPb9un+C1WxGm8pMLk2m52aSp2iHIRiGMbzvaZiDBViEPO57L4HUISlyQd6XD+TDRqksJZoB+BLy0Rv2frMp</latexit><latexit sha1_base64="t0n0Xo/Wzg+1LsPItSQSlV3lQQQ=">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</latexit>

北極： ⌃ = 12 , ei 0 = 1<latexit sha1_base64="WjTitsjOym2zzCSsIaDqLFzZM1o=">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</latexit>• ソリトン中心： ( 0 , 3 ) = (±⇡/2, ±⇡/2)<latexit sha1_base64="rsyl7XD3BxjfM5Utr36R36GPSI0=">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</latexit>• U(1)不変： ei✓⌧ ei⌧ ⇡/2 e i✓⌧ = ei⌧ ⇡/2<latexit sha1_base64="fxKv0MNN+rrh/OSrbL/1xxnX9vw=">AAAC3XichVE9S8NAGH4Tv6vWqovgEiwVF+u1ioogCC6OfvUDjIYkXvUwXyTXooaOLiKuDk4KIuLPcPEPOHRxF8cKLg6+SQOi1fqG3D33vO/z3nN3mmMwjxNSE8S29o7Oru6eWG9ff3wgMTiU9+yyq9Ocbhu2W9RUjxrMojnOuEGLjktVUzNoQTtYDvKFCnU9Zlub/Mih26a6Z7ES01WOlJI49GXXlGh1xw8Bq8p8n3JVkrlaVqarzdmAlh02lf3KTf4qjS1KrdRKIknSJAypGWQikIQoVu3ELciwCzboUAYTKFjAERuggoffFmSAgIPcNvjIuYhYmKdQhRhqy1hFsUJF9gDHPVxtRayF66CnF6p13MXA30WlBCnyRO5InTySe/JCPv7s5Yc9Ai9HOGsNLXWUgdORjfd/VSbOHPa/VC09cyjBfOiVoXcnZIJT6A195fiivrGwnvLHyTV5Rf9XpEYe8ARW5U2/WaPrlxDDB8j8vO5mkM+mM7Pp7NpMcmkheopuGIUxmMD7noMlWIFVyOG+z0K70C/ERUU8Ec/E80apKESaYfgW4sUnBna3Rg==</latexit>

3

3

3

3

S2
<latexit sha1_base64="nnPkcG7t+RIRMU+j8YH6nLhj5L0=">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</latexit>• 対称性の自発的破れ： SU(2) ! U(1)<latexit sha1_base64="WRHItD4AECFnmorG1EsN0W+jou4=">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</latexit><latexit sha1_base64="/sFOupL3SYiIVQdueGab6Jj8RYo=">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</latexit>2⇠SU(2)/U(1)S=
ドメインウォールのモジュライ：•<latexit sha1_base64="yYN7TSZM4ircH26qSYA513ax+jo=">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</latexit>

Nitta, Nucl. Phys.B (2015); Eto and Nitta, PRD (2015)

南極：⌃ =

12 , e i 0 =1

非可換vs可換
2• ポテンシャル山頂を登る必要あり
10• π中間子の勾配なし

-1

-2
2

• ポテンシャル山頂を登る必要なし

1

0

-1

-2

• π中間子の勾配あり• ε>0は勾配によるエネルギー増加を抑制ηʼCSL• ε=0, φ3=0のハミルトニアンと運動方程式
" ✓
◆2
1 d 0
H=C
+ (1
2 d⇣
<latexit sha1_base64="qjH8jkrM6Wwcxnann/1IkHmQXA8=">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</latexit>• 解析解<latexit sha1_base64="J7Awx1Tw1LrQ5cUihThRAULlyQw=">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</latexit><latexit sha1_base64="TtIFLH4LPqfMnfq1jhkxTAd51UE=">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</latexit>• 張力 M =

1
=
4tan
exp(⇣
0

Z 1

1

d⇣ H/C = 8

cos 0 )⇣0 )2⇡S

• 臨界値： Sc = 4/⇡<latexit sha1_base64="ckLCcHzWY6Xghjng3LsD9qMadPo=">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</latexit>• S>Scではドメインウォールの張力が負なので、それらが並んだCSLが安定<latexit sha1_base64="z/lVQHGYQySPlmKmA37ybUoLVUs=">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</latexit>

0 = 2am✓◆⇣,k + ⇡
k

d 0
S
d⇣

#

,

d2 0
= sin 02d⇣

ε=0, φ3 0
• ε=0, φ3 0のハミルトニアン<latexit sha1_base64="XUQe3h0ZJEFTjVQVfm1UdckoXkg=">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</latexit>

" ✓
◆2
H
1 1 d +
=
+ (1
C
2 2
d⇣

cos + )

<latexit sha1_base64="hkRoYq0rFFvzEFyEejV+7y6iMHM=">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</latexit>

± ⌘

0±

d +
S
d⇣

#

3

" ✓
◆2
1 1 d
+
+ (1
2 2
d⇣

cos

)

d
S
d⇣

#

φ は完全に分離しており、各々のハミルトニアンはφ0の半分<latexit sha1_base64="oQ6dK7uj2AXNjj6HmU9BHLRCz2E=">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</latexit>• φ+の解：+ = 4tan• 張力： M+ = 4<latexit sha1_base64="23EcH3+a55klojGryE6Wwv/Pq7s=">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</latexit>

1• φ-の解：= 4tan 1 exp (⇣• 張力： M

=4<latexit sha1_base64="YnqUC5J0n0QHzlpRUdk8gLfUvd0=">AAACpnichVHLShxBFD22eWjn4agbwU2RwTBZzFAtEkUQFDeuxNc4gm063W3NTGG/6K4Z1GZ+wB9w4UpBRPwMN9lkmYifELI04MZF7vQ0hESS3KLq3nvqnlunqpzIk4ni/LZP63/y9NnzgUH9xctXr4cKwyObSdiKXVF1Qy+Mtxw7EZ4MRFVJ5YmtKBa273ii5uwtdvdrbREnMgw21EEkdny7Eci6dG1FkFVYMKOmtMpsjk2x1Ix9puyg8yEtG50sE/tRh5meqKuSbh4KZbMyy7xV1s1YNprqnVUo8grPjD0OjDwoIreVsHABE7sI4aIFHwIBFMUebCQ0tmGAIyJsBylhMUUy2xfoQCdui6oEVdiE7tHaoGw7RwPKuz2TjO3SKR7NmJgME/wLv+R3/BO/4t/4w197pVmPrpYD8k6PKyJr6Ghs/f6/LJ+8QvMX65+aFeqYybRK0h5lSPcWbo/fPjy+W59dm0jf8jP+nfSf8lt+TTcI2j/c81WxdgKdPsD487kfB5uTFeN9ZXJ1qjg/m3/FAMbxBiV672nMYwkrqNK5F/iMr7jRStqyVtVqvVKtL+eM4jfTPv4Em1KhNA==</latexit>

exp (⇣⇣+ )⇡S<latexit sha1_base64="XBUswqLS/lTXfnumR+ovQbE7zxs=">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</latexit>• 臨界値： Sc = 4/⇡

⇣ )

⇡S

• 臨界値： Sc = 4/⇡<latexit sha1_base64="ckLCcHzWY6Xghjng3LsD9qMadPo=">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</latexit><latexit sha1_base64="ckLCcHzWY6Xghjng3LsD9qMadPo=">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</latexit>

S>4/πではアップ・ダウンCSL両方が生じた状態が最も安定な状態となる✓◆⇣ ⇣±,k + ⇡⇣± ：重心はもジュライ（並進のNG mode）± = 2amk<latexit sha1_base64="ijihHIj9pB4aKJsqJVDewQ+9Yqk=">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</latexit><latexit sha1_base64="NTKjM1+Ce7BE9+/DIPfKYuIrb70=">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</latexit>ηʼCSLとup/down CSLの関係
アップ間の距離はSで決定ダウン間の距離はSで決定

d<latexit sha1_base64="mtkF1XgDfUOOyDRWbSCrdEAgdbg=">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</latexit>

アップ・ダウン間の距離はモジュライηʼCSLはup/down CSLのd=0の特殊な状況！

φ 間の相互作用<latexit sha1_base64="iPWmG/sC7jIHPZ6KE9qUho2UG2A=">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</latexit>• εに依存するポテンシャル• ε>0=斥力

• ε<0=引力

V✏ =

✏
8

✓

d +
d⇣

◆2

✏
8

✓

d
d⇣

◆2

✏d +d
+
4 d⇣ d⇣ε 0,β=0での相図
ηCSL (Abelian CSL)QCD vacuum

up/down CSL(Non-abelian CSL)

フェロ・フェリ磁性• 磁場中のQCD物質におけるトポロジカル項

Son and Zhitnitsky, PRD (2004); Son and Stephanov, PRD (2008)

qu µB
qd µB
Ltop =
r +·B+r2
2
4⇡
4⇡<latexit sha1_base64="TUxfKq2IH0eL002qDp6D4QXu7P4=">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</latexit>·B• アップ・ダウンソリトンの磁化＝フェリ磁性<latexit sha1_base64="2rsnfVolOA7xI0RyHCbAXEorh9I=">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</latexit>

M+ =qu µ B
r +,
2
4⇡

M =

• ηのソリトンの磁化＝フェロ磁性<latexit sha1_base64="i/+6Saq267eqn96soMveF32dTNU=">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</latexit>

M⌘ =

1 eµB
r
0
2
3 4⇡

qd µ Br
2
4⇡

QCDアノマリーの効果⇣<latexit sha1_base64="p+M2JA437FrLLs51BA8tvsxNFHk=">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</latexit>• QCDアノマリーの効果を含めたポテンシャル C =p

A2 + (4mB)2 , tan = A/(4mB)<latexit sha1_base64="VhvDdYLcjv6/Fyih6cLHLgT2M5Q=">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</latexit>

V = sin (1cos2 0 ) + cos (1cos 0 cos 3 )QCDアノマリーの効果が大きくなるとtriplet mesonの方向がフラットになるので
φ3方向のドメインウォールが抑制される。

⌘

• NACSL (β=0, ε>0)：• NACSL (β 0, ε>0)：アップとダウン間の距離を近づけてηCSLにしようとする

2

2

✏ = 0.1<latexit sha1_base64="yhxUDgUkG0XWhNysYxzhI+Laix0=">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</latexit>✏ = 0.1<latexit sha1_base64="yhxUDgUkG0XWhNysYxzhI+Laix0=">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</latexit>✏ = 0.2✏ = 0.2✏ = 0.5✏ = 0.5





5

10

実線（点線）＝φ0(φ3)

15

5

10

実線（点線）＝φ+(φ-)

15まとめと展望• 「回転するバリオン物質の相構造」を考えた• 基底状態は「非可換カイラルソリトン格子」- 非可換CSL=S2の自由度を持ち、パリティを破るソリトンによる結晶状態• そのソリトンは「反強磁性アイソスピン鎖」を構成している• 反強磁性アイソスピン鎖は「フェリ磁性」を示す• 相構造のA（QCDアノマリーの強さ）とεの依存性• 3フレーバーへの拡張