Anomalies and unusual stability of multicomponent Luttinger liquids in Zn×Zn spin chains
Anomalies and unusual stability of multicomponent Luttinger liquids in Zn×Zn spin chains
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Zn-Zn 自旋链中多组分 Luttinger 液体的异常和异常稳定性
DOI：
10.1103/physrevb.104.045151
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发表时间：
2021
影响因子：
3.7
通讯作者：
Barkeshli, Maissam
中科院分区：
文献类型：
--
作者：
Alavirad, Yahya;Barkeshli, Maissam
我们研究了平移不变自旋链，其中每个单元格包含一个内部对称的状态投影表示，推广了自旋-1/2 XYZ链。这种自旋链具有广义的Lieb-Schultz-Mattis （LSM）约束，我们证明了某些组分Luttinger液体具有满足这些LSM约束的正确异常。因为，使用数值和解析方法，我们发现这种具有最近邻相互作用的自旋链在广泛的微观参数范围内似乎是无间隙的，并且由双组分共形不变Luttinger液体描述。这意味着只有在离散的微观对称中才会出现守恒的U(1)电荷。值得注意的是，尽管在场论中明显存在对称性允许的相关算子，但系统在异常大的参数范围内仍然保持无间隙。这表明，要么这些自旋链隐藏着以前未发现的守恒量，要么由于晶格哈密顿量的挫折效应，场论的参数只是不寻常。我们认为，在(1)forodd的对称链和(2)all的对称链中预计会出现类似的特征。最后，我们提出了具有这种LSM异常的场论的最小中心电荷的下界增长的可能性。
We study translationally invariant spin chains where each unit cell contains an-state projective representation of ainternal symmetry, generalizing the spin-1/2 XYZ chain. Such spin chains possess a generalized Lieb-Schultz-Mattis (LSM) constraint, and we demonstrate that certain-component Luttinger liquids possess the correct anomalies to satisfy these LSM constraints. For, using both numerical and analytical approaches, we find that such spin chains with nearest-neighbor interactions appear to be gapless for a wide range of microscopic parameters and described by a two-component conformally invariant Luttinger liquid. This implies the emergence ofconserved U(1) charges from only discrete microscopic symmetries. Remarkably, the system remains gapless for an unusually large parameter regime despite the apparent existence of symmetry-allowed relevant operators in the field theory. This suggests that either these spin chains have hidden conserved quantities not previously identified, or the parameters of the field theory are simply unusual due to frustration effects of the lattice Hamiltonian. We argue that similar features are expected to occur in (1)symmetric chains forodd and (2)symmetric chains for all. Finally, we suggest the possibility of a lower bound growing withon the minimum central charge of field theories that possess such LSM anomalies.