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I discuss a class of translationally invariant spin chains where each unit cell contains an nstate projective representation of a $\mathbb{Z}_n\times\mathbb{Z}_n$ internal symmetry, generalizing the spin1/2 XYZ chain. Such spin chains possess a generalized LiebSchulzMattis (LSM) constraint. We demonstrate that certain (n1)component Luttinger liquids possess the correct anomalies to satisfy these LSM constraints. For n=3, using both numerical and analytical approaches, we find that such spin chains with nearestneighbor interactions appear to be gapless for a wide range of microscopic parameters and described by a twocomponent conformally invariant Luttinger liquid. This implies the emergence of (n1) conserved U(1) charges from only discrete microscopic symmetries. Remarkably, the system remains gapless for an unnaturally large parameter regime despite the apparent existence of symmetryallowed 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 unnatural due to the frustration effects of the lattice Hamiltonian. We argue that similar features are expected to occur in: (1) $\mathbb{Z}_n\times\mathbb{Z}_n$ symmetric chains for n odd, and (2) $\mathbb{S}_n\times\mathbb{Z}_n$ symmetric chains for all n>2. Finally, we suggest the possibility of a lower bound growing with n on the minimum central charge of field theories that possess such LSM anomalies.
\n\nSPEAKER: Yayha Alavirad, University of Maryland, College Park 190 ESB false
Special ICMT Seminar: : Anomalies and unnatural stability of multicomponent Luttinger liquids in : Anomalies and unnatural stability of multicomponent Luttinger liquids in Z_n X Z_n spin chains spin chains
Speaker 
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Yayha Alavirad, University of Maryland, College Park 

Date:  11/19/2019 
Time:  11 a.m. 
Location:  190 ESB 
Sponsor:  The Institute for Condensed Matter Theory 
Event Type:  Seminar/Symposium 
I discuss a class of translationally invariant spin chains where each unit cell contains an nstate projective representation of a $\mathbb{Z}_n\times\mathbb{Z}_n$ internal symmetry, generalizing the spin1/2 XYZ chain. Such spin chains possess a generalized LiebSchulzMattis (LSM) constraint. We demonstrate that certain (n1)component Luttinger liquids possess the correct anomalies to satisfy these LSM constraints. For n=3, using both numerical and analytical approaches, we find that such spin chains with nearestneighbor interactions appear to be gapless for a wide range of microscopic parameters and described by a twocomponent conformally invariant Luttinger liquid. This implies the emergence of (n1) conserved U(1) charges from only discrete microscopic symmetries. Remarkably, the system remains gapless for an unnaturally large parameter regime despite the apparent existence of symmetryallowed 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 unnatural due to the frustration effects of the lattice Hamiltonian. We argue that similar features are expected to occur in: (1) $\mathbb{Z}_n\times\mathbb{Z}_n$ symmetric chains for n odd, and (2) $\mathbb{S}_n\times\mathbb{Z}_n$ symmetric chains for all n>2. Finally, we suggest the possibility of a lower bound growing with n on the minimum central charge of field theories that possess such LSM anomalies.

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