6/30/2022 Quantum Matter in Mathematics and Physics

Speaker: Linhao Li (ISSP, U Tokyo)

Title:  Boundary conditions and LSM anomalies of conformal field
theories in 1+1 dimensions

Abstract: In this talk, we will study a relationship between
conformally invariant boundary conditions and anomalies of conformal
field theories (CFTs) in 1+1 dimensions. For a given CFT with a global
symmetry, we consider symmetric gapping potentials which are relevant
perturbations to the CFT. If a gapping potential is introduced only in
a subregion of the system, it provides a certain boundary condition to
the CFT. From this equivalence, if there exists a Cardy boundary state
which is invariant under a symmetry, then the CFT can be gapped with a
unique ground state by adding the corresponding gapping potential.
This means that the symmetry of the CFT is anomaly free. Using this
approach, we will systematically deduce the anomaly-free conditions
for various types of CFTs with several different symmetries.  When the
symmetry of the CFT is anomalous, it implies a Lieb-Schultz-Mattis
type ingappability of the system. Our results are consistent with,
where available, known results in the literature. Moreover, we extend
the discussion to other symmetries including spin groups and
generalized time-reversal symmetries. As an application, we propose 1d
LSM theorem involving magnetic space group symmetries on the lattice.
The extended LSM theorems apply to systems with a broader class of
spin interactions, such as Dzyaloshinskii-Moriya interactions and
chiral three-spin interactions.

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