Identification of the phase of a many-body quantum system is an important but in general hard problem in condensed matter physics. Quite often, symmetries play an essential role and a notable principle is the Lieb-Schultz-Mattis (LSM) theorem and its generalizations, stating that under certain conditions on symmetries and filling fractions the system cannot be a trivial symmetric insulator — being “ingappable”. The famous Haldane conjecture can be embedded into such an LSM-type ingappability in SU(2) spin chains with a lattice translational symmetry. This SU(2) ingappability implies a classification of critical theories of spin chains according to a connectedness of conformal field theories (CFT) defined by renormalization-group flows among them. In this talk, we will discuss about the generalization to SU(N) spin systems in arbitrary dimensions. Due to N>2, ingappabilities cannot fully characterize the critical-phase classification. We propose a refinement given by quantum symmetry anomaly and ’t Hooft anomaly matching. The SU(N) CFTs are classified into N classes by their distinct mixed anomaly between SU(N) and translational symmetry at low energy, a one-to-one correspondence with the Young-tableaux numbers mod N per unit cell. A further generalization to higher dimensions needs a tilted boundary condition which realizes a dimension reduction with a well-defined thermodynamic limit.
Condensed Matter Seminar: Yuan Yao, Tokyo,”Symmetry-protected critical phases in SU(N) spin systems motivated by ingappabilities”
Thursday, October 24, 2019 - 1:00pm to 2:00pm
Sloane Physics Laboratory (SPL), Room 52
217 Prospect StreetNew Haven, CT 06511