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TT: Fachverband Tiefe Temperaturen

TT 56: Focus Session: Recent Progresses in Criticality in the Presence of Boundaries and Defects II (joint session DY/TT)

TT 56.1: Invited Talk

Wednesday, March 20, 2024, 15:00–15:30, A 151

Conformal boundary conditions of symmetric quantum critical states — •Long Zhang — University of Chinese Academy of Sciences, Beijing 100190, China

Some quantum critical states cannot be smoothly deformed into each other without either crossing some multicritical points or explicitly breaking certain symmetries even if they belong to the same universality class. This brings up the notion of ``symmetry-enriched'' quantum criticality. While recent works in the literature focused on critical states with robust degenerate edge modes, we propose that the conformal boundary condition (b.c.) is a more generic characteristic of such quantum critical states. In the first part of this talk, we show that in two families of quantum spin chains, which generalize the Ising and the three-state Potts models, the quantum critical point between a symmetry-protected topological phase and a symmetry-breaking order realizes a conformal b.c. distinct from the simple Ising and Potts chains at both the physical and the entangling boundaries. Furthermore, we argue that the conformal b.c. can be derived from the bulk effective field theory, which realizes a novel bulk-boundary correspondence in symmetry-enriched quantum critical states. In the second part, we will show the effect of finite-entanglement scaling of matrix-product states on their conformal b.c. at both the physical and the entangling boundaries.

Keywords: quantum criticality; spin chains; symmetry-protected topological states; conformal boundary condition; entanglement spectrum