SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains

Abstract

We construct a class of conformal boundary states in the $\mathrm{SU}(n{)}_1$ Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding $\mathrm{Spin}(n{)}_2\subset \mathrm{SU}(n{)}_1$. These boundary states are beyond the standard Cardy construction and possess $\mathrm{SO}(n)$ symmetry. The $\mathrm{SU}(n)$ Uimin-Lai-Sutherland (ULS) spin chains, which realize the $\mathrm{SU}(n{)}_1$ WZW model on the lattice, allow us to identify these boundary states as the ground states of the $\mathrm{SO}(n)$ Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the $\mathrm{SU}(n)$ ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

24 pages, 4 figures

References in corpus (18)

• What is an integrable quench?
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• AdS/dCFT one-point functions of the SU(3) sector
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
• Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories
• Infinite Matrix Product States for long range SU(N) spin models
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain
• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Quantum many-body scars in spin models with multibody interactions
• Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: $\mathrm{SO}(n)$ spin chains
• Derivations for the MPS overlap formulas of rational spin chains
• Impurity screening by defects in (1+1)$d$ quantum critical systems
• Exact g-function without strings
• SO(n) AKLT Chains as Symmetry Protected Topological Quantum Ground States
• Exact overlaps for "all" integrable matrix product states of rational spin chains