Non-Hermitian fixed points
Relaxing Hermiticity changes which critical theories can be realized and how their universal data are defined. I study complex fixed points in the bulk and non-unitary boundaries and interfaces, including interfaces embedded in otherwise unitary theories. Connecting explicit lattice constructions with conformal spectra and consistency conditions helps identify which familiar constraints survive beyond unitarity and where new structures are needed.
Papers
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Exactly solvable non-unitary conformal interfaces in unitary CFTs
Preprint · arXiv:2606.32035 (2026)
We construct exactly solvable lattice interfaces that preserve conformal symmetry while introducing non-unitarity into an otherwise unitary bulk theory. Matching the lattice and CFT descriptions requires independent incoming and outgoing boundary states with a biorthogonal pairing, and yields a non-unitary generalization of Cardy's consistency condition. The effective central charge governing interface entanglement can be complex; in a subclass where it stays real, it can grow without bound.
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Reclaiming the Lost Conformality in a Non-Hermitian Quantum 5-State Potts Model
Physical Review Letters 133, 076504 (2024)
Adding a non-Hermitian interaction to the quantum five-state Potts chain exposes a conjugate pair of complex critical points associated with its weakly first-order transition. We identify conformal towers in the lattice spectrum and extract scaling dimensions and operator product expansion coefficients. This provides a microscopic realization of complex CFTs and direct access to their conformal data.
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Boundary criticality of complex conformal field theory: A case study in the non-Hermitian 5-state Potts model
SciPost Physics 19, 164 (2025)
We identify free, fixed, and mixed conformal boundary conditions in the non-Hermitian five-state Potts chain at its complex bulk fixed point. The spectra of open chains organize into conformal towers that reveal the boundary operator content. Kramers–Wannier duality relates different boundary conditions, extending the study of complex CFTs from bulk conformal data to boundary critical phenomena.