Conformal invariance in non-Hermitian free-fermion critical systems

Chang-Tse Hsieh^1,2,3*

¹Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan
²Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, Taiwan
³Center for Quantum Science and Engineering, National Taiwan University, Taipei, Taiwan
⁴Center for Interdisciplinary Theoretical and Mathematical Sciences, RIKEN, Wako, Japan

* Presenter:Chang-Tse Hsieh, email:cthsieh@phys.ntu.edu.tw

Conformal invariance typically emerges in critical systems where the correlation length diverges, which is generally the case for Hermitian quantum systems without a spectral gap (in the thermodynamic limit). However, the situation becomes more subtle when Hermiticity is broken. In this talk, I will discuss when a non-Hermitian gapless quantum system can exhibit conformal invariance, focusing on free fermions in 1+1 dimensions. Certain universal characteristics of such systems—including a negative central charge and logarithmic couplings associated with indecomposable Jordan cell structures in the spectrum—are identified and computed in both continuum field theory and lattice formulations.

Keywords: non-Hermitian quantum physics, critical phenomena, conformal field theory, exceptional point