Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses

Research Question and Approach

This study investigates the equilibrium thermodynamic properties of non-Hermitian (NH) Dirac fermions in a magnetic field, using monolayer graphene as a primary model. While NH physics is often associated with nonequilibrium dynamics, the authors focus on a stationary, real-spectrum regime where the system can be mapped to a Hermitian representative via a similarity transformation. The researchers analyze how a non-Hermitian deformation—which renormalizes the Dirac velocity—affects caloric and magnetic responses, such as heat capacity, entropy, and orbital magnetic moments, under different thermodynamic constraints.

The central contribution is the derivation of scaling relations that relate NH thermodynamic observables to their Hermitian counterparts. The NH deformation uniformly compresses the Landau-level spectrum by a factor determined by the non-Hermitian parameter. This spectral compression is equivalent to replacing the physical magnetic field with an effective magnetic field.

At a fixed projected filling factor (PFF), the chemical potential and heat capacity follow the compressed ladder of Landau levels, effectively rescaling the Hermitian response. At a fixed chemical potential, the Landau-level crossings generate oscillatory caloric and magnetic responses that are shifted in field according to the same spectral compression. The authors also demonstrate that the total orbital magnetic moment and the moment per particle scale differently due to the interplay between the compressed energy spectrum and the physical orbital degeneracy set by the applied magnetic field.

This work provides a rigorous thermodynamic framework for real-spectrum non-Hermitian quantum matter. By establishing that these systems can be treated using a modified Gibbs ensemble, the authors offer a systematic way to predict how gain-loss imbalances or nonreciprocal couplings influence measurable quantities like heat capacity and magnetic susceptibility. This framework serves as a foundation for future studies incorporating electron-electron interactions and disorder, which are essential for understanding realistic experimental platforms.