非厄米狄拉克费米子的平衡热力学：热响应与磁响应
Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses
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中文总结 AI 辅助
该研究建立了磁场中实谱非厄米狄拉克费米子的平衡热力学标度关系，通过相似变换实现非厄米系统到厄米模型的映射，揭示了不同条件下的热与磁响应规律，为非厄米量子物质研究提供了热力学框架。
中文摘要 AI 辅助
我们建立了磁场中实谱非厄米狄拉克费米子平衡热力学的标度关系。假设系统相对于拟厄米哈密顿量达到热平衡，通过相似变换可将相同外场下的该系统映射为具有约化速度的厄米狄拉克模型，同时朗道能级谱也可表示为约化有效磁场的形式。该结构给出了不同热力学系综下化学势、熵、热容及轨道磁响应的标度关系。在固定投影填充因子（PFF）时，自洽化学势遵循压缩的朗道能级梯级，正则热力学函数为经重标度的厄米响应；在固定化学势时，朗道能级交叉产生由相同谱压缩支配的振荡热响应与磁响应。固定PFF下的准静态非厄米形变进一步给出绝热温度标度。更广泛而言，这些结果为实谱非厄米量子物质建立了热力学框架，并为在同一形式体系中纳入相互作用与无序效应提供了起点。
英文摘要
We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.
