热力学极限下的绝热定理：体域中存在能隙的系统
Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk
AI总结：
本研究针对扩展费米子系统，仅假设体域存在谱能隙，证明了广义超绝热定理，同时验证该定理在有限系统体域中也成立，误差衰减快于系统尺寸的任意逆幂次。
摘要：
我们证明了扩展费米子系统的广义超绝热定理，该定理仅假设系统在体域中存在谱能隙。更确切地说，我们假设无限系统具有唯一基态，且对应的GNS哈密顿量在其零本征值之上存在谱能隙。此外，我们表明类似的绝热定理在有限系统的体域中同样成立，其误差的消失速度快于系统尺寸的任意逆幂次，尽管对应的有限体积哈密顿量不一定具有谱能隙。
英文摘要：
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite volume Hamiltonians need not have a spectral gap.
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