无限费米子晶格系统中KMS态的局域性
Locality of KMS states for infinite fermionic lattice systems
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中文总结 AI 辅助
本研究针对无限费米子晶格系统，利用量子信念传播与Lieb-Robinson界，证明在广延扰动下，指数衰减与局域不可区分性可导出拉伸指数衰减，并建立相关性与局域性原理间的联系。
中文摘要 AI 辅助
我们研究了无限费米子晶格的热平衡态如何响应哈密顿量的扰动。我们的主要结果涉及对选定KMS态的广延扰动。我们证明，在广延扰动下，指数衰减的相关性和指数局域不可区分性会导致扰动态的 stretched-exponential 相关性衰减。初始态和扰动态都不需要是唯一的，从而允许在相共存存在的情况下研究稳定性。我们的方法使用量子信念传播（QBP），我们直接在底层 $C^*$-代数上建立该方法。将QBP与Lieb--Robinson界相结合，我们展示了相关性衰减、局域扰动局域地扰动的原理以及局域不可区分性之间的蕴含关系，从而在所述衰减、支撑和均匀性假设下，为迹态的扰动闭合了这一循环。对于均匀聚类条件下的广延扰动，我们还获得了局域平衡期望的可微路径，并以其变化量线性地受扰动的相互作用范数约束。
英文摘要
We study how thermal equilibrium states of infinite fermionic lattices respond to perturbations of the Hamiltonian. Our main result concerns extensive perturbations of a chosen KMS state. We show that exponential decay of correlations and exponential local indistinguishability under the extensive perturbation yield stretched-exponential decay of correlations for the perturbed state. Neither the initial nor the perturbed state is required to be unique, allowing stability to be studied in the presence of phase coexistence. Our approach uses Quantum Belief Propagation (QBP), which we establish directly on the underlying $C^*$-algebra. Combining QBP with Lieb--Robinson bounds, we show implications between decay of correlations, the principle that local perturbations perturb locally, and local indistinguishability, closing the cycle for perturbations of the tracial state under the stated decay, support and uniformity assumptions. For extensive perturbations under uniform clustering conditions, we also obtain a differentiable path of local equilibrium expectations and bound their change linearly in the interaction norm of the perturbation.
发表机构
- Fachbereich Mathematik, Universität Tübingen（蒂宾根大学数学系）
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