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キーワード:
Quantum Physics, quant-ph, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
要旨:
This work is concerned with thermal quantum states of Hamiltonians on spin
and fermionic lattice systems with short range interactions. We provide results
leading to a local definition of temperature, thereby extending the notion of
"intensivity of temperature" to interacting quantum models. More precisely, we
derive a perturbation formula for thermal states. The influence of the
perturbation is exactly given in terms of a generalized covariance. For this
covariance, we prove exponential clustering of correlations above a universal
critical temperature that upper bounds physical critical temperatures such as
the Curie temperature. As a corollary, we obtain that above the critical
temperature, thermal states are stable against distant Hamiltonian
perturbations. Moreover, our results imply that above the critical temperature,
local expectation values can be approximated efficiently in the error and the
system size.
