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- W2466260079 abstract "We consider the problem of determining the energy distribution of quantum states that satisfy exponential decay of correlation and product states, with respect to a quantum local hamiltonian on a spin lattice. For a quantum state on a $D$-dimensional lattice that has correlation length $sigma$ and has average energy $e$ with respect to a given local hamiltonian (with $n$ local terms, each of which has norm at most $1$), we show that the overlap of this state with eigenspace of energy $f$ is at most $exp(-((e-f)^2sigma)^{frac{1}{D+1}}/n^{frac{1}{D+1}}Dsigma)$. This bound holds whenever $|e-f|>2^{D}sqrt{nsigma}$. Thus, on a one dimensional lattice, the tail of the energy distribution decays exponentially with the energy. For product states, we improve above result to obtain a Gaussian decay in energy, even for quantum spin systems without an underlying lattice structure. Given a product state on a collection of spins which has average energy $e$ with respect to a local hamiltonian (with $n$ local terms and each local term overlapping with at most $m$ other local terms), we show that the overlap of this state with eigenspace of energy $f$ is at most $exp(-(e-f)^2/nm^2)$. This bound holds whenever $|e-f|>msqrt{n}$." @default.
- W2466260079 created "2016-07-22" @default.
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- W2466260079 date "2015-08-31" @default.
- W2466260079 modified "2023-09-27" @default.
- W2466260079 title "A Chernoff-type bound for local hamiltonian systems on quantum lattice" @default.
- W2466260079 hasPublicationYear "2015" @default.
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