Variational-Correlations Approach to Quantum Many-body Problems
- URL: http://arxiv.org/abs/2001.06510v1
- Date: Fri, 17 Jan 2020 19:52:54 GMT
- Title: Variational-Correlations Approach to Quantum Many-body Problems
- Authors: Arbel Haim, Richard Kueng, Gil Refael
- Abstract summary: We investigate an approach for studying the ground state of a quantum many-body Hamiltonian.
The challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix.
We demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result.
- Score: 1.9336815376402714
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate an approach for studying the ground state of a quantum
many-body Hamiltonian that is based on treating the correlation functions as
variational parameters. In this approach, the challenge set by the
exponentially-large Hilbert space is circumvented by approximating the
positivity of the density matrix, order-by-order, in a way that keeps track of
a limited set of correlation functions. In particular, the density-matrix
description is replaced by a correlation matrix whose dimension is kept linear
in system size, to all orders of the approximation. Unlike the conventional
variational principle which provides an upper bound on the ground-state energy,
in this approach one obtains a lower bound instead. By treating several
one-dimensional spin $1/2$ Hamiltonians, we demonstrate the ability of this
approach to produce long-range correlations, and a ground-state energy that
converges to the exact result. Possible extensions, including to higher-excited
states are discussed.
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