A second-quantized red herring in full configuration-interaction Monte Carlo

Details A second-quantized red herring in full configuration-interaction Monte Carlo A second-quantized red herring in full configuration-interaction Monte Carlo

2012-02-02

arxiv.org/abs/1202.0525v1

Physics

Computational Physics

2.5 pages, 2 figures

Scientific paper

Full configuration-interaction quantum Monte Carlo (FCI-QMC) is a Monte Carlo method that allows for exact solution of the ground state of fermionic Hamiltonians (albeit at exponential cost). FCI-QMC involves stochastic projection to the ground state, working in a basis of second- quantized determinants. While a Fermi sign problem still exists within FCI-QMC, it has been suggested that even without annihilation the sign problem is fundamentally distinct from that of more standard techniques such as diffusion Monte Carlo, as a result of working in determinant space. Furthermore, it is widely believed that this distinction is at least partially responsible for the success of FCI-QMC in mitigating the sign problem. In this paper, we show that second quantization is a red herring; the sign problem of FCI-QMC comes from the conventional instability to a bosonic ground state, and in fact FCI-QMC without annihilation can be equated step-by-step to a first-quantized algorithm where anti-symmetry comes only from initial conditions.

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