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Computer Physics Communications

The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies

Stephan A. Baeurle

Published Jun 30, 2003• 8 citations
Publisher
DOI
10.1016/s0010-4655(03)00284-4

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We report on the specific features of the sign problem in the classical auxiliary field methodology and the strategies employed for its alleviation. In particular, we focus on a new technique based on the method of Gaussian equivalent representation of Efimov and Nogovitsin [Physica (Amsterdam) 234A, 506 (1996)]] with which we could ameliorate the convergence properties significantly. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach.

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We explore a novel and straightforward solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method applied to many-body systems for more than a decade. We present a solution to the sign problem that has plagued the Auxiliary-field Monte Carlo (AFMC) method for more than a decade and report a breakthrough where excellent agreement between AFMC and exact CI calculations for fully realistic nuclear applications is achieved. This result offers the capability, unmatched by other methods, to achieve exact solutions for large-scale quantum many-body systems.
Frustrated spin systems generically suffer from the negative sign problem inherent in Monte Carlo methods. Since the severity of this problem is formulation dependent, optimization strategies can be put forward. We introduce a phase pinning approach in the realm of the auxiliary field quantum Monte Carlo algorithm. If we can find an antiunitary operator that commutes with the one-body Hamiltonian coupled to the auxiliary field, then the phase of the action is pinned to 0 and $\ensuremath{\pi}$. For generalized Kitaev models, we can successfully apply this strategy and observe a remarkable improvement of the average sign. We use this method to study the thermodynamical and dynamical properties of the Kitaev-Heisenberg model down to temperatures corresponding to half of the exchange coupling constant. Our dynamical data reveal finite temperature properties of ordered and spin-liquid phases inherent in this model.
We report on the specific features of the sign problem in the classical auxiliary field methodology and the strategies employed for its alleviation. In particular, we focus on a new technique based on the method of Gaussian equivalent representation of Efimov and Nogovitsin [Physica (Amsterdam) 234A, 506 (1996)]] with which we could ameliorate the convergence properties significantly. We believe that this technique can also provide an interesting possibility to reduce the sign problem of other methods of computer simulation based on a functional integral approach.