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Progress of Theoretical Physics

Re-Structuring Method for the Negative Sign Problem in Quantum Spin Systems

Tomo Munehisa, Yasuko Munehisa

Published Aug 1, 1994• 0 citations
Publisher

Abstract

We present detailed discussion on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states in the path integral formulation. We observed our approach brings remarkable improvement in the negative sign problem when applied to one-dimensional quantum spin-1/2 system with next-nearest-neighbor interactions. In this paper we add some descriptions on our method and show results from analyses by the exact diagonalization and by the transfer matrix method of the system on a small chain. These results also indicate that our method works quite effectively.

DOI
10.1143/ptp.92.309

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We present detailed discussion on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states in the path integral formulation. We observed our approach brings remarkable improvement in the negative sign problem when applied to one-dimensional quantum spin-1/2 system with next-nearest-neighbor interactions. In this paper we add some descriptions on our method and show results from analyses by the exact diagonalization and by the transfer matrix method of the system on a small chain. These results also indicate that our method works quite effectively.
We present detailed discussion on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states in the path integral formulation. We observed our approach brings remarkable improvement in the negative sign problem when applied to one-dimensional quantum spin-1/2 system with next-nearest-neighbor interactions. In this paper we add some descriptions on our method and show results from analyses by the exact diagonalization and by the transfer matrix method of the system on a small chain. These results also indicate that our method works quite effectively.
We present a quantum-number projection technique which enables us to exactly treat spin, momentum, and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization-group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next-nearest-neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.
We apply the transfer-matrix density matrix renormalization group (DMRG) approach to frustrated quantum spin chains, down to T=0.025KT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.025\mathrm{K}T=0.025K in the thermodynamic limit. The incommensurability problem of exact diagonalization and the negative sign problem of quantum Monte Carlo vanish completely. For illustration, we give results for chains with next-nearest-neighbor frustration and for the delta chain, which has been a testbed for many thermodynamic methods. The DMRG approach proves to be an extremely powerful method for the old problem of the thermodynamics of frustrated systems.