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arXiv:hep-lat/9810001 · Nuclear Physics B - Proceedings Supplements

Correlation functions from quantum cluster algorithms: application to U(1) quantum spin and quantum link models

A. Tsapalis

Published Mar 1, 1999• 0 citations
arXivHTMLPDF
DOI
10.1016/s0920-5632(99)85190-1

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Quantum Link Models with dynamical matter coupled to spin-12 U(1)\frac{1}{2} \ \rm U(1)21​ U(1) gauge fields in $d=2+1 $ and 3+13+13+1 can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies (Ge,Go)=(d, −d)(G_e,G_o) = (d,\ -d)(Ge​,Go​)=(d, −d), where ddd is the spatial dimension and eee and ooo are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.
Quantum Link Models with dynamical matter coupled to spin-12 U(1)\frac{1}{2} \ \rm U(1)21​ U(1) gauge fields in $d=2+1 $ and 3+13+13+1 can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies (Ge,Go)=(d, −d)(G_e,G_o) = (d,\ -d)(Ge​,Go​)=(d, −d), where ddd is the spatial dimension and eee and ooo are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.