We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.

Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme / Carleo, G.; Becca, F.; Moroni, S.; Baroni, S.. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 82:4(2010), pp. 046710.1-046710.10. [10.1103/PhysRevE.82.046710]

Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme

Carleo, G.;Becca, F.;Moroni, S.;Baroni, S.
2010-01-01

Abstract

We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.
2010
82
4
1
10
046710
http://link.aps.org/doi/10.1103/PhysRevE.82.046710
https://arxiv.org/abs/1003.3696
Carleo, G.; Becca, F.; Moroni, S.; Baroni, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13521
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