874 research outputs found
Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
We show that the two recently proposed methods to compute Renyi entanglement
entropies in the realm of determinant quantum Monte Carlo methods for fermions
are in principle equivalent, but differ in sampling strategies. The analogy
allows to formulate a numerically stable calculation of the entanglement
spectrum at strong coupling. We demonstrate the approach by studying static and
dynamical properties of the entanglement hamiltonian across the interaction
driven quantum phase transition between a topological insulator and quantum
antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited
to fermion systems and can readily be adapted to world-line based simulations
of bosonic systems.Comment: 8 pages, 5 figure
Efficient calculation of imaginary time displaced correlation functions in the projector auxiliary field quantum Monte-Carlo algorithm
The calculation of imaginary time displaced correlation functions with the
auxiliary field projector quantum Monte-Carlo algorithm provides valuable
insight (such as spin and charge gaps) in the model under consideration. One of
the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189
(1996).] have proposed a numerically stable method to compute those quantities.
Although precise this method is expensive in CPU time. Here, we present an
alternative approach which is an order of magnitude quicker, just as precise,
and very simple to implement. The method is based on the observation that for a
given auxiliary field the equal time Green function matrix, , is a
projector: .Comment: 4 papes, 1 figure in eps forma
Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
In numerical simulations, spontaneously broken symmetry is often detected by
computing two-point correlation functions of the appropriate local order
parameter. This approach, however, computes the square of the local order
parameter, and so when it is {\it small}, very large system sizes at high
precisions are required to obtain reliable results. Alternatively, one can pin
the order by introducing a local symmetry breaking field, and then measure the
induced local order parameter infinitely far from the pinning center. The
method is tested here at length for the Hubbard model on honeycomb lattice,
within the realm of the projective auxiliary field quantum Monte Carlo
algorithm. With our enhanced resolution we find a direct and continuous quantum
phase transition between the semi-metallic and the insulating antiferromagnetic
states with increase of the interaction. The single particle gap in units of
the Hubbard tracks the staggered magnetization. An excellent data collapse
is obtained by finite size scaling, with the values of the critical exponents
in accord with the Gross-Neveu universality class of the transition.Comment: 7 pages, 6 figures, Published versio
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