1,009 research outputs found
A new, globally convergent Riemannian conjugate gradient method
This article deals with the conjugate gradient method on a Riemannian
manifold with interest in global convergence analysis. The existing conjugate
gradient algorithms on a manifold endowed with a vector transport need the
assumption that the vector transport does not increase the norm of tangent
vectors, in order to confirm that generated sequences have a global convergence
property. In this article, the notion of a scaled vector transport is
introduced to improve the algorithm so that the generated sequences may have a
global convergence property under a relaxed assumption. In the proposed
algorithm, the transported vector is rescaled in case its norm has increased
during the transport. The global convergence is theoretically proved and
numerically observed with examples. In fact, numerical experiments show that
there exist minimization problems for which the existing algorithm generates
divergent sequences, but the proposed algorithm generates convergent sequences.Comment: 22 pages, 8 figure
Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
We consider a model of Dirac fermions in dimensions with dynamically
generated, anticommuting SO(3) N\'eel and Z Kekul\'e mass terms that
permits sign-free quantum Monte Carlo simulations. The phase diagram is
obtained from finite-size scaling and includes a direct and continuous
transition between the N\'eel and Kekul\'e phases. The fermions remain gapped
across the transition, and our data support an emergent SO(4) symmetry unifying
the two order parameters. While the bare symmetries of our model do not allow
for spinon-carrying Z vortices in the Kekul\'e mass, the emergent SO(4)
invariance permits an interpretation of the transition in terms of deconfined
quantum criticality. The phase diagram also features a tricritical point at
which N\'eel, Kekul\'e, and semimetallic phases meet. The present, sign-free
approach can be generalized to a variety of other mass terms and thereby
provides a new framework to study exotic critical phenomena.Comment: 5 pages, 5 figures, to appear in Phys. Rev. Let
Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models
The absence of negative sign problem in quantum Monte Carlo simulations of
spin and fermion systems has different origins. World-line based algorithms for
spins require positivity of matrix elements whereas auxiliary field approaches
for fermions depend on symmetries such as particle-hole. For negative-sign-free
spin and fermionic systems, we show that one can formulate a negative-sign-free
auxiliary field quantum Monte Carlo algorithm that allows Kondo coupling of
fermions with the spins. Using this general approach, we study a half-filled
Kondo lattice model on the Honeycomb lattice with geometric frustration. In
addition to the conventional Kondo insulator and anti-ferromagnetically ordered
phases, we find a partial Kondo screened state where spins are selectively
screened so as to alleviate frustration, and the lattice rotation symmetry is
broken nematically.Comment: 6 pages, 5 figures, supplemental materia
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