1,645 research outputs found
Itinerant quantum critical point with frustration and non-Fermi-liquid
Employing the self-learning quantum Monte Carlo algorithm, we investigate the
frustrated transverse-field triangle-lattice Ising model coupled to a Fermi
surface. Without fermions, the spin degrees of freedom undergoes a second-order
quantum phase transition between paramagnetic and clock-ordered phases. This
quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to
the (2+1)D XY universality class. In the presence of fermions, spin
fluctuations introduce effective interactions among fermions and distort the
bare Fermi surface towards an interacting one with hot spots and Fermi pockets.
Near the QCP, non-Fermi-liquid behavior are observed at the hot spots, and the
QCP is rendered into a different universality with Hertz-Millis type exponents.
The detailed properties of this QCP and possibly related experimental systems
are also discussed.Comment: 9 pages, 8 figure
Competing pairing channels in the doped honeycomb lattice Hubbard model
Proposals for superconductivity emerging from correlated electrons in the
doped Hubbard model on the honeycomb lattice range from chiral singlet
to triplet pairing, depending on the considered range of doping and
interaction strength, as well as the approach used to analyze the pairing
instabilities. Here, we consider these scenarios using large-scale dynamic
cluster approximation (DCA) calculations to examine the evolution in the
leading pairing symmetry from weak to intermediate coupling strength. These
calculations focus on doping levels around the van Hove singularity (VHS) and
are performed using DCA simulations with an interaction-expansion
continuous-time quantum Monte Carlo cluster solver. We calculated explicitly
the temperature dependence of different uniform superconducting pairing
susceptibilities and found a consistent picture emerging upon gradually
increasing the cluster size: while at weak coupling the singlet pairing
dominates close to the VHS filling, an enhanced tendency towards -wave
triplet pairing upon further increasing the interaction strength is observed.
The relevance of these systematic results for existing proposals and ongoing
pursuits of odd-parity topological superconductivity are also discussed.Comment: 7 pages, 5 figure
Self-Learning Determinantal Quantum Monte Carlo Method
Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful
general-purpose numerical method recently introduced to simulate many-body
systems. In this work, we implement this method in the framework of
determinantal quantum Monte Carlo simulation of interacting fermion systems.
Guided by a self-learned bosonic effective action, our method uses a cumulative
update [arXiv:1611.09364] algorithm to sample auxiliary field configurations
quickly and efficiently. We demonstrate that self-learning determinantal Monte
Carlo method can reduce the auto-correlation time to as short as one near a
critical point, leading to -fold speedup. This enables to
simulate interacting fermion system on a lattice for the first
time, and obtain critical exponents with high accuracy.Comment: 5 pages, 4 figure
Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
The spontaneous generation of charge-density-wave order in a Dirac fermion
system via the natural mechanism of electron-phonon coupling is studied in the
framework of the Holstein model on the honeycomb lattice. Using two independent
and unbiased quantum Monte Carlo methods, the phase diagram as a function of
temperature and coupling strength is determined. It features a quantum critical
point as well as a line of thermal critical points. Finite-size scaling appears
consistent with fermionic Gross-Neveu-Ising universality for the quantum phase
transition, and bosonic Ising universality for the thermal phase transition.
The critical temperature has a maximum at intermediate couplings. Our findings
motivate experimental efforts to identify or engineer Dirac systems with
sufficiently strong and tunable electron-phonon coupling.Comment: 4+3 pages, 4+2 figure
A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems
Much recent research effort has been directed to the development of efficient
algorithms for solving minimax problems with theoretical convergence guarantees
due to the relevance of these problems to a few emergent applications. In this
paper, we propose a unified single-loop alternating gradient projection (AGP)
algorithm for solving nonconvex-(strongly) concave and (strongly)
convex-nonconcave minimax problems. AGP employs simple gradient projection
steps for updating the primal and dual variables alternatively at each
iteration. We show that it can find an -stationary point of the
objective function in (resp.
) iterations under
nonconvex-strongly concave (resp. nonconvex-concave) setting. Moreover, its
gradient complexity to obtain an -stationary point of the
objective function is bounded by
(resp., ) under the strongly
convex-nonconcave (resp., convex-nonconcave) setting. To the best of our
knowledge, this is the first time that a simple and unified single-loop
algorithm is developed for solving both nonconvex-(strongly) concave and
(strongly) convex-nonconcave minimax problems. Moreover, the complexity results
for solving the latter (strongly) convex-nonconcave minimax problems have never
been obtained before in the literature
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