15,264 research outputs found
Detecting crystal symmetry fractionalization from the ground state: Application to spin liquids on the kagome lattice
In quantum spin liquid states, the fractionalized spinon excitations can
carry fractional crystal symmetry quantum numbers, and this symmetry
fractionalization distinguishes different topologically ordered spin liquid
states. In this work we propose a simple way to detect signatures of such
crystal symmetry fractionalizations from the crystal symmetry representations
of the ground state wave function. We demonstrate our method on projected
spin liquid wave functions on the kagome lattice, and show that
it can be used to classify generic wave functions. Particularly our method can
be used to distinguish several proposed candidates of spin liquid
states on the kagome lattice.Comment: main text: 6 pages, 1 figure. supplemental material: 8 pages, 2
figures. Added a few references and the journal referenc
Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators
The surface of a three-dimensional topological electron system often hosts
symmetry-protected gapless surface states. With the effect of electron
interactions, these surface states can be gapped out without symmetry breaking
by a surface topological order, in which the anyon excitations carry anomalous
symmetry fractionalization that cannot be realized in a genuine two-dimensional
system. We show that for a mirror-symmetry-protected topological crystalline
insulator with mirror Chern number , its surface can be gapped out by an
anomalous topological order, where all anyons carry
mirror-symmetry fractionalization . The identification of such
anomalous crystalline symmetry fractionalization implies that in a
two-dimensional spin liquid the vison excitation cannot carry
if the spinon carries or a half-integer spin.Comment: 6+8 pages, 2 figures. v2: added a new section in the supplemental
material, the journal reference and some other change
Loops, sign structures and emergent Fermi statistics in three-dimensional quantum dimer models
We introduce and study three-dimensional quantum dimer models with positive
resonance terms. We demonstrate that their ground state wave functions exhibit
a nonlocal sign structure that can be exactly formulated in terms of loops, and
as a direct consequence, monomer excitations obey Fermi statistics. The sign
structure and Fermi statistics in these "signful" quantum dimer models can be
naturally described by a parton construction, which becomes exact at the
solvable point.Comment: 9 pages, 12 figure
Self-Learning Monte Carlo Method
Monte Carlo simulation is an unbiased numerical tool for studying classical
and quantum many-body systems. One of its bottlenecks is the lack of general
and efficient update algorithm for large size systems close to phase transition
or with strong frustrations, for which local updates perform badly. In this
work, we propose a new general-purpose Monte Carlo method, dubbed self-learning
Monte Carlo (SLMC), in which an efficient update algorithm is first learned
from the training data generated in trial simulations and then used to speed up
the actual simulation. We demonstrate the efficiency of SLMC in a spin model at
the phase transition point, achieving a 10-20 times speedup.Comment: add more refs and correct some typo
Self-Learning Monte Carlo Method in Fermion Systems
We develop the self-learning Monte Carlo (SLMC) method, a general-purpose
numerical method recently introduced to simulate many-body systems, for
studying interacting fermion systems. Our method uses a highly-efficient update
algorithm, which we design and dub "cumulative update", to generate new
candidate configurations in the Markov chain based on a self-learned bosonic
effective model. From general analysis and numerical study of the double
exchange model as an example, we find the SLMC with cumulative update
drastically reduces the computational cost of the simulation, while remaining
statistically exact. Remarkably, its computational complexity is far less than
the conventional algorithm with local updates
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
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