172 research outputs found
Non-local scaling operators with entanglement renormalization
The multi-scale entanglement renormalization ansatz (MERA) can be used, in
its scale invariant version, to describe the ground state of a lattice system
at a quantum critical point. From the scale invariant MERA one can determine
the local scaling operators of the model. Here we show that, in the presence of
a global symmetry , it is also possible to determine a class of
non-local scaling operators. Each operator consist, for a given group element
, of a semi-infinite string \tGamma_g with a local operator
attached to its open end. In the case of the quantum Ising model,
, they correspond to the disorder operator ,
the fermionic operators and , and all their descendants.
Together with the local scaling operators identity , spin
and energy , the fermionic and disorder scaling operators ,
and are the complete list of primary fields of the Ising
CFT. Thefore the scale invariant MERA allows us to characterize all the
conformal towers of this CFT.Comment: 4 pages, 4 figures. Revised versio
Tensor network study of the shastry-sutherland model with weak interlayer coupling
The layered material SrCu2(BO3)2 has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu2(BO3)2 under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around J′′/J ∼ 0.05 than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu2(BO3)2 to be around J′′/ J ∼ 0.04 − 0.027 at ambient pressure.</p
Spin-orbital quantum liquid on the honeycomb lattice
In addition to low-energy spin fluctuations, which distinguish them from band
insulators, Mott insulators often possess orbital degrees of freedom when
crystal-field levels are partially filled. While in most situations spins and
orbitals develop long-range order, the possibility for the ground state to be a
quantum liquid opens new perspectives. In this paper, we provide clear evidence
that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a
quantum spin-orbital liquid. The absence of any form of symmetry breaking -
lattice or SU(N) - is supported by a combination of semiclassical and numerical
approaches: flavor-wave theory, tensor network algorithm, and exact
diagonalizations. In addition, all properties revealed by these methods are
very accurately accounted for by a projected variational wave-function based on
the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that
state, correlations are algebraic because of the presence of a Dirac point at
the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the
honeycomb lattice is an algebraic quantum spin-orbital liquid. This model
provides a good starting point to understand the recently discovered
spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest
to choose optical lattices with honeycomb geometry in the search for quantum
liquids in ultra-cold four-color fermionic atoms.Comment: 10 pages, 7 figure
Detecting a topologically ordered phase from unbiased infinite projected entangled-pair state simulations
We present an approach to identify topological order based on unbiased
infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do
not impose a virtual symmetry on the tensors during the optimization of the
tensor network ansatz. As an example we consider the ground state of the toric
code model in a magnetic field exhibiting topological order. The
optimization is done by an efficient energy minimization approach based on a
summation of tensor environments to compute the gradient. We show that the
optimized tensors, when brought into the right gauge, are approximately
symmetric, and they can be fully symmetrized a posteriori to generate a stable
topologically ordered state, yielding the correct topological entanglement
entropy and modular S and U matrices. To compute the latter we develop a
variant of the corner-transfer matrix method which is computationally more
efficient than previous approaches based on the tensor renormalization group.Comment: 16 pages, 14 figure
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
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