52 research outputs found
Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
Entanglement renormalization techniques are applied to numerically
investigate the ground state of the spin-1/2 Heisenberg model on a kagome
lattice. Lattices of N={36,144,inf} sites with periodic boundary conditions are
considered. For the infinite lattice, the best approximation to the ground
state is found to be a valence bond crystal (VBC) with a 36-site unit cell,
compatible with a previous proposal. Its energy per site, E=-0.43221, is an
exact upper bound and is lower than the energy of any previous (gapped or
algebraic) spin liquid candidate for the ground state.Comment: 6 pages, 7 figures, RevTeX 4. Revised version with improved numerical
results
Entanglement renormalization in two spatial dimensions
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice size; at a quantum critical point, the simulation cost becomes independent of the lattice size and infinite systems can be analyzed. We demonstrate the performance of the scheme by investigating the low energy properties of the 2D quantum Ising model on a square lattice of linear size L={6,9,18,54,∞} with periodic boundary conditions. We compute the ground state and evaluate local observables and two-point correlators. We also produce accurate estimates of the critical magnetic field and critical exponent β. A calculation of the energy gap shows that it scales as 1/L at the critical point
Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms
The ability of entanglement renormalization (ER) to generate a proper
real-space renormalization group (RG) flow in extended quantum systems is
analysed in the setting of harmonic lattice systems in D=1 and D=2 spatial
dimensions. A conceptual overview of the steps involved in momentum-space RG is
provided and contrasted against the equivalent steps in the real-space setting.
The real-space RG flow, as generated by ER, is compared against the exact
results from momentum-space RG, including an investigation of a critical fixed
point and the effect of relevant and irrelevant perturbations.Comment: 14 pages, 11 figures, substantial revision
Entanglement renormalization in fermionic systems
We demonstrate, in the context of quadratic fermion lattice models in one and
two spatial dimensions, the potential of entanglement renormalization (ER) to
define a proper real-space renormalization group transformation. Our results
show, for the first time, the validity of the multi-scale entanglement
renormalization ansatz (MERA) to describe ground states in two dimensions, even
at a quantum critical point. They also unveil a connection between the
performance of ER and the logarithmic violations of the boundary law for
entanglement in systems with a one-dimensional Fermi surface. ER is recast in
the language of creation/annihilation operators and correlation matrices.Comment: 5 pages, 4 figures Second appendix adde
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
Low energy excitations of the kagome antiferromagnet and the spin gap issue
In this paper we report the latest results of exact diagonalizations of SU(2)
invariant models on various lattices (square, triangular, hexagonal,
checkerboard and kagome lattices). We focus on the low lying levels in each S
sector. The differences in behavior between gapless systems and gapped ones are
exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on
the kagome lattice is discussed. A rough estimate of the spin susceptibility in
such an hypothesis is given.The evolution of the intra-S channel spectra under
the effect of a small perturbation is consistent with the proximity of a
quantum critical point. We emphasize that the very small intra-S channel energy
scale observed in exact spectra is a very interesting information to understand
the low T dynamics of this model.Comment: 6 pages, 5 figures, revised version with a more extended discussion
on the issue of a possible proximity with a quantum critical point, a few
more details and references, a modified Fig
Algorithms for entanglement renormalization
We describe an iterative method to optimize the multi-scale entanglement
renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians
on a D-dimensional lattice. For translation invariant systems the cost of this
optimization is logarithmic in the linear system size. Specialized algorithms
for the treatment of infinite systems are also described. Benchmark simulation
results are presented for a variety of 1D systems, namely Ising, Potts, XX and
Heisenberg models. The potential to compute expected values of local
observables, energy gaps and correlators is investigated.Comment: 23 pages, 28 figure
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
This work explores the use of a tree tensor network ansatz to simulate the
ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting
the entropic area law, the tree tensor network ansatz seems to produce
quasi-exact results in systems with sizes well beyond the reach of exact
diagonalisation techniques. We describe an algorithm to approximate the ground
state of a local Hamiltonian on a L times L lattice with the topology of a
torus. Accurate results are obtained for L={4,6,8}, whereas approximate results
are obtained for larger lattices. As an application of the approach, we analyse
the scaling of the ground state entanglement entropy at the quantum critical
point of the model. We confirm the presence of a positive additive constant to
the area law for half a torus. We also find a logarithmic additive correction
to the entropic area law for a square block. The single copy entanglement for
half a torus reveals similar corrections to the area law with a further term
proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly
improved numerical results for the scaling of the entropies and several new
sections. The manuscript has now 19 pages and 30 Figure
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