1,210 research outputs found
Isometric Tensor Network States in Two Dimensions
Tensor network states (TNS) are a promising but numerically challenging tool
for simulating two-dimensional (2D) quantum many-body problems. We introduce an
isometric restriction of the TNS ansatz that allows for highly efficient
contraction of the network. We consider two concrete applications using this
ansatz. First, we show that a matrix-product state representation of a 2D
quantum state can be iteratively transformed into an isometric 2D TNS. Second,
we introduce a 2D version of the time-evolving block decimation algorithm
(TEBD) for approximating the ground state of a Hamiltonian as an isometric
TNS, which we demonstrate for the 2D transverse field Ising model.Comment: 5 pages, 4 figure
Kinetic ferromagnetism on a kagome lattice
We study strongly correlated electrons on a kagome lattice at 1/6 and 1/3
filling. They are described by an extended Hubbard Hamiltonian. We are
concerned with the limit |t|<<V<<U with hopping amplitude t, nearest-neighbor
repulsion V and on-site repulsion U. We derive an effective Hamiltonian and
show, with the help of the Perron-Frobenius theorem, that the system is
ferromagnetic at low temperatures. The robustness of ferromagnetism is
discussed and extensions to other lattices are indicated.Comment: 4 pages, 2 color eps figures; updated version published in Phys. Rev.
Lett.; one reference adde
Spectral functions and optical conductivity of spinless fermions on a checkerboard lattice
We study the dynamical properties of spinless fermions on the checkerboard
lattice. Our main interest is the limit of large nearest-neighbor repulsion
as compared with hopping . The spectral functions show broad low-energy
excitation which are due to the dynamics of fractionally charged excitations.
Furthermore, it is shown that the fractional charges contribute to the
electrical current density.Comment: 9 Pages, 9 Figure
Charge degrees in the quarter-filled checkerboard lattice
For a systematic study of charge degrees of freedom in lattices with
geometric frustration, we consider spinless fermions on the checkerboard
lattice with nearest-neighbor hopping and nearest-neighbor repulsion at
quarter-filling. An effective Hamiltonian for the limit is given to
lowest non-vanishing order by the ring exchange (). We show
that the system can equivalently be described by hard-core bosons and map the
model to a confining U(1) lattice gauge theory.Comment: Proceedings of ICM200
Characterization and stability of a fermionic \nu=1/3 fractional Chern insulator
Using the infinite density matrix renormalization group method on an infinite
cylinder geometry, we characterize the fractional Chern insulator state
in the Haldane honeycomb lattice model at filling of the lowest band
and check its stability. We investigate the chiral and topological properties
of this state through (i) its Hall conductivity, (ii) the topological
entanglement entropy, (iii) the charge spectral flow of the many body
entanglement spectrum, and (iv) the charge of the anyons. In contrast to
numerical methods restricted to small finite sizes, the infinite cylinder
geometry allows us to access and characterize directly the metal to fractional
Chern insulator transition. We find indications it is first order and no
evidence of other competing phases. Since our approach does not rely on any
band or subspace projection, we are able to prove the stability of the
fractional state in the presence of interactions exceeding the band gap, as has
been suggested in the literature. As a by-product we discuss the signatures of
Chern insulators within this technique.Comment: published versio
Strongly correlated fermions on a kagome lattice
We study a model of strongly correlated spinless fermions on a kagome lattice
at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian.
An effective Hamiltonian in the desired strong correlation regime is derived,
from which the spectral functions are calculated by means of exact
diagonalization techniques. We present our numerical results with a view to
discussion of possible signatures of confinement/deconfinement of fractional
charges.Comment: 10 pages, 10 figure
Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
The antiferromagnetic spin- Heisenberg model on a kagome lattice is one
of the most paradigmatic models in the context of spin liquids, yet the precise
nature of its ground state is not understood. We use large scale density matrix
normalization group simulations (DMRG) on infinitely long cylinders and find
indications for the formation of a gapless Dirac spin liquid. First, we use
adiabatic flux insertion to demonstrate that the spin gap is much smaller than
estimated from previous DMRG simulation. Second, we find that the momentum
dependent excitation spectrum, as extracted from the DMRG transfer matrix,
exhibits Dirac cones that match those of a -flux free fermion model (the
parton mean-field ansatz of a Dirac spin liquid)Comment: 15 pages, 16 figure
Infinite density matrix renormalization group for multicomponent quantum Hall systems
While the simplest quantum Hall plateaus, such as the state in
GaAs, can be conveniently analyzed by assuming only a single active Landau
level participates, for many phases the spin, valley, bilayer, subband, or
higher Landau level indices play an important role. These `multi-component'
problems are difficult to study using exact diagonalization because each
component increases the difficulty exponentially. An important example is the
plateau at , where scattering into higher Landau levels chooses
between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address
the methodological issues required to apply the infinite density matrix
renormalization group to quantum Hall systems with multiple components and
long-range Coulomb interactions, greatly extending accessible system sizes. As
an initial application we study the problem of Landau level mixing in the state. Within the approach to Landau level mixing used here, we find
that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian
state over a range of Landau level mixing up to the experimentally relevant
values.Comment: 12 pages, 9 figures. v2 added more data for different amounts of
Landau level mixing at 5/2 fillin
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