35 research outputs found
Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
We use the topological entanglement entropy (TEE) as an efficient tool to
fully characterize the Abelian phase of a
spin liquid emerging as the ground state of topological color code (TCC), which
is a class of stabilizer states on the honeycomb lattice. We provide the fusion
rules of the quasiparticle (QP) excitations of the model by introducing single-
or two-body operators on physical spins for each fusion process which justify
the corresponding fusion outcome. Beside, we extract the TEE from Renyi
entanglement entropy (EE) of the TCC, analytically and numerically by finite
size exact diagonalization on the disk shape regions with contractible
boundaries. We obtain that the EE has a local contribution, which scales
linearly with the boundary length in addition to a topological term, i.e. the
TEE, arising from the condensation of closed strings in the ground state. We
further investigate the ground state dependence of the TEE on regions with
non-contractible boundaries, i.e. by cutting the torus to half cylinders, from
which we further identify multiple independent minimum entropy states (MES) of
the TCC and then extract the U and S modular matrices of the system, which
contain the self and mutual statistics of the anyonic QPs and fully
characterize the topological phase of the TCC. Eventually, we show that, in
spite of the lack of a local order parameter, TEE and other physical quantities
obtained from ground state wave function such as entanglement spectrum (ES) and
ground state fidelity are sensitive probes to study the robustness of a
topological phase. We find that the topological order in the presence of a
magnetic field persists until the vicinity of the transition point, where the
TEE and fidelity drops to zero and the ES splits severely, signaling breakdown
of the topological phase of the TCC
Thermal bosons in 3d optical lattices via tensor networks
Ultracold atoms in optical lattices are one of the most promising
experimental setups to simulate strongly correlated systems. However, efficient
numerical algorithms able to benchmark experiments at low-temperatures in
interesting 3d lattices are lacking. To this aim, here we introduce an
efficient tensor network algorithm to accurately simulate thermal states of
local Hamiltonians in any infinite lattice, and in any dimension. We apply the
method to simulate thermal bosons in optical lattices. In particular, we study
the physics of the (soft-core and hard-core) Bose-Hubbard model on the infinite
pyrochlore and cubic lattices with unprecedented accuracy. Our technique is
therefore an ideal tool to benchmark realistic and interesting optical-lattice
experiments.Comment: 6 pages, 4 figures + Appendi
One directional Polarized Neutron Reflectometry with optimized reference layer method
In the past decade, several neutron reflectometry methods for determining the
modulus and phase of the complex reflection coefficient of an unknown
multilayer thin film have been worked out among which the method of variation
of surroundings and reference layers are of highest interest. These methods
were later modified for measurement of the polarization of the reflected beam
instead of the measurement of the intensities. In their new architecture, these
methods not only suffered from the necessity of change of experimental setup,
but also another difficulty was added to their experimental implementations.
This deficiency was related to the limitations of the technology of the neutron
reflectometers that could only measure the polarization of the reflected
neutrons in the same direction as the polarization of the incident beam. As the
instruments are limited, the theory has to be optimized so that the experiment
could be performed. In a recent work, we developed the method of variation of
surroundings for one directional polarization analysis. In this new work, the
method of reference layer with polarization analysis has been optimized to
determine the phase and modulus of the unknown film with measurement of the
polarization of the reflected neutrons in the same direction as the
polarization of the incident beam
Quantum phase transition in the Kitaev-Potts model
The stability of the topological order phase induced by the Kitaev
model, which is a candidate for fault-tolerant quantum computation, against the
local order phase induced by the 3-State Potts model is studied. We show that
the low energy sector of the Kitaev-Potts model is mapped to the Potts model in
the presence of transverse magnetic field. Our study relies on two high-order
series expansion based on continuous unitary transformations in the limits of
small- and large-Potts couplings as well as mean-field approximation. Our
analysis reveals that the topological phase of the Kitaev model breaks
down to the Potts model through a first order phase transition. We capture the
phase transition by analysis of the ground state energy, one-quasiparticle gap
and geometric measure of entanglement.Comment: 12 pages, 10 figures, Accepted for publication in Physical Review
Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
The infinite Projected Entangled-Pair State (iPEPS) algorithm is one of the
most efficient techniques for studying the ground-state properties of
two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here,
we show how the algorithm can be adapted to explore nearest-neighbor local
Hamiltonians on the ruby and triangle-honeycomb lattices, using the Corner
Transfer Matrix (CTM) renormalization group for 2D tensor network contraction.
Additionally, we show how the CTM method can be used to calculate the ground
state fidelity per lattice site and the boundary density operator and
entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the
iPEPS method to the ruby model with anisotropic interactions and explore the
ground-state properties of the system. We further extract the phase diagram of
the model in different regimes of the couplings by measuring two-point
correlators, ground state fidelity and EE on an infinite cylinder. Our phase
diagram is in agreement with previous studies of the model by exact
diagonalization.Comment: 12 pages, 18 figur
Topological RVB quantum spin liquid on the ruby lattice
We construct a short-range resonating valence-bond state (RVB) on the ruby
lattice, using projected entangled-pair states (PEPS) with bond dimension
. By introducing non-local moves to the dimer patterns on the torus, we
distinguish four distinct sectors in the space of dimer coverings, which is a
signature of the topological nature of the RVB wave function. Furthermore, by
calculating the reduced density matrix of a bipartition of the RVB state on an
infinite cylinder and exploring its entanglement entropy, we confirm the
topological nature of the RVB wave function by obtaining non-zero topological
contribution, , consistent with that of a
topological quantum spin liquid. We also calculate the ground-state energy of
the spin- antiferromagnetic Heisenberg model on the ruby lattice
and compare it with the RVB energy. Finally, we construct a quantum-dimer model
for the ruby lattice and discuss it as a possible parent Hamiltonian for the
RVB wave function.Comment: 10 pages, 10 figure
Thin film growth by using random shape cluster deposition
The growth of a rough and porous thin surface by deposition of randomly
shaped clusters with different sizes over an initially flat linear substrate is
simulated, using Monte Carlo technique. Unlike the ordinary Random Deposition,
our approach results in aggregation of clusters which produces a porous bulk
with correlation along the surface and the surface saturation occurs in long
enough deposition times. The scaling exponents; the growth, roughness, and
dynamic exponents are calculated based on the time scale. Moreover, the
porosity and its dependency to the time and clusters size are also calculated.
We also study the influence of clusters size on the scaling exponent, as well
as on the global porosity
Spin- Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
Using the infinite Projected Entangled Pair States (iPEPS) algorithm, we
study the ground-state properties of the spin- quantum Heisenberg
antiferromagnet on the star lattice in the thermodynamic limit. By analyzing
the ground-state energy of the two inequivalent bonds of the lattice in
different unit-cell structures, we identify two competing Valence-Bond-Solid
(VBS) phases for different antiferromagnetic Heisenberg exchange couplings.
More precisely, we observe (i) a VBS state which respects the full symmetries
of the Hamiltonian, and (ii) a resonating VBS state which, in contrast to
previous predictions, has a six-site unit-cell order and breaks symmetry.
We also studied the ground-state phase diagram by measuring the ground-state
fidelity and energy derivatives, and further confirmed the continuous nature of
the quantum phase transition in the system. Moreover, an analysis of the
isotropic point shows that its ground state is also a VBS as in (i), which is
as well in contrast with previous predictions.Comment: 9 pages, 11 figure
Robustness of a topological phase: Topological color code in parallel magnetic field
The robustness of the topological color code, which is a class of error
correcting quantum codes, is investigated under the influence of an uniform
magnetic field on the honeycomb lattice. Our study relies on two high-order
series expansions using perturbative continuous unitary transformations in the
limit of low and high fields, exact diagonalization and a classical
approximation. We show that the topological color code in a single parallel
field is isospectral to the Baxter-Wu model in a transverse field on the
triangular lattice. It is found that the topological phase is stable up to a
critical field beyond which it breaks down to the polarized phase by a
first-order phase transition. The results also suggest that the topological
color code is more robust than the toric code, in the parallel magnetic field.Comment: 11 pages, 8 figure
Quantum phase transitions out of a Z2 x Z2 topological phase
We investigate the low-energy spectral properties and robustness of the
topological phase of color code, which is a quantum spin model for the aim of
fault-tolerant quantum computation, in the presence of a uniform magnetic field
or Ising interactions, using high-order series expansion and exact
diagonalization. In a uniform magnetic field, we find 1st-order phase
transitions in all field directions. In contrast, our results for the Ising
interactions unveil that for strong enough Ising couplings, the Z2 x Z2
topological phase of color code breaks down to symmetry broken phases by 1st-
or 2nd-order phase transitions.Comment: 10 pages, 11 figure