99 research outputs found
Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin- Heisenberg chain
We study different phases of the one-dimensional bond-alternating spin-
Heisenberg model by using the symmetry fractionalization mechanism. We employ
the infinite matrix-product state representation of the ground state (through
the infinite-size density matrix renormalization group algorithm) to obtain
inequivalent projective representations of the (unbroken) symmetry groups of
the model, which are used to identify the different phases. We find that the
model exhibits trivial as well as symmetry-protected topological phases. The
symmetry-protected topological phases are Haldane phases on even/odd bonds,
which are protected by the time-reversal (acting on the spin as
), parity (permutation of the chain about a specific
bond), and dihedral (-rotations about a pair of orthogonal axes)
symmetries. Additionally, we investigate the phases of the most general
two-body bond-alternating spin- model, which respects the time-reversal,
parity, and dihedral symmetries, and obtain its corresponding twelve different
types of the symmetry-protected topological phases.Comment: 9 pages, 5 figure
Quantum phase transition as an interplay of Kitaev and Ising interactions
We study the interplay between the Kitaev and Ising interactions on both
ladder and two dimensional lattices. We show that the ground state of the
Kitaev ladder is a symmetry-protected topological (SPT) phase, which is
protected by a symmetry. It is confirmed by
the degeneracy of the entanglement spectrum and non-trivial phase factors
(inequivalent projective representations of the symmetries), which are obtained
within infinite matrix-product representation of numerical density matrix
renormalization group. We derive the effective theory to describe the
topological phase transition on both ladder and two-dimensional lattices, which
is given by the transverse field Ising model with/without next-nearest neighbor
coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken
ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum
critical point and its corresponding central charge are provided by the
effective theory, which are in full agreement with the numerical results, i.e.,
the divergence of entanglement entropy at the critical point, change of the
entanglement spectrum degeneracy and a drop in the ground-state fidelity. The
central charge of the critical points are either c=1 or c=2, with the
magnetization and correlation exponents being 1/4 and 1/2, respectively. In the
absence of frustration, the 2D lattice shows a topological phase transition
from the spin-liquid state to the long-range ordered Ising phase
at finite ratio of couplings, while in the presence of frustration, an
order-by-disorder transition is induced by the Kitaev term. The 2D classical
spin-liquid phase is unstable against the addition of Kitaev term toward an
ordered phase before the transition to the spin-liquid state.Comment: 16 pages, 18 figure
Real space renormalization of Majorana fermions in quantum nano-wire superconductors
We have applied the real space quantum renormalization group approach to
study the topological quantum phase transition in the one-dimensional chain of
a spinless p-wave superconductor. We investigate the behavior of local
compressibility and ground-state fidelity of the Kitaev chain. We show that the
topological phase transition is signaled by the maximum of local
compressibility at the quantum critical point tuned by the chemical potential.
Moreover, a sudden drop of the ground-state fidelity and the divergence of
fidelity susceptibility at the topological quantum critical point have been
used as a proper indicators for the topological quantum phase transition, which
signals the appearance of Majorana fermions. We also present the scaling
analysis of ground-state fidelity near the critical point that manifests the
universal information about the topological phase transition.Comment: 7 pages, 9 figures; to appear in Journal of the Physical Society of
Japan (JPSJ
Phase Diagram of the One Dimensional model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
We have studied the phase diagram of the one dimensional model
with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor
interactions. We have applied the quantum renormalization group (QRG) approach
to get the stable fixed points and the running of coupling constants. The
second order QRG has been implemented to get the self similar Hamiltonian. This
model shows a rich phase diagram which consists of different phases which
possess the quantum spin-fluid and dimer phases in addition to the classical
N\'{e}el and ferromagnetic ones. The border between different phases has been
shown as a projection onto two different planes in the phase space
Second order quantum renormalisation group of XXZ chain with next nearest neighbour interactions
We have extended the application of quantum renormalisation group (QRG) to
the anisotropic Heisenberg model with next-nearest neighbour (n-n-n)
interaction. The second order correction has to be taken into account to get a
self similar renormalized Hamiltonian in the presence of n-n-n-interaction. We
have obtained the phase diagram of this model which consists of three different
phases, i.e, spin-fluid, dimerised and Ne'el types which merge at the
tri-critical point. The anisotropy of the n-n-n-term changes the phase diagram
significantly. It has a dominant role in the Ne'el-dimer phase boundary. The
staggered magnetisation as an order parameter defines the border between
fluid-Ne'el and Ne'el-dimer phases. The improvement of the second order RG
corrections on the ground state energy of the Heisenberg model is presented.
Moreover, the application of second order QRG on the spin lattice model has
been discussed generally. Our scheme shows that higher order corrections lead
to an effective Hamiltonian with infinite range of interactions.Comment: 10 pages, 4 figures and 1 tabl
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