1,341 research outputs found
Quantum orders in an exact soluble model
We find all the exact eigenstates and eigenvalues of a spin-1/2 model on
square lattice: . We show
that the ground states for have different quantum orders
described by Z2A and Z2B projective symmetry groups. The phase transition at
represents a new kind of phase transitions that changes quantum orders
but not symmetry. Both the Z2A and Z2B states are described by lattice
gauge theories at low energies. They have robust topologically degenerate
ground states and gapless edge excitations.Comment: 4 pages, RevTeX4, More materials on topological/quantum orders and
quantum computing can be found in http://dao.mit.edu/~we
Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF) and tetrafluorosilane (SiF)
Accurate quartic anharmonic force fields for CF and SiF have been
calculated using the CCSD(T) method and basis sets of quality. Based on
the {\it ab initio} force field with a minor empirical adjustment, the
vibrational energy levels of these two molecules and their isotopomers are
calculated by means of high order Canonical Van Vleck Perturbation Theory(CVPT)
based on curvilinear coordinates. The calculated energies agree very well with
the experimental data. The full quadratic force field of CF is further
refined to the experimental data. The symmetrization of the Cartesian basis for
any combination bands of group molecules is discussed using the circular
promotion operator for the doubly degenerate modes, together with tabulated
vector coupling coefficients. The extraction of the spectroscopic constants
from our second order transformed Hamiltonian in curvilinear coordinates is
discussed, and compared to a similar procedure in rectilinear coordinates.Comment: (submitted to J. Chem. Phys.
Symmetry protected topological orders of 1D spin systems with D2+T symmetry
In [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped
symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete
spin rotation and time reversal symmetries. In this
paper, using a generalized approach, we study all the 16 possible gapped
symmetric quantum phases of 1D integer spin systems with only symmetry.
Those phases are beyond Landau symmetry breaking theory and cannot be
characterized by local order parameters, since they do not break any symmetry.
They correspond to 16 symmetry protected topological (SPT) orders. We show that
all the 16 SPT orders can be fully characterized by the physical properties of
the symmetry protected degenerate boundary states (end `spins') at the ends of
a chain segment. So we can measure and distinguish all the 16 SPT orders
experimentally. We also show that all these SPT orders can be realized in S=1
spin ladder models. The gapped symmetric phases protected by subgroups of
are also studied. Again, all these phases can be distinguished by
physically measuring their end `spins'.Comment: 10+page
String and Membrane condensation on 3D lattices
In this paper, we investigate the general properties of lattice spin models
that have string and/or membrane condensed ground states. We discuss the
properties needed to define a string or membrane operator. We study three 3D
spin models which lead to Z_2 gauge theory at low energies. All the three
models are exactly soluble and produce topologically ordered ground states. The
first model contains both closed-string and closed-membrane condensations. The
second model contains closed-string condensation only. The ends of open-strings
behave like fermionic particles. The third model also has condensations of
closed membranes and closed strings. The ends of open strings are bosonic while
the edges of open membranes are fermionic. The third model contains a new type
of topological order.Comment: 10 pages, RevTeX
Topological surface states in three-dimensional magnetic insulators
An electron moving in a magnetically ordered background feels an effective
magnetic field that can be both stronger and more rapidly varying than typical
externally applied fields. One consequence is that insulating magnetic
materials in three dimensions can have topologically nontrivial properties of
the effective band structure. For the simplest case of two bands, these "Hopf
insulators" are characterized by a topological invariant as in quantum Hall
states and Z_2 topological insulators, but instead of a Chern number or parity,
the underlying invariant is the Hopf invariant that classifies maps from the
3-sphere to the 2-sphere. This paper gives an efficient algorithm to compute
whether a given magnetic band structure has nontrivial Hopf invariant, a
double-exchange-like tight-binding model that realizes the nontrivial case, and
a numerical study of the surface states of this model.Comment: 4 pages, 2 figures; published versio
Translation-symmetry protected topological orders on lattice
In this paper we systematically study a simple class of translation-symmetry
protected topological orders in quantum spin systems using slave-particle
approach. The spin systems on square lattice are translation invariant, but may
break any other symmetries. We consider topologically ordered ground states
that do not spontaneously break any symmetry. Those states can be described by
Z2A or Z2B projective symmetry group. We find that the Z2A translation
symmetric topological orders can still be divided into 16 sub-classes
corresponding to 16 new translation-symmetry protected topological orders. We
introduced four topological indices at , , , to characterize those 16 new
topological orders. We calculated the topological degeneracies and crystal
momenta for those 16 topological phases on even-by-even, even-by-odd,
odd-by-even, and odd-by-odd lattices, which allows us to physically measure
such topological orders. We predict the appearance of gapless fermionic
excitations at the quantum phase transitions between those symmetry protected
topological orders. Our result can be generalized to any dimensions. We find
256 translation-symmetry protected Z2A topological orders for a system on 3D
lattice
Tensor-product representations for string-net condensed states
We show that general string-net condensed states have a natural
representation in terms of tensor product states (TPS) . These TPS's are built
from local tensors. They can describe both states with short-range entanglement
(such as the symmetry breaking states) and states with long-range entanglement
(such as string-net condensed states with topological/quantum order). The
tensor product representation provides a kind of 'mean-field' description for
topologically ordered states and could be a powerful way to study quantum phase
transitions between such states. As an attempt in this direction, we show that
the constructed TPS's are fixed-points under a certain wave-function
renormalization group transformation for quantum states.Comment: 11 pages. RevTeX
Quantum ether: photons and electrons from a rotor model
We give an example of a purely bosonic model -- a rotor model on the 3D cubic
lattice -- whose low energy excitations behave like massless U(1) gauge bosons
and massless Dirac fermions. This model can be viewed as a ``quantum ether'': a
medium that gives rise to both photons and electrons. It illustrates a general
mechanism for the emergence of gauge bosons and fermions known as ``string-net
condensation.'' Other, more complex, string-net condensed models can have
excitations that behave like gluons, quarks and other particles in the standard
model. This suggests that photons, electrons and other elementary particles may
have a unified origin: string-net condensation in our vacuum.Comment: 10 pages, 6 figures, RevTeX4. Home page http://dao.mit.edu/~we
Tensor product representation of topological ordered phase: necessary symmetry conditions
The tensor product representation of quantum states leads to a promising
variational approach to study quantum phase and quantum phase transitions,
especially topological ordered phases which are impossible to handle with
conventional methods due to their long range entanglement. However, an
important issue arises when we use tensor product states (TPS) as variational
states to find the ground state of a Hamiltonian: can arbitrary variations in
the tensors that represent ground state of a Hamiltonian be induced by local
perturbations to the Hamiltonian? Starting from a tensor product state which is
the exact ground state of a Hamiltonian with topological order,
we show that, surprisingly, not all variations of the tensors correspond to the
variation of the ground state caused by local perturbations of the Hamiltonian.
Even in the absence of any symmetry requirement of the perturbed Hamiltonian,
one necessary condition for the variations of the tensors to be physical is
that they respect certain symmetry. We support this claim by
calculating explicitly the change in topological entanglement entropy with
different variations in the tensors. This finding will provide important
guidance to numerical variational study of topological phase and phase
transitions. It is also a crucial step in using TPS to study universal
properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure
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