1,520 research outputs found
Infinite matrix product states, boundary conformal field theory, and the open Haldane-Shastry model
We show that infinite Matrix Product States (MPS) constructed from conformal
field theories can describe ground states of one-dimensional critical systems
with open boundary conditions. To illustrate this, we consider a simple
infinite MPS for a spin-1/2 chain and derive an inhomogeneous open
Haldane-Shastry model. For the spin-1/2 open Haldane-Shastry model, we derive
an exact expression for the two-point spin correlation function. We also
provide an SU() generalization of the open Haldane-Shastry model and
determine its twisted Yangian generators responsible for the highly degenerate
multiplets in the energy spectrum.Comment: 5+7 pages, 4 figures, published version, a typo in the twisted
Yangian generators corrected (thanks to the authors of arXiv:1511.08613 for
pointing out this typo
Majorana Edge States in Interacting Two-chain Ladders of Fermions
In this work we study interacting spinless fermions on a two-chain ladder
with inter-chain pair tunneling while single-particle tunneling is suppressed
at low energy. The model embodies a symmetry associated with the
fermion parity on each chain. We find that when the system is driven to the
strong-coupling phase by the pair tunneling, Majorana excitations appear on the
boundary. Such Majorana edge states correspond to two-fold degeneracy of ground
states distinguished by different fermion parity on each chain, thus
representing a generalization of one-dimensional topological superconductors.
We also characterize the stability of the ground state degeneracy against local
perturbations. Lattice fermion models realizing such effective field theory are
discussed.Comment: 6 pages, 1 figur
Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
We introduce a family of many-body quantum states that describe interacting
spin one-half hard-core particles with bosonic or fermionic statistics on
arbitrary one- and two-dimensional lattices. The wave functions at lattice
filling fraction are derived from deformations of the
Wess-Zumino-Witten model and are related to the
Halperin fractional quantum Hall states. We derive long-range
SU(2) invariant parent Hamiltonians for these states which in two dimensions
are chiral -- models with additional three-body interaction terms. In
one dimension we obtain a generalisation to open chains of a periodic
inverse-square -- model proposed in [Z. N. C. Ha and F. D. M. Haldane,
Phys. Rev. B , 9359 (1992)]. We observe that the gapless
low-energy spectrum of this model and its open-boundary generalisation can be
described by rapidity sets with the same generalised Pauli exclusion principle.
A two-component compactified free boson conformal field theory is identified
that has the same central charge and scaling dimensions as the periodic bosonic
inverse-square -- model.Comment: 19 pages, 2 figures. v2: minor corrections and partial rewriting of
section IV B
Symmetry-protected intermediate trivial phases in quantum spin chains
Symmetry-protected trivial (SPt) phases of matter are the product-state
analogue of symmetry-protected topological (SPT) phases. This means, SPt phases
can be adiabatically connected to a product state by some path that preserves
the protecting symmetry. Moreover, SPt and SPT phases can be adiabatically
connected to each other when interaction terms that break the symmetries
protecting the SPT order are added in the Hamiltonian. It is also known that
spin-1 SPT phases in quantum spin chains can emerge as effective intermediate
phases of spin-2 Hamiltonians. In this paper we show that a similar scenario is
also valid for SPt phases. More precisely, we show that for a given spin-2
quantum chain, effective intermediate spin-1 SPt phases emerge in some regions
of the phase diagram, these also being adiabatically connected to non-trivial
intermediate SPT phases. We characterize the phase diagram of our model by
studying quantities such as the entanglement entropy, symmetry-related order
parameters, and 1-site fidelities. Our numerical analysis uses Matrix Product
States (MPS) and the infinite Time-Evolving Block Decimation (iTEBD) method to
approximate ground states of the system in the thermodynamic limit. Moreover,
we provide a field theory description of the possible quantum phase transitions
between the SPt phases. Together with the numerical results, such a description
shows that the transitions may be described by Conformal Field Theories (CFT)
with central charge c=1. Our results are in agreement, and further generalize,
those in [Y. Fuji, F. Pollmann, M. Oshikawa, Phys. Rev. Lett. 114, 177204
(2015)].Comment: 7 pages, 5 figures, 1 table, revised version. Accepted in PR
All spin-1 topological phases in a single spin-2 chain
Here we study the emergence of different Symmetry-Protected Topological (SPT)
phases in a spin-2 quantum chain. We consider a Heisenberg-like model with
bilinear, biquadratic, bicubic, and biquartic nearest-neighbor interactions, as
well as uniaxial anisotropy. We show that this model contains four different
effective spin-1 SPT phases, corresponding to different representations of the
symmetry group, where
is some -rotation in the spin internal space and is time-reversal. One
of these phases is equivalent to the usual spin-1 Haldane phase, while the
other three are different but also typical of spin-1 systems. The model also
exhibits an -Haldane phase. Moreover, we also find that the transitions
between the different effective spin-1 SPT phases are continuous, and can be
described by a conformal field theory. At such transitions, indirect
evidence suggests a possible effective field theory of four massless Majorana
fermions. The results are obtained by approximating the ground state of the
system in the thermodynamic limit using Matrix Product States via the infinite
Time Evolving Block Decimation method, as well as by effective field theory
considerations. Our findings show, for the first time, that different large
effective spin-1 SPT phases separated by continuous quantum phase transitions
can be stabilized in a simple quantum spin chain.Comment: 7 pages, 6 figures, revised version. To appear in PR
Momentum polarization: an entanglement measure of topological spin and chiral central charge
Topologically ordered states are quantum states of matter with topological
ground state degeneracy and quasi-particles carrying fractional quantum numbers
and fractional statistics. The topological spin is an
important property of a topological quasi-particle, which is the Berry phase
obtained in the adiabatic self-rotation of the quasi-particle by . For
chiral topological states with robust chiral edge states, another fundamental
topological property is the edge state chiral central charge . In this paper
we propose a new approach to compute the topological spin and chiral central
charge in lattice models by defining a new quantity named as the momentum
polarization. Momentum polarization is defined on the cylinder geometry as a
universal subleading term in the average value of a "partial translation
operator". We show that the momentum polarization is a quantum entanglement
property which can be computed from the reduced density matrix, and our
analytic derivation based on edge conformal field theory shows that the
momentum polarization measures the combination of
topological spin and central charge. Numerical results are obtained for two
example systems, the non-Abelian phase of the honeycomb lattice Kitaev model,
and the Laughlin state of a fractional Chern insulator described by a
variational Monte Carlo wavefunction. The numerical results verifies the
analytic formula with high accuracy, and further suggests that this result
remains robust even when the edge states cannot be described by a conformal
field theory. Our result provides a new efficient approach to characterize and
identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure
Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
Here we evaluate the many-body entanglement properties of a generalized SU(n)
valence bond solid state on a chain. Our results follow from a derivation of
the transfer matrix of the system which, in combination with symmetry
properties, allows for a new, elegant and straightforward evaluation of
different entanglement measures. In particular, the geometric entanglement per
block, correlation length, von Neumann and R\'enyi entropies of a block,
localizable entanglement and entanglement length are obtained in a very simple
way. All our results are in agreement with previous derivations for the SU(2)
case.Comment: 4 pages, 2 figure
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