937 research outputs found
Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
We address the breakdown of the bulk-boundary correspondence observed in
non-Hermitian systems, where open and periodic systems can have distinct phase
diagrams. The correspondence can be completely restored by considering the
Hamiltonian's singular value decomposition instead of its eigendecomposition.
This leads to a natural topological description in terms of a flattened
singular decomposition. This description is equivalent to the usual approach
for Hermitian systems and coincides with a recent proposal for the
classification of non-Hermitian systems. We generalize the notion of the
entanglement spectrum to non-Hermitian systems, and show that the edge physics
is indeed completely captured by the periodic bulk Hamiltonian. We exemplify
our approach by considering the chiral non-Hermitian Su-Schrieffer-Heger and
Chern insulator models. Our work advocates a different perspective on
topological non-Hermitian Hamiltonians, paving the way to a better
understanding of their entanglement structure.Comment: 6+5 pages, 8 figure
S3 Quantum Hall Wavefunctions
We construct a family of quantum Hall Hamiltonians whose ground states, at
least for small system sizes, give correlators of the S3 conformal field
theories. The ground states are considered as trial wavefunctions for quantum
Hall effect of bosons at filling fraction nu=3/4 interacting either via delta
function interaction or delta function plus dipole interaction. While the S3
theories can be either unitary or nonunitary, we find high overlaps with exact
diagonalizations only for the nonunitary case, suggesting that these
wavefunctions may correspond to critical points, possibly analogous to the
previously studied Gaffnian wavefunction. These wavefunctions give an explicit
example which cannot be fully characterized by their thin-torus limit or by
their pattern of zeros.Comment: 4+epsilon pages. 1 figure. Revised version includes: 1 additional
author; additional numerical work; several minor corrections. Our main
results are unchange
Spin-singlet Gaffnian wave function for fractional quantum Hall systems
We characterize in detail a wave function conceivable in fractional quantum
Hall systems where a spin or equivalent degree of freedom is present. This wave
function combines the properties of two previously proposed quantum Hall wave
functions, namely the non-Abelian spin-singlet state and the nonunitary
Gaffnian wave function. This is a spin-singlet generalization of the
spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In
this paper we present evidence demonstrating that the SSG corresponds to the
ground state of a certain local Hamiltonian, which we explicitly construct,
and, further, we provide a relatively simple analytic expression for the unique
ground-state wave functions, which we define as the zero energy eigenstates of
that local Hamiltonian. In addition, we have determined a certain nonunitary,
rational conformal field theory which provides an underlying description of the
SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit.
In order to verify our construction, we implement two recently proposed
techniques for the analysis of fractional quantum Hall trial states: The "spin
dressed squeezing algorithm", and the "generalized Pauli principle".Comment: 15 pages, 2 figures. Version 3 fixes a typographical error in the
Hamiltonian, Eq 3. Version 2 incorporates referee and editorial suggestions.
The original title "Putting a Spin on the Gaffnian" was deemed to be too
inappropriate for PR
Dynamics of composite Haldane spin chains in IPA-CuCl3
Magnetic excitations in the quasi-one-dimensional antiferromagnet IPA-CuCl3
are studied by cold neutron inelastic scattering. Strongly dispersive gap
excitations are observed. Contrary to previously proposed models, the system is
best described as an asymmetric quantum spin ladder. The observed spectrum is
interpreted in terms of ``composite'' Haldane spin chains. The key difference
from actual S=1 chains is a sharp cutoff of the single-magnon spectrum at a
certain critical wave vector.Comment: 4 pages 4 figure
Scaling of the magnetic response in doped antiferromagnets
A theory of the anomalous scaling of the dynamic magnetic response
in cuprates at low doping is presented. It is based on the memory function
representation of the dynamical spin suceptibility in a doped antiferromagnet
where the damping of the collective mode is constant and large, whereas the
equal-time spin correlations saturate at low . Exact diagonalization results
within the t-J model are shown to support assumptions. Consequences, both for
the scaling function and the normalization amplitude, are well in agreement
with neutron scattering results.Comment: 4 pages, 4 figure
Evidence for an incommensurate magnetic resonance in La(2-x)Sr(x)CuO(4)
We study the effect of a magnetic field (applied along the c-axis) on the
low-energy, incommensurate magnetic fluctuations in superconducting
La(1.82)Sr(0.18)CuO(4). The incommensurate peaks at 9 meV, which in zero-field
were previously shown to sharpen in q on cooling below T_c [T. E. Mason et al.,
Phys. Rev. Lett. 77, 1604 (1996)], are found to broaden in q when a field of 10
T is applied. The applied field also causes scattered intensity to shift into
the spin gap. We point out that the response at 9 meV, though occurring at
incommensurate wave vectors, is comparable to the commensurate magnetic
resonance observed at higher energies in other cuprate superconductors.Comment: 8 pages, including 4 figure
Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers
Considering experimental results obtained on three prototype compounds, TMMC,
CsCoCl3 (or CsCoBr3) and Cu Benzoate, we discuss the importance of non-linear
excitations in the physics of quantum (and classical) antiferromagnetic spin
chains.Comment: Invited at the International Symposium on Cooperative Phenomena of
Assembled Metal Complexes, November 15-17, 2001, Osaka, Japa
Spin-resonance modes of the spin-gap magnet TlCuCl_3
Three kinds of magnetic resonance signals were detected in crystals of the
spin-gap magnet TlCuCl_3.
First, we have observed the microwave absorption due to the excitation of the
transitions between the singlet ground state and the excited triplet states.
This mode has the linear frequency-field dependence corresponding to the
previously known value of the zero-field spin-gap of 156 GHz and to the closing
of spin-gap at the magnetic field H_c of about 50 kOe.
Second, the thermally activated resonance absorption due to the transitions
between the spin sublevels of the triplet excitations was found. These
sublevels are split by the crystal field and external magnetic field.
Finally, we have observed antiferromagnetic resonance absorption in the
field-induced antiferromagnetic phase above the critical field H_c. This
resonance frequency is strongly anisotropic with respect to the direction of
the magnetic field.Comment: v.2: typo correction (one of the field directions was misprinted in
the v.1
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