23,548 research outputs found
Fermionic spin excitations in two and three-dimensional antiferromagnets
Spin excitations in an ordered Heisenberg magnet are magnons--bosons with
spin 1. That may change when frustration and quantum fluctuations suppress the
order and restore the spin-rotation symmetry. We show that spin excitations in
the Heisenberg antiferromagnet on kagome are spinons--fermions with
spin 1/2. In the ground state the system can be described as a collection of
small, heavy pairs of spinons with spin 0. A magnetic excitation of lowest
energy amounts to breaking up a pair into two spinons at a cost of .Comment: 4 pages, 4 figures, accepted version of the manuscrip
Attacks on the Search-RLWE problem with small errors
The Ring Learning-With-Errors (RLWE) problem shows great promise for
post-quantum cryptography and homomorphic encryption. We describe a new attack
on the non-dual search RLWE problem with small error widths, using ring
homomorphisms to finite fields and the chi-squared statistical test. In
particular, we identify a "subfield vulnerability" (Section 5.2) and give a new
attack which finds this vulnerability by mapping to a finite field extension
and detecting non-uniformity with respect to the number of elements in the
subfield. We use this attack to give examples of vulnerable RLWE instances in
Galois number fields. We also extend the well-known search-to-decision
reduction result to Galois fields with any unramified prime modulus q,
regardless of the residue degree f of q, and we use this in our attacks. The
time complexity of our attack is O(nq2f), where n is the degree of K and f is
the residue degree of q in K. We also show an attack on the non-dual (resp.
dual) RLWE problem with narrow error distributions in prime cyclotomic rings
when the modulus is a ramified prime (resp. any integer). We demonstrate the
attacks in practice by finding many vulnerable instances and successfully
attacking them. We include the code for all attacks
Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
We propose 1D and 2D lattice wave functions constructed from the SU(n)_1
Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all
spins in the lattice transform under SU(n) fundamental representations, we
obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model
as a special case. In 2D, we show that the wave function converges to a class
of Halperin's multilayer fractional quantum Hall states and belongs to chiral
spin liquids. Our result reveals a hidden SU(n) symmetry for this class of
Halperin states. When the spins sit on bipartite lattices with alternating
fundamental and conjugate representations, we provide numerical evidence that
the state in 1D exhibits quantum criticality deviating from the expected
behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids
being consistent with the prediction of the SU(n)_1 WZW model.Comment: 28 pages, 9 figures, published versio
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