230 research outputs found
Non-linear sigma model approach to quantum spin chains
We introduce and motivate the study of quantum spin chains on a
one-dimensional lattice. We classify the varieties of methods that have been
used to study these models into three categories, - a) exact methods to study
specific models b) field theories to describe fluctuations about the classical
ordered phases and c) numerical methods. We then discuss the
-- model in some detail and end with a few comments on open
problems.Comment: 8 pages, Proceedings of CMDAYS05, Berhampur, to be published in
Indian Jnl of Physic
Semiclassical and field theoretic studies of Heisenberg antiferromagnetic chains with frustration and dimerization
The Heisenberg antiferromagnetic spin chain with both dimerization and
frustration is studied. The classical ground state has three phases (a Neel
phase, a spiral phase and a colinear phase), around which a planar spin-wave
analysis is performed. In each phase, we discuss a non-linear sigma model field
theory describing the low energy excitations. A renormalization group analysis
of the SO(3) matrix-valued field theory of the spiral phase leads to the
conclusion that the theory becomes and Lorentz invariant
at long distances. This theory is analytically known to have a massive spin-1/2
excitation. We also show that solitons in the field theory lead to a
double degeneracy in the spectrum for half-integer spins.Comment: 18 pages in latex, 2 figures in postscrip
Spin polarised scanning tunneling probe for helical Luttinger liquids
We propose a three terminal spin polarized stm setup for probing the helical
nature of the Luttinger liquid edge state that appears in the quantum spin Hall
system. We show that the three-terminal tunneling conductance strongly depends
on the angle () between the magnetization direction of the tip and the
local orientation of the electron spin on the edge while the two terminal
conductance is independent of this angle. We demonstrate that chiral injection
of an electron into the helical Luttinger liquid (which occurs when is
zero or ) is associated with fractionalization of the spin of the injected
electron in addition to the fractionalization of its charge. We also point out
a spin current amplification effect induced by the spin fractionalization.Comment: Final version to appear in Phys. Rev. Let
Fractional Quantum Hall Effect States as Exact Ground States
We construct many particle Hamiltonians for which the Laughlin and Jain
wavefunctions are exact ground states. The Hamiltonians involve fermions in a
magnetic field and with inter-particle interactions. For the Laughlin
wave-functions,the interactions involve two- and three-body correlations
similar to the Chern-Simons interactions, whereas for the projected Jain
wave-functions, N-body interactions (which cannot be explicitly written down in
general) are involved.Comment: Several changes, particularly in interpretatio
A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires
We study the renormalization group flows of the two terminal conductance of a
superconducting junction of two Luttinger liquid wires. We compute the power
laws associated with the renormalization group flow around the various fixed
points of this system using the generators of the SU(4) group to generate the
appropriate parameterization of a S-matrix representing small deviations from a
given fixed point S-matrix (obtained earlier in Phys. Rev. B 77, 155418
(2008)), and we then perform a comprehensive stability analysis. In particular,
for the non-trivial fixed point which has intermediate values of transmission,
reflection, Andreev reflection and crossed Andreev reflection, we show that
there are eleven independent directions in which the system can be perturbed,
which are relevant or irrelevant, and five directions which are marginal. We
obtain power laws associated with these relevant and irrelevant perturbations.
Unlike the case of the two-wire charge-conserving junction, here we show that
there are power laws which are non-linear functions of V(0) and V(2k_{F})
(where V(k) represents the Fourier transform of the inter-electron interaction
potential at momentum k). We also obtain the power law dependence of linear
response conductance on voltage bias or temperature around this fixed point.Comment: Final version to appear in Phys. Rev.
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