286 research outputs found
Phase diagram of a 1 dimensional spin-orbital model
We study a 1 dimensional spin-orbital model using both analytical and
numerical methods. Renormalization group calculations are performed in the
vicinity of a special integrable point in the phase diagram with SU(4)
symmetry. These indicate the existence of a gapless phase in an extended region
of the phase diagram, missed in previous studies. This phase is SU(4) invariant
at low energies apart from the presence of different velocities for spin and
orbital degrees of freedom. The phase transition into a gapped dimerized phase
is in a generalized Kosterlitz-Thouless universality class. The phase diagram
of this model is sketched using the density matrix renormalization group
technique.Comment: 11 pages, 5 figures, new references adde
An asymptotic formula for marginal running coupling constants and universality of loglog corrections
Given a two-loop beta function for multiple marginal coupling constants, we
derive an asymptotic formula for the running coupling constants driven to an
infrared fixed point. It can play an important role in universal loglog
corrections to physical quantities.Comment: 16 pages; typos fixed, one appendix removed for quick access to the
main result; to be published in J. Phys.
Magnetic impurities in the one-dimensional spin-orbital model
Using one-dimensional spin-orbital model as a typical example of quantum spin
systems with richer symmetries, we study the effect of an isolated impurity on
its low energy dynamics in the gapless phase through bosonization and
renormalization group methods. In the case of internal impurities, depending on
the symmetry, the boundary fixed points can be either an open chain with a
residual spin or (and) orbital triplet left behind, or a periodic chain.
However, these two fixed points are indistinguishable in the sense that in both
cases, the lead-correction-to-scaling boundary operators (LCBO) only show
Fermi-liquid like corrections to thermodynamical quantities. (Except the
possible Curie-like contributions from the residual moments in the latter
cases.) In the case of external (Kondo) impurities, the boundary fixed points,
depending on the sign of orbital couplings, can be either an open chain with an
isolated orbital doublet due to Kondo screening or it will flow to an
intermediate fixed point with the same LCBO as that of the two-channel Kondo
problem. Comparison with the Kondo effect in one-dimensional (1D) Heisenberg
spin chain and multi-band Hubbard models is also made.Comment: 7 pages, No figur
Quantum phase transitions of the asymmetric three-leg spin tube
We investigate quantum phase transitions of the S=1/2 three-leg
antiferromagnetic spin tube with asymmetric inter-chain (rung) exchange
interactions. On the basis of the electron tube system, we propose a useful
effective theory to give the global phase diagram of the asymmetric spin tube.
In addition, using other effective theories we raise the reliability of the
phase diagram. The density-matrix renormalization-group and the numerical
diagonalization analyses show that the finite spin gap appears in a narrow
region around the rung-symmetric line, in contrast to a recent paper by
Nishimoto and Arikawa [Phys. Rev. B78, 054421 (2008)]. The numerical
calculations indicate that this global phase diagram obtained by use of the
effective theories is qualitatively correct. In the gapless phase on the phase
diagram, the numerical data are fitted by a finite-size scaling in the c=1
conformal field theory. We argue that all the phase transitions between the
gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless
universality class.Comment: 12 pages, 7 figures, 2 column, final versio
Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
We investigate the phase diagram of a generalized spin-1/2 quantum
antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange
interactions. We consider the exactly soluble models associated with the
problem, obtain the exact ground states which exist for certain parameter
regimes, and apply a variety of perturbative techniques in the regime of strong
ring-exchange coupling. By combining these approaches with considerations
related to the discrete Z_4 symmetry of the model, we present the complete
phase diagram.Comment: 17 pages, 10 figure
Magnetic properties of an SU(4) spin-orbital chain
In this paper, we study the magnetic properties of the one-dimensional SU(4)
spin-orbital model by solving its Bethe ansatz solution numerically. It is
found that the magnetic properties of the system for the case of
differs from that for the case of . The magnetization curve and
susceptibility are obtained for a system of 200 sites. For , the
phase diagram depending on the magnetic field and the ratio of Land\'e factors,
, is obtained. Four phases with distinct magnetic properties are
found.Comment: 4 pages, 2 figure
Effects of a magnetic field on the one-dimensional spin-orbital model
We study the effects of a uniform magnetic field on the one-dimensional
spin-orbital model in terms of effective field theories. Two regions are
examined: one around the SU(4) point (J=K/4) and the other with K<<J. We found
that when , the spin and orbital correlation functions exhibit
power-law decay with nonuniversal exponents. In the region with J>K/4, the
excitation spectrum has a gap. When the magnetic field is beyond some critical
value, a quantum phase transition occurs. However, the correlation functions
around the SU(4) point and the region with K<<J exhibit distinct behavior. This
results from different structures of excitation spectra in both regime.Comment: 22 pages, no figure
An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain
We study the phase transition of isotropic spin-1 models in the vicinity of
the Uimin-Lai-Sutherland model by using the SU(3)_1 WZW model with certain
marginal perturbations. The unstable RG trajectory by a marginally relevant
perturbation generates a mass gap for the Haldane phase, and thus the
universality class of the transition from the massless phase to the Haldane
phase at ULS point becomes the BKT type. Our results support recent numerical
studies by F\'ath and S\'olyom. In the massless phase, we calculate logarithmic
finite-size corrections of the energy for the SU(\nu)-symmetric and asymmetric
models.Comment: 19 pages, RevTe
SU(4) Spin-Orbital Two-Leg Ladder, Square and Triangle Lattices
Based on the generalized valence bond picture, a Schwinger boson mean field
theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg
SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy
gap, in good agreement with recent numerical calculations. In two-dimensional
square and triangle lattices, the SU(4) Schwinger bosons condense at
(\pi/2,\pi/2) and (\pi/3,\pi/3), respectively. Spin, orbital, and coupled
spin-orbital static susceptibilities become singular at the wave vectors, twice
of which the bose condensation arises at. It is also demonstrated that there
are spin, orbital, and coupled spin-orbital long-range orderings in the ground
state.Comment: 5 page
Non-Abelian Bosonization and Haldane's Conjecture
We study the long wavelength limit of a spin S Heisenberg antiferromagnetic
chain. The fermionic Lagrangian obtained corresponds to a perturbed level 2S
SU(2) Wess-Zumino-Witten model. This effective theory is then mapped into a
compact U(1) boson interacting with Z_{2S} parafermions. The analysis of this
effective theory allows us to show that when S is an integer there is a mass
gap to all excitations, whereas this gap vanishes in the half-odd-integer spin
case. This gives a field theory treatment of the so-called Haldane's conjecture
for arbitrary values of the spin S.Comment: 9 pages REVTeX, no figure
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