251 research outputs found
Phase Diagram of the One Dimensional model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
We have studied the phase diagram of the one dimensional model
with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor
interactions. We have applied the quantum renormalization group (QRG) approach
to get the stable fixed points and the running of coupling constants. The
second order QRG has been implemented to get the self similar Hamiltonian. This
model shows a rich phase diagram which consists of different phases which
possess the quantum spin-fluid and dimer phases in addition to the classical
N\'{e}el and ferromagnetic ones. The border between different phases has been
shown as a projection onto two different planes in the phase space
Magnetization plateaux in dimerized spin ladder arrays
We investigate the ground state magnetization plateaux appearing in spin 1/2
two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and
dimerized zig-zag interchain couplings. Using both Abelian bosonization and
Lanczos methods we find that the system yields rather unusual plateaux and
exhibits massive and massless phases for specific choices or ``tuning'' of
exchange interactions. The relevance of this behavior in the study of
NH_4CuCl_3 is discussed.Comment: 9 pages, RevTeX, 11 postscript figure
Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field
The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonian
and external magnetic fields exceeding the saturation field Bs is considered.
We show that the problem can be exactly mapped onto an effective tight-binding
impurity problem. It allows to obtain explicit exact expressions for the
two-magnon Green's functions for arbitrary dimension and number of
interactions. We apply this theory to a quasi-one dimensional helimagnet with
ferromagnetic nearest neighbor J1 < 0 and antiferromagnetic next-nearest
neighbor J2 > 0 interactions. An outstanding feature of the excitation spectrum
is the existence of two-magnon bound states. This leads to deviations of the
saturation field Bs from its classical value Bs(classical) which coincides with
the one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661
the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin
zone. Based on the two-magnon approach, we propose general analytic expressions
for the saturation field Bs, confirming known previous results for
one-dimensional isotropic systems, but explore also the role of interchain and
long-ranged intrachain interactions as well as of the exchange anisotropy.Comment: 21 pages, 6 Figures. submitted to Phys. Rev.
Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes
We study XXZ Heisenberg models on frustrated triangular lattices wrapped
around a cylinder. In addition to having interesting magnetic phases, these
models are equivalent to Bose-Hubbard models that describe the physical problem
of adsorption of noble gases on the surface of carbon nanotubes. We find
analytical results for the possible magnetization plateau values as a function
of the wrapping vectors of the cylinder, which in general introduce extra
geometric frustration besides the one due to the underlying triangular lattice.
We show that for particular wrapping vectors , which correspond to the
zig-zag nanotubes, there is a macroscopically degenerate ground state in the
classical Ising limit. The Hilbert space for the degenerate states can be
enumerated by a mapping first into a path in a square lattice wrapped around a
cylinder (a Bratteli diagram), and then to free fermions interacting with a
single degree of freedom. From this model we obtain the spectrum in
the anisotropic Heisenberg limit, showing that it is gapless. The continuum
limit is a conformal field theory with compactification radius set
by the physical tube radius. We show that the compactification radius
quantization is exact in the projective limit, and that
higher order corrections reduce the value of . The particular case of a
tube, which corresponds to a 2-leg ladder with cross links, is
studied separately and shown to be gapped because the fermion mapped problem
contains superconducting pairing terms.Comment: 10 pages, 11 figure
Fermionic description of spin-gap states of antiferromagnetic Heisenberg ladders in a magnetic field
Employing the Jordan-Wigner transformation on a unique path and then making a
mean-field treatment of the fermionic Hamiltonian, we semiquantitatively
describe the spin-gap states of Heisenberg ladders in a field. The appearance
of magnetization plateaux is clarified as a function of the number of legs.Comment: 2 pages, 3 figures embedded, J. Phys. Soc. Jpn. Vol. 71, No. 6, 1607
(2002
Quasi-periodic spin chains in a magnetic field
We study the interplay between a (quasi) periodic coupling array and an
external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization
plateaux are obtained by means of Abelian bosonization methods which give rise
to a sufficient quantization condition. The investigation of magnetic phase
diagrams via exact diagonalization of finite clusters finds a complete
agreement with the continuum treatment in a variety of situations.Comment: 4 pages RevTeX, 5 PostScript figures included. Final version to
appear in PR
Magnetic phase diagram of the spin-1/2 antiferromagnetic zigzag ladder
We study the one-dimensional spin-1/2 Heisenberg model with antiferromagnetic
nearest-neighbor J_1 and next-nearest-neighbor J_2 exchange couplings in
magnetic field h. With varying dimensionless parameters J_2/J_1 and h/J_1, the
ground state of the model exhibits several phases including three gapped phases
(dimer, 1/3-magnetization plateau, and fully polarized phases) and four types
of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2,
spin-density-wave (SDW_2), and vector chiral phases. From extensive numerical
calculations using the density-matrix renormalization-group method, we
investigate various (multiple-)spin correlation functions in detail, and
determine dominant and subleading correlations in each phase. For the
one-component TLLs, i.e., the TLL1, SDW_2, and vector chiral phases, we fit the
numerically obtained correlation functions to those calculated from effective
low-energy theories of TLLs, and find good agreement between them. The
low-energy theory for each critical TLL phase is thus identified, together with
TLL parameters which control the exponents of power-law decaying correlation
functions. For the TLL2 phase, we develop an effective low-energy theory of
two-component TLL consisting of two free bosons (central charge c=1+1), which
explains numerical results of entanglement entropy and Friedel oscillations of
local magnetization. Implications of our results to possible magnetic phase
transitions in real quasi-one-dimensional compounds are also discussed.Comment: 22 pages, 17 figures. v2: published versio
Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field
We study the one-dimensional spin-1/2 Heisenberg chain with competing
ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor
J_2 exchange couplings in the presence of magnetic field. We use both numerical
approaches (the density matrix renormalization group method and exact
diagonalization) and effective field-theory approach, and obtain the
ground-state phase diagram for wide parameter range of the coupling ratio
J_1/J_2. The phase diagram is rich and has a variety of phases, including the
vector chiral phase, the nematic phase, and other multipolar phases. In the
vector chiral phase, which appears in relatively weak magnetic field, the
ground state exhibits long-range order (LRO) of vector chirality which
spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of
antiferro-nematic spin correlation, and arises as a result of formation of
two-magnon bound states in high magnetic fields. Similarly, the higher
multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed
through binding of p magnons near the saturation fields, showing quasi-LRO of
antiferro-multipolar spin correlations. The multipolar phases cross over to
spin density wave phases as the magnetic field is decreased, before
encountering a phase transition to the vector chiral phase at a lower field.
The implications of our results to quasi-one-dimensional frustrated magnets
(e.g., LiCuVO_4) are discussed.Comment: v1. 20 pages, 18 figures: v2: 21 pages, 19 figures, Title modified
slightly. Some references, Fig.16, and a note are added. To appear in Phys.
Rev.
Instanton effects and chiral symmetry breaking in QCD2
We discuss the spontaneous breakdown of chiral symmetry in Quantum
Chromodynamics by considering gluonic instanton configurations in the partition
function. It is shown that in order to obtain nontrivial fermionic correlators
in a two dimensional gauge theory for the strong interactions among quarks, a
regular instanton background has to be taken into account. We work over
massless quarks in the -fundamental- representation of SU(N_c). For large N_c,
massive quarks are also considered.Comment: 4 pages, uses espcrc2.sty (attached), updated reference
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