4,306 research outputs found
Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras
We extend the results of spin ladder models associated with the Lie algebras
to the case of the orthogonal and symplectic algebras $o(2^n),\
sp(2^n)$ where n is the number of legs for the system. Two classes of models
are found whose symmetry, either orthogonal or symplectic, has an explicit n
dependence. Integrability of these models is shown for an arbitrary coupling of
XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late
Exactly solvable su(N) mixed spin ladders
It is shown that solvable mixed spin ladder models can be constructed from
su(N) permutators. Heisenberg rung interactions appear as chemical potential
terms in the Bethe Ansatz solution. Explicit examples given are a mixed
spin-1/2 spin-1 ladder, a mixed spin-1/2 spin-3/2 ladder and a spin-1 ladder
with biquadratic interactions.Comment: 7 pages, Latex, Presented at the Baxter Revolution in Mathematical
Physics Conference, Feb 13-19, 200
Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
Using Yang and Yang's particle-hole description, we present a thorough
derivation of the thermodynamic Bethe ansatz equations for a general
fermionic system in one-dimension for both the repulsive and
attractive regimes under the presence of an external magnetic field. These
equations are derived from Sutherland's Bethe ansatz equations by using the
spin-string hypothesis. The Bethe ansatz root patterns for the attractive case
are discussed in detail. The relationship between the various phases of the
magnetic phase diagrams and the external magnetic fields is given for the
attractive case. We also give a quantitative description of the ground state
energies for both strongly repulsive and strongly attractive regimes.Comment: 22 pages, 2 figures, slight improvements, some extra reference
Magnetic Susceptibility of an integrable anisotropic spin ladder system
We investigate the thermodynamics of a spin ladder model which possesses a
free parameter besides the rung and leg couplings. The model is exactly solved
by the Bethe Ansatz and exhibits a phase transition between a gapped and a
gapless spin excitation spectrum. The magnetic susceptibility is obtained
numerically and its dependence on the anisotropy parameter is determined. A
connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in
the strong coupling regime is made and our results for the magnetic
susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.
Evidence for the super Tonks-Girardeau gas
We provide evidence in support of a recent proposal by Astrakharchik at al.
for the existence of a super Tonks-Girardeau gas-like state in the attractive
interaction regime of quasi-one-dimensional Bose gases. We show that the super
Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in
the integrable interacting Bose gas for which the bosons acquire hard-core
behaviour. The gas-like state properties vary smoothly throughout a wide range
from strong repulsion to strong attraction. There is an additional stable
gas-like phase in this regime in which the bosons form two-body bound states
behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the
super T-G gas-like stat
Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions
Paired states, trions and quarteting states in one-dimensional SU(4)
attractive fermions are investigated via exact Bethe ansatz calculations. In
particular, quantum phase transitions are identified and calculated from the
quarteting phase into normal Fermi liquid, trionic states and spin-2 paired
states which belong to the universality class of linear field-dependent
magnetization in the vicinity of critical points. Moreover, unified exact
results for the ground state energy, chemical potentials and complete phase
diagrams for isospin attractive fermions with external fields
are presented. Also identified are the magnetization plateaux of
and , where is the magnetization saturation value. The
universality of finite-size corrections and collective dispersion relations
provides a further test ground for low energy effective field theory.Comment: 13 pages, 4 figure
Exact solution for random walks on the triangular lattice with absorbing boundaries
The problem of a random walk on a finite triangular lattice with a single
interior source point and zig-zag absorbing boundaries is solved exactly. This
problem has been previously considered intractable.Comment: 10 pages, Latex, IOP macro
Quantum phase diagram of an exactly solved mixed spin ladder
We investigate the quantum phase diagram of the exactly solved mixed
spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of
a magnetic field the model exhibits three quantum phases associated with su(2),
su(4) and su(6) symmetries. In the presence of a strong magnetic field, there
is a third and full saturation magnetization plateaux within the strong
antiferromagnetic rung coupling regime. Gapless and gapped phases appear in
turn as the magnetic field increases. For weak rung coupling, the fractional
magnetization plateau vanishs and exhibits new quantum phase transitions.
However, in the ferromagnetic coupling regime, the system does not have a third
saturation magnetization plat eau. The critical behaviour in the vicinity of
the critical points is also derived systematically using the TBA.Comment: 20 pages, 2 figure
Phase diagram of the su(8) quantum spin tube
We calculate the phase diagram of an integrable anisotropic 3-leg quantum
spin tube connected to the su(8) algebra. We find several quantum phase
transitions for antiferromagnetic rung couplings. Their locations are
calculated exactly from the Bethe Ansatz solution and we discuss the nature of
each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur
Exactly solvable models and ultracold Fermi gases
Exactly solvable models of ultracold Fermi gases are reviewed via their
thermodynamic Bethe Ansatz solution. Analytical and numerical results are
obtained for the thermodynamics and ground state properties of two- and
three-component one-dimensional attractive fermions with population imbalance.
New results for the universal finite temperature corrections are given for the
two-component model. For the three-component model, numerical solution of the
dressed energy equations confirm that the analytical expressions for the
critical fields and the resulting phase diagrams at zero temperature are highly
accurate in the strong coupling regime. The results provide a precise
description of the quantum phases and universal thermodynamics which are
applicable to experiments with cold fermionic atoms confined to one-dimensional
tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16
pages, 6 figure
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