8 research outputs found
Generalization of the U_q(gl(N)) algebra and staggered models
We develop a technique of construction of integrable models with a Z_2
grading of both the auxiliary (chain) and quantum (time) spaces. These models
have a staggered disposition of the anisotropy parameter. The corresponding
Yang-Baxter Equations are written down and their solution for the gl(N) case
are found. We analyze in details the N=2 case and find the corresponding
quantum group behind this solution. It can be regarded as quantum
U_{q,B}(gl(2)) group with a matrix deformation parameter qB with (qB)^2=q^2.
The symmetry behind these models can also be interpreted as the tensor product
of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator
related to deformation parameter -1.Comment: 12 pages ; Latex2
Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds
We investigate the low-temperature phase diagram of the exactly solved su(4)
two-leg spin ladder as a function of the rung coupling and magnetic
field by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a
magnetic field the model exhibits three quantum phases, while in the presence
of a strong magnetic field there is no singlet ground state for ferromagnetic
rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in
the regime H H_{c2} and a
Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical
behaviour derived using the TBA is consistent with the existing experimental,
numerical and perturbative results for the strong coupling ladder compounds.
This includes the spin excitation gap and the critical fields H_{c1} and
H_{c2}, which are in excellent agreement with the experimental values for the
known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12}
N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap
for the weak coupling compounds
with , such as (VO)_2 P_2 O_7, and also show that
the gap opens for arbitrary .Comment: 10 pages, 3 figure
Integrable Ladder t-J Model with Staggered Shift of the Spectral Parameter
The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2
grading along both chain and time directions is presented and an integrable
model of t-J type with staggered disposition along a chain of shifts of the
spectral parameter is constructed. The Hamiltonian of the model is computed in
fermionic formulation. It involves three neighbour site interactions and
therefore can be considered as a zig-zag ladder model. The Algebraic Bethe
Ansatz technique is applied and the eigenstates, along with eigenvalues of the
transfer matrix of the model are found. In the thermodynamic limit, the lowest
energy of the model is formed by the quarter filling of the states by fermions
instead of usual half filling.Comment: Latex2e with amsfonts package; 16 page
Multi-leg integrable ladder models
20 pages; Latex2e with epic,eepic macrosWe construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang-Baxter equations. This construction yields P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry