Effect of quantum fluctuations on structural phase transitions in SrTiO_3 and BaTiO_3

Using path-integral Monte Carol simulations and an ab initio effective Hamiltonian, we study the effects of quantum fluctuations on structural phase transitions in the cubic perovskite compounds SrTiO3 and BaTiO3. We find quantum fluctuations affect ferroelectric (FE) transitions more strongly than antiferrodistortive (AFD) ones, even though the effective mass of a single FE local mode is larger. For SrTiO3 we find that the quantum fluctuations suppress the FE transition completely, and reduce the AFD transition temperature from 130K to 110K. For BaTiO3, quantum fluctuations do not affect the order of the transition, but do reduce the transition temperature by 35-50 K. The implications of the calculations are discussed.Comment: Revtex (preprint style, 14 pages) + 2 postscript figures. A version in two-column article style with embedded figures is available at http://electron.rutgers.edu/~dhv/preprints/index.html#wz_qs

Twisted Quantum Affine Superalgebra Uq[sl(2∣2)(2)]U_q[sl(2|2)^{(2)}], Uq[osp(2∣2)]U_q[osp(2|2)] Invariant R-matrices and a New Integrable Electronic Model

We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra $U_q[osp(2|2)]$. We work out the tensor product decomposition explicitly and find the decomposition is not completely reducible. Associated with this 4-dimensional grade star representation we derive two $U_q[osp(2|2)]$ invariant R-matrices: one of them corresponds to $U_q[sl(2|2)^{(2)}]$ and the other to $U_q[osp(2|2)^{(1)}]$. Using the R-matrix for $U_q[sl(2|2)^{(2)}]$, we construct a new $U_q[osp(2|2)]$ invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly, this model reduces, in the $q=1$ limit, to the one proposed by Essler et al which has a larger, $sl(2|2)$, symmetry.Comment: 17 pages, LaTex fil

Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: Uq(gl(m∣n))U_q(gl(m|n))}

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum Yang-Baxter equation associated with the one-parameter family of irreps of $U_q(gl(m|n))$, thus obtaining R-matrices which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected

On Type-I Quantum Affine Superalgebras

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple generators (``extra $q$-Serre relations") which need to be imposed to properly define \uqgh and $U_q(osp(2|2n)^{(1)})$. We present a general technique for deriving the spectral parameter dependent R-matrices from quantum affine superalgebras. We determine the R-matrices for the type-I affine superalgebra $U_q(sl(m|n)^{(1)})$ in various representations, thereby deriving new solutions of the spectral-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R-matrices depending on two additional spectral-like parameters, providing generalizations of the free-fermion model.Comment: 23 page

A New Supersymmetric and Exactly Solvable Model of Correlated Electrons

A new lattice model is presented for correlated electrons on the unrestricted $4^L$-dimensional electronic Hilbert space $\otimes_{n=1}^L{\bf C}^4$ (where $L$ is the lattice length). It is a supersymmetric generalization of the Hubbard model, but differs from the extended Hubbard model proposed by Essler, Korepin and Schoutens. The supersymmetry algebra of the new model is superalgebra $gl(2|1)$. The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter $U$, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreps of $gl(2|1)$. On a one-dimensional lattice, the model is exactly solvable by the Bethe ansatz.Comment: 10 pages, LaTex. (final version to appear in Phys.Rev.Lett.

First-principles investigation of 180-degree domain walls in BaTiO_3

We present a first-principles study of 180-degree ferroelectric domain walls in tetragonal barium titanate. The theory is based on an effective Hamiltonian that has previously been determined from first-principles ultrasoft-pseudopotential calculations. Statistical properties are investigated using Monte Carlo simulations. We compute the domain-wall energy, free energy, and thickness, analyze the behavior of the ferroelectric order parameter in the interior of the domain wall, and study its spatial fluctuations. An abrupt reversal of the polarization is found, unlike the gradual rotation typical of the ferromagnetic case.Comment: Revtex (preprint style, 13 pages) + 3 postscript figures. A version in two-column article style with embedded figures is available at http://electron.rutgers.edu/~dhv/preprints/index.html#pad_wal