arXiv subjects

Tetsuo Deguchi

Publications and source records attributed to Tetsuo Deguchi.

84 records · Page 5Linked to original sources

arXiv2001

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.

cond-mat.stat-mech↗

arXiv2000

Characteristic length of random knotting for cylindrical self-avoiding polygons

We discuss the probability of random knotting for a model of self-avoiding polygons whose segments are given by cylinders of unit length with radius $r$. We show numerically that the characteristic length of random knotting is roughly approximated by an exponential function of the chain thickness $r$.

cond-mat.stat-mech↗

arXiv2000

The sl_2 loop algebra symmetry of the six-vertex model at roots of unity

We demonstrate that the six vertex model (XXZ spin chain) with $Δ=(q+q^{-1})/2$ and $q^{2N}=1$ has an invariance under the loop algebra of $sl_2$ which produces a special set of degenerate eigenvalues. For $Δ=0$ we compute the multiplicity of the degeneracies using Jordan Wigner techniques

cond-mat.stat-mech↗

arXiv1998

A gapless charge mode induced by the boundary states in the half-filled Hubbard open-chain

We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with L sites, where only one of the boundary sites has a different value of chemical potential. We consider the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. By an analytic method we show that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. It follows that there is a ``surface phase transition'' at some critical value p_c; when p p_c.

cond-mat.stat-mech↗

arXiv1997

Magnetic susceptibility and low-temperature specific-heat of integrable 1-D Hubbard model under open-boundary conditions

The magnetic susceptibility and the low-temperature specific heat of the 1-dimensional Hubbard model under the integrable open-boundary conditions are discussed through the Bethe ansatz with the string hypothesis. The contributions of the boundary fields to both the susceptibility and the specific heat are obtained, and their exact expressions are analytically derived.

cond-mat.str-el↗

arXiv1997

Exact solutions of 1-D Hubbard model with open boundary conditions and the conformal dimensions under boundary magnetic fields

The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we obtain the energy spectrum of the open chain and discuss the effects of boundary magnetic fields applied only at the edges of the chain. Several physical implications of the finite-size spectrum are discussed from the viewpoint of the boundary conformal field theories (BCFT); the conformal dimension of the spin excitation is quite sensitive to the boundary magnetic fields, and this sensitivity can be explained in terms of the $π/2$-phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.

cond-mat.str-el↗

arXiv1997

Diagonalization of 2-D inhomogeneous model related to the Hubbard model

We found the eigenvalues of the transfer matrix for the 2-D inhomogeneous statistical model with twisted boundary condition by using the analytic Bethe Ansatz method. In the uniform case, the derived hamiltonian generalizes the 1-D Hubbard model with the twisted boundary. We also give the energy spectra for the derived hamiltonian.

cond-mat.stat-mech↗

arXiv1996

Analytic Bethe Ansatz for 1-D Hubbard model and twisted coupled XY model

We found the eigenvalues of the transfer matrices for the 1-D Hubbard model and for the coupled XY model with twisted boundary condition by using the analytic Bethe Ansatz method. Under a particular condition the two models have the same Bethe Ansatz equations. We have also proved that the periodic 1-D Hubbard model is exactly equal to the coupled XY model with nontrivial twisted boundary condition at the level of hamiltonians and transfer matrices.

cond-mat↗

arXiv1993

Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial

We discuss multivariable invariants of colored links associated with the $N$-dimensional root of unity representation of the quantum group. The invariants for $N>2$ are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When $(N,3)=1$ and $N$ is odd, the invariant does not vanish for the parallel link (cable) of the knot $3_1$, while the Alexander polynomial vanishes for the cable link.

hep-th↗

arXiv1992

A New Algorithm for Numerical Calculation of Link Invariants

We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^α$ with respect to the system size $N$ . This method gives a new tool for determining topology of knotted closed loops in three dimensions using computers.

hep-th↗

arXiv1992

Invariants of Colored Links and a Property of the Clebsch-Gordan Coefficients of $U_q(g)$

We show that multivariable colored link invariants are derived from the roots of unity representations of $U_q(g)$. We propose a property of the Clebsch-Gordan coefficients of $U_q(g)$, which is important for defining the invariants of colored links. For $U_q(sl_2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the multivariable Alexander polynomial.

hep-th↗

arXiv1992

Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the root of unity representations ($N$-dimensional representations with $q^{2N}=1$) of $U_q(sl(2))$. We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the color representations of $U_q(sl(2))$. We construct invariants of trivalent colored oriented framed graphs from color representations of $U_q(sl(2))$.

hep-th↗