Chigak Itoi

Renormalization group flow in one and two matrix models

Abstract Large- N renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling constants by taking account of reparametrization identities. Despite the nonlinearity of the equation, the location of fixed points and the scaling exponents can be extracted from the equation. They agree with the spectrum of relevant operators in the exact solution. A linearized β-function approximates well the global phase structure which includes several nontrivial fixed points. The global renormalization group flow suggests a kind of c -theorem in two-dimensional quantum gravity.

Quantum spin nanotubes?frustration, competing orders and criticalities

Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Néel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced.

Strongly reduced gap in the zigzag spin chain with a ferromagnetic interchain coupling

We study a spin-(1/2) Heisenberg zigzag-spin-chain model near decoupled two chains. Taking into account a symmetry breaking perturbation, we discuss the existence of an energy gap in the ferromagnetic interchain coupling as well as the antiferromagnetic one. In the ferromagnetic model, a marginally relevant fixed line reduces the gap strongly, so that the correlation length becomes an astronomical length scale even in order one coupling. This result agrees with density-matrix renormalization group results.

Nonlinear Renormalization Group Equation for Matrix Models

Abstract An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to vector models, where it is linear. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.

Quantum phase transitions of the asymmetric three-leg spin tube

We investigate quantum phase transitions of the

The spin factor in knots and a relativistic treatment of the Bose-Fermi trasmutation in second-quantized theories

S=\frac{1}{2}

Renormalization group approach to multiple-arc random matrix models

three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the

Geometric description for spinning particles in three dimensions and Chern-Simons-Polyakov theory

c=1

Universal wide correlators in non-gaussian orthogonal, unitary and symplectic random matrix ensembles

conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class.

Spin-Chirality Separation and S_3-Symmetry Breakings in the Magnetization Plateau of the Quantum Spin Tube

Abstract The transmutation of a charged scalar field into a Dirac field is studied. The self-energy of the scalar particle coupled with the Chern-Simons gauge field is evaluated without the loop-splitting regularization. A relation between the spin factor and the self-energy is clarified with the help of a topological feature of a knot. The propagation of a spinning particle in three dimensions is described in terms of the functional integral over random paths with the spin factor. It is shown that the partition function of the charged scalar field is exactly identical with that of a Dirac field in the language of the functional integral.