Numerical Latent Heat Observation of the q=5 Potts Model

Site energy of the five-state ferromagnetic Potts model is numerically calculated at the first-order transition temperature using corner transfer matrix renormalization group (CTMRG) method. The calculated energy of the disordered phase $U^{+}$ is clearly different from that of the ordered phase $U^{-}$. The obtained latent heat $L = U^{-} - U^{+}$ is 0.027, which quantitatively agrees with the exact solution.Comment: 2 pages, Latex(JPSJ style files are included), 2 ps figures, submitted to J. Phys. Soc. Jpn.(short note

Product Wave Function Renormalization Group: construction from the matrix product point of view

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG) method applied to two-dimensional classical lattice models. We use the fact that the largest-eigenvalue eigenvector of T can be approximated by a state vector created from the upper or lower half of a finite size cluster. Decomposition of the obtained state vector into the MPS gives a way of extending the MPS, at the system size increment process in the infinite system DMRG algorithm. As a result, we successfully give the physical interpretation of the product wave function renormalization group (PWFRG) method, and obtain its appropriate initial condition.Comment: 8 pages, 8 figure

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.Comment: 8 pages, LaTeX (using jpsj.sty), 4 non-embedded figures, submitted to J. Phys. Soc. Jp

Incommensurate structures studied by a modified Density Matrix Renormalization Group Method

A modified density matrix renormalization group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest- neighbor Ising (ATNNI) model and the anisotropic triangular next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i. e. the non-existence of the Lifshitz point in phase diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB, presented at MECO'24 1999 (Wittenberg, Germany

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Implication of Compensator Field and Local Scale Invariance in the Standard Model

We introduce Weyl's scale symmetry into the standard model (SM) as a local symmetry. This necessarily introduces gravitational interactions in addition to the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X U(1). The only other new ingredients are a new scalar field \sigma and the gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that the system admits the St\" uckelberg-type compensator. The \sigma couples to the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\" uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg formalism corresponds to \sigma = M_P, and the Hilbert action is induced automatically. In this sense, our model presents yet another mechanism for breaking scale invariance at the classical level. We show that our model naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The necessary ingredients for describing chaotic inflation in the SM as entertained by Bezrukov and Shaposhnikov [17] have been provided by our original model [8]. We regret their omission in citing our original model [8

Phase Transition of the Ising model on a Hyperbolic Lattice

The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group (CTMRG) method. Calculated correlation length is always finite even at the transition temperature, where mean-field like behavior is observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure

Structure of Metastable States in Phase Transitions with High-Spin Low-Spin Degree of Freedom

Difference of degeneracy of the low-spin (LS) and high-spin (HS) states causes interesting entropy effects on spin-crossover phase transitions and charge transfer phase transitions in materials composed of the spin-crossover atoms. Mechanisms of the spin-crossover (SC) phase transitions have been studied by using Wajnflasz model, where the degeneracy of the spin states (HS or LS) is taken into account and cooperative natures of the spin-crossover phase transitions have been well described. Recently, a charge transfer (CT) phase transition due to electron hopping between LS and HS sites has been studied by using a generalized Wajnflasz model. In the both systems of SC and CT, the systems have a high temperature structure (HT) and a low temperature structure (LT), and the change between them can be a smooth crossover or a discontinuous first order phase transition depending on the parameters of the systems. Although apparently the standard SC system and the CT system are very different, it is shown that both models are equivalent under a certain transformation of variables. In both systems, the structure of metastable state at low temperatures is a matter of interest. We study temperature dependence of fraction of HT systematically in a unified model, and find several structures of equilibrium and metastable states of the model as functions of system parameters. In particular, we find a reentrant type metastable branch of HT in a low temperature region, which would play an important role to study the photo-irradiated processes of related materials.Comment: 19 pages, 11 figure

Density Matrix and Renormalization for Classical Lattice Models

We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are briefly discussed.Comment: 21 pages, Latex, 14 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems

Hyperbolic Deformation on Quantum Lattice Hamiltonians

A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to $\cosh j \lambda$, where $j$ is the lattice index and where $\lambda \ge 0$ is a deformation parameter. In the limit $\lambda \to 0$ the Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians is induced by the corner Hamiltonians. As a simple example, we investigate the ground state of the deformed $S = 1/2$ Heisenberg spin chain by use of the density matrix renormalization group (DMRG) method. It is shown that the ground state is dimerized when $\lambda$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $\lambda$.Comment: 5 pages, 4 figure