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Kohei Motegi

Publications and source records attributed to Kohei Motegi.

48 records · Page 3Linked to original sources
arXiv2012

Long time asymptotics of the totally asymmetric simple exclusion process

We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find the relaxation times starting from the step and alternating initial conditions are governed by different eigenvalues of the Markov matrix. In both cases, the scaling exponents of the leading asymptotic amplitudes with respect to the total number of sites are found to be -1. We also study the asymptotics of correlation functions such as the emptiness formation probability.

cond-mat.stat-mech↗
arXiv2012

Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process

The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profile and the existence of the excessive particle currents. Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes of the local densities and currents, we find the scaling exponents with respect to the total number of sites to be -3/2 and -1 respectively.

cond-mat.stat-mech↗
arXiv2012

Spin-spin correlation functions of the q-VBS state of an integer spin model

We consider the valence-bond-solid ground state of the q-deformed higher-spin AKLT model (q-VBS state). We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of the q-VBS state. We compute the longitudinal and transverse spin-spin correlation functions, and determine the correlation amplitudes and correlation lengths for real q.

math-ph↗
arXiv2011

Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions

Correlation functions of the six and nineteen vertex models on an N \times N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by use of the quantum inverse scattering method. The correlation functions which are not "boundary" can be expressed as a linear sum of the boundary correlation functions. For the nineteen vertex model, the boundary correlation functions are shown to be expressed in terms of those for the six vertex model.

math-ph↗
arXiv2011

A note on a boundary one point function for the six vertex model with reflecting end

A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and left reflecting end. It is expressible in terms of a special kind of coordinate space wave functions, which can be expressed as determinants.

math-ph↗
arXiv2010

Two point functions for the six vertex model with reflecting end

The two point functions, which give the probability that the spins turn down at the boundaries, are studied for the six vertex model on a $2N \times N$ lattice with domain wall boundary condition and left reflecting end. We consider two types of two point functions, and express them using determinants.

math-ph↗
arXiv2010

The matrix product representation for the q-VBS state of one-dimensional higher integer spin model

The generalized q-deformed valence-bond-solid groundstate of one-dimensional higher integer spin model is studied. The Schwinger boson representation and the matrix product representation of the exact groundstate is determined, which recovers the former results for the spin-1 case or the isotropic limit. As an application, several correlation functions are evaluated from the matrix product representation.

math-ph↗
arXiv2010

Reflection equation for the N=3 Cremmer-Gervais R-matrix

We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety $\mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$ and $ \mathbb{C} \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$.

math-ph↗
arXiv2008

Density matrix for the kink ground state of the ferromagnetic XXZ chain

The exact expression for the density matrix of the kink ground state of the ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also analyzed. As a consequence, we find that the spin-spin correlation functions decay exponentially for large distances, while the string formation probabilities exhibit Gaussian decay for large strings. We also evaluate the entanglement entropy, which shows interesting behaviors due to the lack of the translational invariance of the state.

cond-mat.stat-mech↗
arXiv2008

Correlation functions of an interacting spinless fermion model at finite temperature

We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time one-particle Green's function at arbitrary particle density is expressed as a multiple integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits.

cond-mat.stat-mech↗
arXiv2008

Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density-density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.

cond-mat.stat-mech↗