arXiv subjects

Kazumitsu Sakai

Publications and source records attributed to Kazumitsu Sakai.

At least 37 records · Page 2Linked to original sources

arXiv2012

Multiple Schramm-Loewner evolutions for conformal field theories with Lie algebra symmetries

We provide multiple Schramm-Loewner evolutions (SLEs) to describe the scaling limit of multiple interfaces in critical lattice models possessing Lie algebra symmetries. The critical behavior of the models is described by Wess-Zumino-Witten (WZW) models. Introducing a multiple Brownian motion on a Lie group as well as that on the real line, we construct the multiple SLE with additional Lie algebra symmetries. The connection between the resultant SLE and the WZW model can be understood via SLE martingales satisfied by the correlation functions in the WZW model. Due to interactions among SLE traces, these Brownian motions have drift terms which are determined by partition functions for the corresponding WZW model. As a concrete example, we apply the formula to the su(2)k-WZW model. Utilizing the fusion rules in the model, we conjecture that there exists a one-to-one correspondence between the partition functions and the topologically inequivalent configurations of the SLE traces. Furthermore, solving the Knizhnik-Zamolodchikov equation, we exactly compute the probabilities of occurrence for certain configurations (i.e. crossing probabilities) of traces for the triple SLE.

math-ph↗

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↗

arXiv2011

Thermodynamic properties of quantum sine-Gordon spin chain system KCuGaF6

We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF6 by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field H a transverse staggered magnetic field h is induced in this compound owing to the staggered component of the g tensor and the Dzyaloshinskii-Moriya interaction with an alternating D vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with H. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for H // c is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions, significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For H // b, a quantum phase transition between gapless and gapped ground states was observed.

cond-mat.str-el↗

arXiv2010

Spectral Properties of Interacting One-Dimensional Spinless Fermions

The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the spin-1/2 XXZ chain, the difference in the statistics of particles causes substantial effects on spectral features, such as gapless points of dispersion relations and line shapes of spectral functions. In this Letter, we clarify the origin of the differences in spectral features between fermionic and bosonic systems in terms of Bethe ansatz solutions. We also confirm that the two-string solutions have considerable spectral weights in the high-energy regime.

cond-mat.str-el↗

arXiv2009

Spectrum in multi-species asymmetric simple exclusion process on a ring

The spectrum of Hamiltonian (Markov matrix) of a multi-species asymmetric simple exclusion process on a ring is studied. The dynamical exponent concerning the relaxation time is found to coincide with the one-species case. It implies that the system belongs to the Kardar-Parisi-Zhang or Edwards-Wilkinson universality classes depending on whether the hopping rate is asymmetric or symmetric, respectively. Our derivation exploits a poset structure of the particle sectors, leading to a new spectral duality and inclusion relations. The Bethe ansatz integrability is also demonstrated.

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↗

arXiv2007

Dynamical correlation functions of the XXZ model at finite temperature

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.

cond-mat.stat-mech↗

arXiv2005

The extension to the transverse momentum of the statistical parton distributions

By extending the statistical distributions to the transverse degree of freedhom, we account for a multiplicative factor in the Fermi-Dirac functions of the light quarks, we were led to introduce in a previous work to comply with experiment. We can also get light antiquark distributions, similar to those we proposed earlier

hep-ph↗

arXiv2005

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.

cond-mat.stat-mech↗

arXiv2004

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg chain. The energy current is related to one of the non-trivial conserved quantities underlying integrability and therefore both the diagonal and off diagonal dynamical correlations of spin and energy current diverge. The energy-energy and spin-energy current correlations at finite temperatures are exactly calculated by a lattice path integral formulation. The low-temperature behavior of the thermomagnetic (magnetic Seebeck) coefficient is also discussed. Due to effects of strong correlations, we observe the magnetic Seebeck coefficient changes sign at certain interaction strengths and magnetic fields.

cond-mat.stat-mech↗

arXiv2004

Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain

The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for -1<Δ\leq 1 and 1<Δ. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.

cond-mat.stat-mech↗

arXiv2003

Exact results for the thermal and magnetic properties of strong coupling ladder compounds

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)$_2$CuBr$_4$$\cdot$2H$_2$O, Cu$_{2}$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$ etc.

cond-mat.stat-mech↗

arXiv2003

Non-dissipative thermal transport in the massive regimes of the XXZ chain

We present exact results on the thermal conductivity of the one-dimensional spin-1/2 XXZ model in the massive antiferromagnetic and ferromagnetic regimes. The thermal Drude weight is calculated by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy as well as analytical results in the low and high temperature limits are presented. At finite temperature, the thermal Drude weight is finite and hence there is non-dissipative thermal transport even in the massive regime. At low temperature, the thermal Drude weight behaves as $D(T)\sim \exp(-δ/T)/\sqrt{T}$ where $δ$ is the one-spinon (respectively one-magnon) excitation energy for the antiferromagnetic (respectively ferromagnetic) regime.

cond-mat.stat-mech↗

arXiv2003

Next Nearest-Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Critical Region

The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.

cond-mat.stat-mech↗

arXiv2003

Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet

We exactly evaluate the third neighbor correlator and all the possible non-zero correlators of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.

cond-mat.stat-mech↗