arXiv subjects

Hiroshi Ueda

Publications and source records attributed to Hiroshi Ueda.

51 records · Page 3Linked to original sources

arXiv2012

Stringy excitation and role of UV gluons in lattice QCD

Using SU(3) quenched lattice QCD, we study ground-state and low-lying even-parity excited-state potentials of quark-antiquark systems in terms of the gluon-momentum component in the Coulomb gauge. By introducing UV-cut in the gluon-momentum space, we investigate the "UV-gluon sensitivity" of the ground-state and excited-state potentials and the stringy excitation quantitatively. Even after cutting off high-momentum gluon component above 1.5GeV, the IR part of the ground-state potential is almost unchanged. On the other hand, the change of excited-state potential is more significant by the cut of UV-gluons. However, even after the removal of UV-gluons, the magnitude of the low-lying gluonic excitation remains to be of the order of 1GeV.

hep-lat↗

arXiv2012

Incommensurate Matrix Product State for Quantum Spin Systems

We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The spin rotations decrease the variational energy with accompanying translational symmetry breaking and the rotational symmetry breaking in the spin space even if the Hamiltonian has the both symmetries. The optimized pitch of rotational operator reflects the commensurate/incommensurate properties of spin-spin correlation functions in the $S=1/2$ Heisenberg chain and the $S=1/2$ ferro-antiferro zigzag chain.

cond-mat.str-el↗

arXiv2012

Quantum Entanglement of Tensor Networks with Symmetry Projections

We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero space give logarithmically increasing mutual information with respect to the system size. In the anti-ferromagnetic $S=1/2$ Heisenberg chain and lattice, the optimized energies become accurate numerically by using variational states of the projected tensor network states, because the projections reflecting symmetries of the ground states generate quantum entanglement.

cond-mat.str-el↗

arXiv2011

Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change

As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detect phase transitions accompanied with periodicity change, where the incommensurate MPS is generated by acting local-spin-rotation operators with the incommensurate periodicity on a uniform MPS. As a commensurate/commensurate change, we calculate the partial ferro -- perfect ferro phase transition in the $S=1/2$ Heisenberg model and its critical exponent of the magnetization curve. As a commensurate/incommensurate change, we calculate the S=1 Heisenberg model with bilinear and biquadratic interactions which has periodicity change in the spin-spin correlation function.

cond-mat.str-el↗

arXiv2011

Determination of Boundary Scattering, Intermagnon Scattering, and the Haldane Gap in Heisenberg Chains

Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian DMRG method. The scattering length $a_{\rm b}$ of the boundary coupling and the inter-magnon scattering length $a$ are determined. The scattering length $a_{\rm b}$ is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap $Δ$, the magnon velocity $v$, and $a$ remain constant at the crossover. Our method allowed estimation of the gap of the S=2 AF chain to be $Δ= 0.0891623(9)$ using a chain length longer than the correlation length $ξ$.

cond-mat.str-el↗

arXiv2011

Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -

We investigate excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f_j^{~} = \cosh j λ, where j is the lattice index and λis the deformation parameter. The elementary excitation is well described by a quasiparticle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap Δin the uniform limit λ\rightarrow 0, by means of a finite size scaling with respect to the system size N and the deformation parameter λ.

cond-mat.str-el↗

arXiv2010

Uniform Matrix Product State in the Thermodynamic Limit

We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the calculation of expectation values can reflect the periodicity of the ground state and indicate optimum periodicity of the matrix product state. We discuss the relation between the periodicity and accuracy of magnetization curves. This approach is free from the error due to finite system size, which works well especially for the magnetic plateau problem.

cond-mat.str-el↗

arXiv2010

Scaling Relation for Excitation Energy Under Hyperbolic Deformation

We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical system, the deformation does not strongly modify the ground state. In this situation, the effective Hamiltonian of the quantum system shows that the quasi particle is weakly bounded around the center of the system. By analyzing this binding effect, we derive scaling relations for the mean-square width of confinement, the energy correction with respect to the excitation gap Δ, and the deformation parameter $λ$. This finite-size scaling allows us to investigate excitation gap of 1D non-deformed bulk quantum systems.

cond-mat.other↗

arXiv2010

Transverse Field Ising Model Under Hyperbolic Deformation

Ground state of the one-dimensional transverse field Ising model is investigated under the hyperbolic deformation, where the energy scale of j-th bond is proportional to the function \cosh ( j λ) that contains a parameter λ. Although the Hamiltonian is position dependent, the ground state is nearly uniform and finitely correlated. We observe the energy cross over between the ordered and disordered state with respect to the transverse field. The model shows first order phase transition, and the discontinuities in the magnetization and entanglement entropy at the transition point detect the Ising universality.

cond-mat.stat-mech↗

arXiv2010

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.

cond-mat.stat-mech↗

arXiv2009

A Classical Background for the Wave Function Prediction in the Infinite System DMRG Method

We report a physical background of the wave function prediction in the infinite system density matrix renormalization group (DMRG) method, from the view point of two-dimensional vertex model, a typical lattice model in statistical mechanics. Singular value decomposition applied to rectangular corner transfer matrices naturally draws matrix product representation for the maximal eigenvector of the row-to-row transfer matrix. The wave function prediction can be expressed as the insertion of an approximate half-column transfer matrix. This insertion process is in accordance with the scheme proposed by McCulloch recently.

cond-mat.stat-mech↗

arXiv2009

Gap Estimation by means of Hyperbolic Deformation

We present a way of numerical gap estimation applicable for one-dimensional infinite uniform quantum systems. Using the density matrix renormalization group method for a non-uniform Hamiltonian, which has deformed interaction strength of $j$-th bond proportional to $\cosh λj$, the uniform Hamiltonian is analyzed as a limit of $λ\to 0$. As a consequence of the deformation, an excited quasi-particle is weakly bounded around the center of the system, and kept away from the system boundary. Therefore, insensitivity of an estimated excitation gap of the deformed system to the boundary allows us to have the bulk excitation gap $Δ(λ)$, and shift in $Δ(λ)$ from $Δ(0)$ is nearly linear in $λ$ when $λ\ll 1$. Efficiency of this estimation is demonstrated through application to the S=1 antiferromagnetic Heisenberg chain. Combining the above estimation and another one obtained from the technique of convergence acceleration for finite-size gaps estimated by numerical diagonalizations, we conclude that the Haldane gap is in $[0.41047905,~0.41047931]$.

cond-mat.stat-mech↗

arXiv2008

Finite-size scaling of string order parameters characterizing the Haldane phase

We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem- size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method to directly observe quantum phase transitions.

cond-mat.str-el↗

arXiv2008

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 $\cosh j λ$, where $j$ is the lattice index and where $λ\ge 0$ is a deformation parameter. In the limit $λ\to 0$ 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 $λ$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $λ$.

quant-ph↗

arXiv2008

Two-Site shift Product Wave Function Renormalization Group Method Applied to Quantum Systems

We report a way of wave function estimation for the density matrix renormalization group (DMRG) method applied to quantum systems, which has 2-site modulation, when the system size extension is necessary in both the finite and the infinite algorithms. The estimation is performed by renormalization group (RG) transformation applied to the ground state wave function, which is represented as the matrix product. This RG scheme is known as the product wave function renormalization group (PWFRG) method. In order to treat the 2-site modulation, the operation of the RG transformation is shifted by amount of 2 lattice sites. It turns out that this 2-site shift algorithm provides better wave function estimation in the thermodynamic limit, compared with the previously known PWFRG algorithm.

quant-ph↗