arXiv subjects

Isao Maruyama

Publications and source records attributed to Isao Maruyama.

At least 19 recordsLinked to original sources

arXiv2026

Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism

We study a spin-$S$ ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization $m=(S-1)/S$, which is a ferromagnetic generalization of the Affleck-Kennedy-Lieb-Tasaki model. We find that the VBS state and an antiferromagnetic ground state with magnetization $m=0$ are degenerate for $S=3/2$ and $S=2$ by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing $S$, the magnetization of the ground states is uniquely determined as the fraction $m=(S-1)/S$. This is not just a ferromagnet, but a quantum ferromagnet due to quantum entanglement inherent in VBS states. In the low-energy excitation spectrum, we find the coexistence of the Haldane gap and Goldstone-like ferromagnetic magnon excitation. This ``magnetic chimera'' clearly appears under a finite magnetic field. Finally, we discuss an application to the measurement-based quantum computation and an extension of the Haldane's conjecture.

cond-mat.str-el↗

arXiv2024

Ferromagnetic Haldane state and dimer multiplet state of quantum ferromagnets

We present a theory of the realization of a ferromagnetic Haldane state in a spin-2 bilinear-biquadratic spin system on an orthogonal-dimer chain. The coexistence of a ferromagnetic state and a Haldane state is due to the rigorous correspondence between the eigenstates of a spin-2 model and a spin-1/2 Heisenberg model; i.e., "eigensystem embedding." Numerical exact-diagonalization calculations indicate that the ground state in the model is a fractionally magnetized M = 3/4 Haldane state. Moreover, a ferromagnetic-dimer multiplet state is an exact ground state on a lattice, where the direct product of dimer singlet states is the ground state in a spin-1/2 Heisenberg model that includes one-, two-, and three-dimensional orthogonal-dimer lattices. Eigensystem embedding demonstrates that a quantum ferromagnet can be obtained for an arbitrary spin S >= 2 in any dimension and for any lattice in which anomalous ground states are realized in a spin-1/2 Heisenberg model.

cond-mat.str-el↗

arXiv2023

Theory of Fractionally-magnetized Quantum Ferromagnet

We present a theory to realize entangled quantum spin states with fractional magnetization. The origin of magnetization reduction is partly emergent antiferromagnetism, that is, spin-liquefaction of ferromagnetism. We study a ferromagnetic bilinear coupling region of the spin-$S$ $({\geqq} 1)$ bilinear-biquadratic spin chain based on (i) a rigorous eigenstate correspondence between the spin-$S$ model and spin-$\frac12$ model and (ii) a numerical exact-diagonalization calculation up to $S=3$. As a result, we obtain a fractional magnetized $M=1-1/(2S)$ phase, where ground states have quantum entanglement-reflecting corresponding spin-$\frac12$ antiferromagnetic ground states in a ferromagnetic background. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices even under a magnetic field. This fractional ferromagnetism opens the new research field of quantum ferromagnets.

cond-mat.str-el↗

arXiv2021

Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem

Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D \geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.

cond-mat.mtrl-sci↗

arXiv2018

Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains

We study the fractionally quantized $Z_N$ Berry phase, $γ_N=0, {2π\over N}, {4π\over N},\ldots, {2(N-1)π\over N}$, to characterize local $N$-mer spin structures at magnetization plateaux in spin-1/2 Heisenberg multimer ($N$-mer) models, i.e., highly frustrated $N$-leg ladder models, which are generalizations of an orthogonal dimer chain and have exact ground states in the strong multimer coupling region. We demonstrate that all $N$ types of Berry phases, which characterize magnetization-plateau phases, appear in a magnetic phase diagram when $N=2$ and $4$. We show that magnetization plateau with magnetization $\langle m\rangle$ and $D$-fold degenerated states has $γ_N=π(\langle m\rangle-1) D$, except for the Haldane phase with $γ_N=0$. In addition, we find that a complementary $Z_N$ Berry phase becomes non-zero in the $S=N/2$ Haldane phase for $N=2$ and 4. Because the exact quantization of the $Z_N$ Berry phases is protected by the translational (or rotational) symmetry along the rung direction, the $Z_N$ Berry phase has the potential to be applied for a wide class of magnetization plateaux in coupled multimer systems.

cond-mat.str-el↗

arXiv2016

Determination of Tomonaga-Luttinger parameters for a two-component liquid

We provide evidence for the mapping of critical spin-1 chains, in particular the SU(3) symmetric bilinear-biquadratic model with additional interactions, to free boson theories using exact diagonalization and the density matrix renormalization group algorithm. Using the correspondence with a conformal field theory with central charge c=2, we determine the analytic formulae for the scaling dimensions in terms of four Tomonaga-Luttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these field-theoretic parameters and track their evolution as a function of the parameters of the lattice model.

cond-mat.str-el↗

arXiv2014

Magnetic correlation effects by the topological zero mode in a hydrogenated graphene vacancy $V_{111}$

Electron correlation effects caused by the topological zero mode of a hydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms is discussed theoretically. A Kondo model is derived from the multi-reference representation of the density functional theory, where exchange scattering processes between the zero mode and low-energy modes in the Dirac cones are estimated. Even when the Dirac cone is slightly off from the charge neutral point, a finite on-site correlation energy, $U_0$, for the zero mode of an isolated $V_{111}$ allows the half-filling of the localized level giving a spin $s=1/2$. The anti-ferromagnetic Kondo screening mediated by higher order scattering processes becomes dominant in the dilute limit of the vacancies. Our estimation of relevant two body interactions certifies appearance of the Kondo effect at low temperatures.

cond-mat.mes-hall↗

arXiv2014

Orbital mixture effect on the Fermi surface-$T_c$ correlation in the cuprate superconductors --- bilayer vs single layer

By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first principles, we have obtained a systematic correlation between the Fermi surface warping and the evaluated $T_c$ for various bilayer as well as single-layer cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component on the Fermi surface leads to both of larger Fermi surface warping and higher $T_c$. The theoretical correlation strikingly resembles a systematic plot for the experimentally observed $T_c$ against the Fermi surface warping due to Pavarini {\it et al.} [Phys. Rev. Lett. {\bf 87}, 047003 (2001)], and the present result unambiguously indicates that the $d_{z^2}$ mixture is a key factor that determines $T_c$ in the cuprates.

cond-mat.supr-con↗

arXiv2013

Material Optimization for Fermi Surface Shape Control of Tl-based Cuprate Superconductors

To show an optimization method of element substitution for cuprate superconductors, we investigate Fermi surface shape of TlR2A2Cu3O9 with R=La, Y, and A=Li, Na, K, Rb, Cs. We adopt the generalized gradient approximation in the density-functional theory (DFT-GGA) for the study of over-doped phases of these unknown cuprates. The electronic structures of crystals optimized by DFT-GGA show systematic element dependence in a Fermi surface shape controlling parameter, r, of Cu dx2-y2 bands, where nearly absent dz2 component at the Fermi level and smaller r keeping t1 suggest enhancement of the superconducting transition temperature within the spin-fluctuation mechanism. For TlYRb2Cu3O9, smaller r by a reduction factor larger than 10% compared to a reference system of TlBa2Ca2Cu3O9 (TBCCO) appears in the outer CuO2 plane, but with 12 % reduction in t1. For TlR2Li2Cu3O9, (R=Y, La), smaller r by a factor larger than 1% appears keeping t1 as large as TBCCO in the inner plane. Our method may be used to predict an optimized material structure referencing known cuprate superconductors.

cond-mat.supr-con↗

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

Sine-square deformation of free fermion systems in one and higher dimensions

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[π(x-1/2)/L], where x is the position of the local Hamiltonian and L is the length of the system in the x direction. It has been revealed that when applied to one-dimensional critical systems the SSD realizes the translationally-invariant ground state which is the same as that of the uniform periodic system. In this paper, we propose a simple theory to explain how the SSD maintains the translational invariance in the ground-state wave function. In particular, for a certain one-dimensional system with SSD, it is shown that the ground state is exactly identical with the Fermi sea of the uniform periodic chain. We also apply the SSD to two-dimensional systems and show that the SSD is able to suppress the boundary modulations from the open edges extremely well, demonstrating that the SSD works in any dimensions and in any directions.

cond-mat.stat-mech↗

arXiv2011

Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.

cond-mat.str-el↗

arXiv2011

Z$_2$ topological number of local quantum clusters in the orthogonal dimer model

We have studied the $Z_2$ topological number defined by the Berry phase for the gapped frustrated systems including the orthogonal dimer model which has a direct product state of local quantum clusters as the exact ground state. The $Z_2$ topological number can clarify what kind of the local quantum clusters is formed to lift the macroscopic degeneracy due to frustration, even when the exact ground state is unknown. As a demonstration, the dimer-singlet and plaquette-singlet phase are identified by two kinds of Z$_2$ topological numbers in the Shastry-Sutherland model and its generalization realized experimentally as SrCu$_2$(BO$_3$)$_2$ and CaV$_4$O$_9$.

cond-mat.mtrl-sci↗

arXiv2010

Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional

Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $λ$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced coupling constant, $λ<1$, is defined to reproduce $n_{GS}({\bf r})$ and the ground state energy. Fixing the charge density, possible phase transitions as level crossings detected in a value of the reduced density functional happen only at discrete points along the $λ$ axis. If the density is $v$-representable also for $λ<1$, accumulation of phase transition points is forbidden when $λ\rightarrow 1$. Relevance of the theorems for the multi-reference density functional theory is discussed.

cond-mat.stat-mech↗

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

Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.

cond-mat.stat-mech↗