arXiv subjects

Hosho Katsura

Publications and source records attributed to Hosho Katsura.

At least 127 records · Page 7Linked to original sources

arXiv2010

Entanglement in valence-bond-solid states on symmetric graphs

We study quantum entanglement in the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model defined on two-dimensional graphs with reflection and/or inversion symmetry. The ground state of this spin model is known as the valence-bond-solid state. We investigate the properties of reduced density matrix of a subsystem which is a mirror image of the other one. Thanks to the reflection symmetry, the eigenvalues of the reduced density matrix can be obtained by numerically diagonalizing a real symmetric matrix whose elements are calculated by Monte Carlo integration. We calculate the von Neumann entropy of the reduced density matrix. The obtained results indicate that there is some deviation from the naive expectation that the von Neumann entropy per valence bond on the boundary between the subsystems is $\ln 2$. This deviation is interpreted in terms of the hidden spin chain along the boundary between the subsystems. In some cases where graphs are on ladders, the numerical results are analytically or algebraically confirmed.

quant-ph↗

arXiv2010

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.

cond-mat.stat-mech↗

arXiv2009

Electro-spinon in one-dimensional Mott insulator

The low-energy dynamical optical response of dimerized and undimerized spin liquid states in a one-dimensional charge transfer Mott insulator is theoretically studied. An exact analysis is given for the low-energy asymptotic behavior using conformal field theory for the undimerized state. In the dimerized state, the infrared absorption due to the bound state of two solitons, i.e, the breather mode, is predicted with an accurate estimate for its oscillator strength, offering a way to detect experimentally the excited singlet state. Effects of external magnetic fields are also discussed.

cond-mat.str-el↗

arXiv2009

Quantum spin Hall effect in a transition metal oxide Na2IrO3

We study theoretically the electronic states in a $5d$ transition metal oxide Na$_2$IrO$_3$, in which both the spin-orbit interaction and the electron correlation play crucial roles. Tight-binding model analysis together with the fisrt-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Due to the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.

cond-mat.str-el↗

arXiv2008

Current-induced dynamics of spiral magnet

We study the dynamics of the spiral magnet under the charge current by solving the Landau-Lifshitz-Gilbert equation numerically. In the steady state, the current ${\vec j}$ induces (i) the parallel shift of the spiral pattern with velocity $v=(β/α)j$ ($α$, $β$: the Gilbert damping coefficients), (ii) the uniform magnetization $M$ parallel or anti-parallel to the current depending on the chirality of the spiral and the ratio $β/ α$, and (iii) the change in the wavenumber $k$ of the spiral. These are analyzed by the continuum effective theory using the scaling argument, and the various nonequilibrium phenomena such as the chaotic behavior and current-induced annealing are also discussed.

cond-mat.str-el↗

arXiv2008

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.

quant-ph↗

arXiv2008

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.

quant-ph↗

arXiv2008

Quantum Dynamics of Multiferroic Helimagnets: a Schwinger-Boson Approach

We study the quantum dynamics/fluctuation of the cycloidal helical magnet in terms of the Schwinger boson approach. In sharp contrast to the classical fluctuation, the quantum fluctuation is collinear in nature which gives rise to the collinear spin density wave state slightly above the helical cycloidal state as the temperature is lowered. Physical properties such as the reduced elliptic ratio of the spiral, the neutron scattering and infrared absorption spectra are discussed from this viewpoint with the possible relevance to the quasi-one dimensional LiCu$_2$O$_2$ and LiCuVO$_4$.

cond-mat.str-el↗

arXiv2008

Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are $S=1,2$ dimerized Heisenberg chains and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.

cond-mat.str-el↗

arXiv2008

Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist

We have discussed a consistency condition of Berry phases defined by a local gauge twist and spatial symmetries of the many body system. It imposes a non trivial gap closing condition under the gauge twist in both finite- and infinite-size systems. It also implies a necessary condition for the gapped and unique ground state. As for the simplest case, it predicts an inevitable gap closing in the Heisenberg chain of half integer spins. Its relation to the Lieb-Schultz-Mattis theorem is discussed based on the symmetries of the twisted Hamiltonian. The discussion is also extended to the (approximately) degenerated multiplet and fermion cases. It restricts the number of the states in the low energy cluster of the spectrum by the filling of the fermions. Constraints by the reflection symmetry are also discussed.

cond-mat.str-el↗

arXiv2007

Entanglement in an SU(n) Valence-Bond-Solid State

We investigate entanglement properties in the ground state of the open/periodic SU($n$) generalized valence-bond-solid state consisting of representations of SU($n$). We obtain exact expression for the reduced density matrix of a block of contiguous spins and explicitly evaluate the von Neumann and the Rényi entropies. We discover that the Rényi entropy is independent of the parameter $α$ in the limit of large block sizes and its value $2 \log n$ coincides with that of von Neumann entropy. We also find the direct relation between the reduced density matrix of the subsystem and edge states for the corresponding open boundary system.

quant-ph↗

arXiv2007

Entanglement Entropy in the Calogero-Sutherland Model

We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the reduced density matrix and the entanglement entropy in the limit of an infinite number of particles traced out. From these results, we obtain an upper bound value of the entanglement entropy. This upper bound has a clear interpretation in terms of fractional exclusion statistics.

cond-mat.stat-mech↗

arXiv2007

Exact Analysis of Entanglement in Gapped Quantum Spin Chains

We investigate the entanglement properties of the valence-bond-solid states with generic integer-spin $S$. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, $2 \log_2 (S+1)$, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose a novel application of the edge state as a qubit for quantum computation.

cond-mat.str-el↗

arXiv2007

Nonequilibrium Kondo problem with spin-dependent chemical potentials: Exact results

We give a brief review of the Kondo effect and exactly solve the nonequilibrium Kondo problem at the special point in the parameter space of the model with spin-dependent chemical potentials. Using the obtained solution, we compute several experimentally observable quantities: charge current, spin current and magnetic properties. Applications to the physically important cases such as the case where the impurity spin is placed in between two ferromagnetically polarized leads are discussed.

cond-mat.str-el↗

arXiv2006

Quantum cloning with nonlocal assistance: Complement of Jozsa's stronger no-cloning theorem

We investigate the cases where a set $S$ of states $\{\ket{ψ_i} \}$ cannot be cloned by itself, but is clonable with the help of another system prepared in state $\hatρ_i$. When $S$ is pair-wise nonorthogonal, it is known that one can generate the copy from $\hatρ_i$ alone, with no interaction with the original system. Here we show that a set containing orthogonal pairs exhibits a property forming a striking contrast; For any such set, there is a choice of $\hatρ_i$ that enables cloning only when the two systems are interacted in a purely quantum manner that is not achievable via classical communication.

quant-ph↗

arXiv2006

Electron localization/delocalization in incommensurate helical magnets

The electronic states in incommensurate (IC) helical magnets are studied theoretically from the viewpoint of the localization/delocalization. It is found that in the multi-band system with relativistic spin-orbit interaction, the electronic wavefunctions show both the extended and localized natures along the helical axis depending on the orbital, helical wavenumber, and the direction of the plane on which spins rotate. Possible realization of this localization is discussed.

cond-mat.str-el↗

arXiv2006

Dynamical magneto-electric coupling in helical magnets

Collective mode dynamics of the helical magnets coupled to electric polarization via spin-orbit interaction is studied theoretically. The soft modes associated with the ferroelectricity are not the transverse optical phonons, as expected from the Lyddane-Sachs-Teller relation, but are the spin waves hybridized with the electric polarization. This leads to the Drude-like dielectric function $ε(ω)$ in the limit of zero magnetic anisotropy. There are two more low-lying modes; phason of the spiral and rotation of helical plane along the polarization axis. The roles of these soft modes in the neutron scattering and antiferromagnetic resonance are revealed, and a novel experiment to detect the dynamical magneto-electric coupling is proposed.

cond-mat.str-el↗

arXiv2006

Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction

We present a theory of Landau-Lifshitz-Gilbert damping $α$ for a localized spin ${\vec S}$ in the junction coupled to the conduction electrons in both leads under an applied volatege $V$. We find the voltage dependence of the damping term reflecting the energy dependence of the density of states. We find the effect is linear in the voltage and cotrolled by particle-hole asymmetry of the leads.

cond-mat.mes-hall↗