arXiv subjects

Mitsuhiro Arikawa

Publications and source records attributed to Mitsuhiro Arikawa.

16 recordsLinked to original sources

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

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↗

arXiv2010

Topological quantum phase transition in the BEC-BCS crossover phenomena

A crossover between the Bose Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local Z_2 Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.

cond-mat.str-el↗

arXiv2009

Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

A topological insulator and its spin analogue as a gapped spin liquid have characteristic low energy excitations (edge states) within the gap when the systems have boundaries. This is the bulk-edge correspondence, which implies that the edge states themselves characterize the gapped bulk spin liquid. Based on the general principle, we analyzed the vector chirality phase of the spin-1/2 ladder with ring exchange by using the edge states and the entanglement entropy.

cond-mat.str-el↗

arXiv2008

Edge states for the n=0 Laudau level in graphene

In the anomalous quantum Hall effect (QHE), a hallmark of graphene, nature of the edge states in magnetic fields poses an important question, since the edge and bulk should be intimately related in QHE. Here we have theoretically studied the edge states, focusing on the E=0 edge mode, which is unusual in that the mode is embedded right within the n=0 bulk Landau level, while usual QHE edge modes reside across adjacent Landau levels. Here we show that the n=0 Landau level, including the edge mode, has a wave function amplitude accumulated along zigzag edges whose width scales with the magnetic length, l_B. This contrasts with the usual QHE where the charge is depleted from the edge. The implications are: (i) The E=0 edge states in strong magnetic fields have a topological origin in the honeycomb lattice, so that they are outside the continuum ("massless Dirac") model. (ii) The edge-mode contribution decays only algebraically into the bulk, but this is "topologically" compensated by the bulk contribution, resulting in the accumulation over l_B. (iii) The real space behavior obtained here should be observable in STM experiments.

cond-mat.mes-hall↗

arXiv2008

Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band

While usual edge states in the quantum Hall effect(QHE) reside between adjacent Landau levels, QHE in graphene has a peculiar edge mode at E=0 that reside right within the n=0 Landau level as protected by the chiral symmetry. We have theoretically studied the edge states to show that the E=0 edge mode, despite being embedded in the bulk Landau level, does give rise to a wave function whose charge is accumulated along zigzag edges. This property, totally outside continuum models, implies that the graphene QHE harbors edges distinct from ordinary QHE edges with their topological origin. In the charge accumulation the bulk states re-distribute their charge significantly, which may be called a topological compensation of charge density. The real space behavior obtained here should be observable in an STM imaging.

cond-mat.mes-hall↗

arXiv2007

Exact density matrix of the Gutzwiller wave function: II. Minority spin component

The density matrix, i.e. the Fourier transform of the momentum distribution, is obtained analytically for all magnetization of the Gutzwiller wave function in one dimension with exclusion of double occupancy per site. The present result complements the previous analytic derivation of the density matrix for the majority spin. The derivation makes use of a determinantal form of the squared wave function, and multiple integrals over particle coordinates are performed with the help of a diagrammatic representation. In the thermodynamic limit, the density matrix at distance x is completely characterized by quantities v_c x and v_s x, where v_s and v_c are spin and charge velocities in the supersymmetric t-J model for which the Gutzwiller wave function gives the exact ground state. The present result then gives the exact density matrix of the t-J model for all densities and all magnetization at zero temperature. Discontinuity, slope, and curvature singularities in the momentum distribution are identified. The momentum distribution obtained by numerical Fourier transform is in excellent agreement with existing result.

cond-mat.str-el↗

arXiv2006

Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field

The dynamical spin structure factor S^{zz}(Q,omega) in the small momentum region is derived analytically for the one-dimensional supersymmetric t-J model with 1/r^2 interaction. Strong spin-charge separation is found in the spin dynamics. The structure factor S^{zz}(Q,omega) with a given spin polarization does not depend on the electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S^{zz}(Q,omega). These results are derived via solution of the SU(2,1) Sutherland model in the strong coupling limit.

cond-mat.str-el↗

arXiv2006

Spinon excitations in the XX chain: spectra, transition rates, observability

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.

cond-mat.str-el↗

arXiv2005

Spin Nematic Phase in S=1 Triangular Antiferromagnets

Spin nematic order is investigated for a S=1 spin model on triangular lattice with bilinear-biquadratic interactions. We particularly studied an antiferro nematic order phase with three-sublattice structure, and magnetic properties are calculated at zero temperature by means of bosonization. Two types of bosonic excitations are found. One is a gapless excitation with linear energy dispersion around $k \sim 0$, and this leads to a finite spin susceptibility at T=0 and would have a specific heat $C(T) \sim T^2$ at low temperatures. These behaviors can explain many of characteristic features of recently discovered spin liquid state in the triangular magnet, NiGa2S4.

cond-mat.str-el↗

arXiv2001

Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction

The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A^+(k,omega) has a simple analytic form with contributions from one spinon, one holon and one antiholon all of which obey fractional statistics. The upper edge of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.

cond-mat.str-el↗

arXiv1999

Exact Dynamics of the SU(K) Haldane-Shastry Model

The dynamical structure factor $S(q,ω)$ of the SU(K) (K=2,3,4) Haldane-Shastry model is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of free quasi-particles which are generalization of spinons in the SU(2) case; the excited states relevant to $S(q,ω)$ consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Near the boundaries of the region where $S(q,ω)$ is nonzero, $S(q,ω)$ shows the power-law singularity. It is found that the divergent singularity occurs only in the lowest edges starting from $(q,ω) = (0,0)$ toward positive and negative q. The analytic result is checked numerically for finite systems via exact diagonalization and recursion methods.

cond-mat.str-el↗

arXiv1999

Exact dynamical structure factor of the degenerate Haldane-Shastry model

The dynamical structure factor $S(q,ω)$ of the K-component (K = 2,3,4) spin chain with the 1/r^2 exchange is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of a free quasi-particle picture which is generalization of the spinon picture in the SU(2) case; the excited states consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Divergent singularities of $S(q,ω)$ at the spectral edges are derived analytically. The analytic result is checked numerically for finite systems.

cond-mat.str-el↗

arXiv1999

Dynamical correlation functions of the spin Calogero-Sutherland model

The thermodynamic limit of the dynamical density and spin-density two-point correlation functions for the spin Calogero-Sutherland model are derived from Uglov's finite-size results. The resultant formula for the density two-point correlation function is consistent with the previous conjecture on the basis of the minimal number of elementary excitations.

cond-mat.str-el↗

arXiv1999

Exact Charge Dynamics in the Supersymmetric t-J Model with Inverse-Square Interaction

Dynamical charge structure factor $N(Q,ω)$ with $Q$ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with $1/r^2$ interaction. Strong spin-charge separation in dynamics is found. $N(Q,ω)$ with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to $N(Q,ω)$. These results together with generalized ones for the SU($K$,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.

cond-mat.str-el↗

arXiv1997

Elementary Excitations and Dynamical Correlation Functions of the Calogero-Sutherland Model with Internal Symmetry

We consider the physical properties of elementary excitations of the Calogero-Sutherland (CS) model with SU(K) internal symmetry. From the results on the thermodynamics of this model, we obtain the charge, spin, and statistics of elementary excitations. Combining this knowledge and the known results on the dynamics in the spinless CS model, we propose the expression for the dynamical correlation functions of the SU(K) CS model. In the asymptotic region, we confirm the consistency of our results with predictions from conformal field theory.

cond-mat.str-el↗