arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

At least 127 records · Page 7Linked to original sources

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.

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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.

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arXiv2008

Topological low-energy modes in N=0 Landau levels of graphene: a possibility of a quantum-liquid ground state

We point out that the zero-energy Landau level of Dirac fermions in graphene can be, in the presence of a repulsive electron-electron interaction, split into two (levels) associated with a "bond ordering" formation having a "Kekule pattern", which respects the chiral symmetry. Since the Kekule pattern has a three-fold degeneracy, domain structures are implied, for which we show that in-gap states localized along the domain boundaries exist as topological states. Based on this a possibility of a quantum-liquid ground state of graphene in magnetic fields is discussed.

cond-mat.mes-hall↗

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.

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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.

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arXiv2008

Topological Aspects of Surface States in Semiconductors

Topological aspects of surface states in semiconductors are studied by an adiabatic deformation which connects a realistic system and a decoupled covalent-bond model. Two topological invariants are focused. One is a quantized Berry phase, and the other is a number of the edge states. A winding number as another topological invariant is also considered. The surface states of Si and Ge at (111), (110), and (100) surfaces are classified by the topological invariants. Surface states of the GaAs as heterosemiconductors are also discussed.

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arXiv2007

Cyclotron radiation and emission in graphene

Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf 48}, 559 (1986)].

cond-mat.mes-hall↗

arXiv2007

Levitation and percolation in quantum Hall systems with correlated disorder

We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui \textit{et al}. Distribution of charge density indicates that the extended states at the center of each Landau band have percolating current paths, which are topologically equivalent to the edge states that exist in a system with boundaries. As increasing the strength of disorder, floating feature is observed in an averaged Hall conductance as a function of filling factor. Its relation to the observed experiments is also discussed.

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arXiv2007

Nontrivial quantized Berry phases for itinerant spin liquids

Quantized Berry phases as local order parameters in t-J models are studied. A texture pattern of the local order parameters is topologically stable due to the quantization of non-Abelian Berry phases defined by low-energy states below a spin gap, which exists in the large J/t case with a few electrons. We have confirmed that itinerant singlets in the wide class of t-J models carry the nontrivial Berry phase pi. In the large J/t case for the one-dimensional t-J model, Berry phases are uniformly pi when the number of electrons is N =4n +2, ($n=0,1,2,...$).

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arXiv2007

Entanglement Entropy of One-dimensional Gapped Spin Chains

We investigate the entanglement entropy (EE) of gapped S=1 and $S=1/2$ spin chains with dimerization. We find that the effective boundary degrees of freedom as edge states contribute significantly to the EE. For the $S=1/2$ dimerized Heisenberg chain, the EE of the sufficiently long chain is essentially explained by the localized $S=1/2$ effective spins on the boundaries. As for S=1, the effective spins are also $S=1/2$ causing a Kennedy triplet that yields a lower bound for the EE. In this case, the residual entanglement reduces substantially by a continuous deformation of the Heisenberg model to that of the AKLT Hamiltonian.

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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.

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arXiv2006

U(1) symmetry breaking in one-dimensional Mott insulator studied by the Density Matrix Renormalization Group method

A new type of external fields violating the particle number preservation is studied in one-dimensional strongly correlated systems by the Density Matrix Renormalization Group method. Due to the U(1) symmetry breaking, the ground state has fluctuation of the total particle number, which implies injection of electrons and holes from out of the chain. This charge fluctuation can be relevant even at half-filling because the particle-hole symmetry is preserved with the finite effective field. In addition, we discuss a quantum phase transition obtained by considering the symmetry-breaking fields as a mean field of interchain-hopping.

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arXiv2006

Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems

Recently by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators is given. One requires the ground state is gapped and is invariant under some anti-unitary operation. A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations. As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU(2) twist only at a specific link and define the Berry connection by the derivative. Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link. We numerically apply this scheme for several spin liquids and show its physical validity.

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arXiv2006

Quantized Berry Phases as Local Order Parameters of Quantum Liquids

We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with frustrations and two dimensional extended Su-Schrieffer-Heeger models associated with a random dimer covering. In each phases, the quantized Berry phases, as 0 or $π$, describe the ground state texture pattern of local singlet bonds and dimer bonds. Also possible applications to large classes of correlated electron systems are discussed.

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arXiv2005

Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.

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arXiv2004

A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet

We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing conventional orders. By twisting parameters of boundary conditions, the non-Abelian Chern number are defined for a few low lying states near the ground state in a finite system, which is a ground state multiplet with a possible (topological) degeneracy. We define the system as a topological insulator when energies of the multiplet are well separated from the above. Translational invariant twists up to a unitary equivalence are crutial to pick up only bulk properties without edge states. As a simple example, the setup is applied for a two-dimensional $XXZ$-spin system with an ising anisotropy where the ground state multiplet is composed of doubly almost degenerate states. It gives a vanishing Chern number due to a symmetry. Also Chern numbers for the generic fractional quantum Hall states are discussed shortly.

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arXiv2004

Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders

We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known standard procedure does not work. As an important example, we give novel expressions for a spin Hall conductance for unitary superconductors with equal spin pairing. Generic topological orders will be treated in this unified manner particularly with nontrivial topological degeneracies.

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