There are two types of edge states in graphene with/without magnetic field. One is a quantum Hall edge state, which is topologically protected against small perturbation. The other is a chiral zero...
Hall conductance $\sigma_{xy}$ as the Chern numbers of the Berry connection in the magnetic Brillouin zone is calculated for a realistic multi band tight-band model of graphene with non-orthogonal...
Topological meaning of Z$_2$ numbers in time reversal invariant systems (2008)
Fukui, T., Fujiwara, T., Hatsugai, Y.
We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is...
Quantized Berry Phases of a Spin-1/2 Frustrated Two-Leg Ladder with Four-Spin Exchange (2008)
Maruyama, I., Hirano, T., Hatsugai, Y.
A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition...
Non-adiabatic effect on Laughlin's argument of the quantum Hall effect (2008)
We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping....
Topological Identification of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange (2008)
Maruyama, I., Hirano, T., Hatsugai, Y.
A spin-1/2 two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local order parameters. Reflecting local objects, non-trivial ($\pi$) Berry phase is founded on a...
Charge and spin stripe in La$_{2-x}$Sr$_{x}$NiO$_{4}$ (x=1/3,1/2) (2007)
Yamamoto, S., Fujiwara, T., Hatsugai, Y.
Electronic structure of stripe ordered La$_{2-x}$Sr$_{x}$NiO$_{4}$ is investigated. The system with x=1/3 is insulator, in LSDA+U calculations, and shows charge and spin stripe, consistent with the...
Hatsugai, Y., Fukui, T., Aoki, H.
We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i)...
We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical...
Hatsugai, Y., Fukui, T., Aoki, H.
Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two-fold interests:...
For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z$_2$ topological order and the spin Chern number proposed by Kane and Mele and by...
Entanglement entropy and the Berry phase in solid states (2006)
The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection...
Hatsugai, Y., Fukui, T., Suzuki, H.
It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers,...
We propose a criterion to determine the existence of zero-energy edge states for a class of particle-hole symmetric systems. A loop is assigned for each system, and its topology and a symmetry play...
Dirac Monopole and Spin Hall Conductance for Anisotropic Superconductivities (2003)
Concept of the topological order is useful to characterize anisotropic superconductivities. The spin Hall conductance distinguishes superconductivities with the same symmetry. The Chern number for...
Superconductivity and Abelian Chiral Anomalies (2003)
Hatsugai, Y., Ryu, S., Kohmoto, M.
Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are...
Anderson Localization and Polarization (2002)
Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson...
Correlation effects on the Fermi surface of the two-dimensional Hubbard model (2002)
Otsuka, Y., Morita, Y., Hatsugai, Y.
Effects of electron correlation on the Fermi surface is investigated for the two-dimensional Hubbard model by the quantum Monte Carlo method. At first, an infinitesimal doping from the half filling...
Zero-modes in the random hopping model (2002)
Brouwer, P. W., Racine, E., Furusaki, A., Hatsugai, Y., Morita, Y., Mudry, C.
If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We...
Anisotropy on the Fermi Surface of the Two-Dimensional Hubbard Model (2001)
Otsuka, Y., Morita, Y., Hatsugai, Y.
We investigate anisotropic charge fluctuations in the two-dimensional Hubbard model at half filling. By the quantum Monte Carlo method, we calculate a momentum-resolved charge compressibility $\kappa...
Mott Transition in the Two-Dimensional Flux Phase (2001)
Effects of the electron-electron interaction in the two-dimensional flux phase are investigated. We treat the half-filled Hubbard model with a magnetic flux $\pi$ per plaquette by the quantum Monte...
A single-parameter family of lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter $h={$B%((BDelta}/t$ (quantum parameter). A topological number is...
Numerical study of disorder effects on the three-dimensional Hubbard model (2000)
Combined effects of interactions and disorder are investigated using a finite temperature quantum Monte Carlo technique for the three-dimensional Hubbard model with random potentials of a finite...
Landau Levels from the Bethe Ansatz Equations (1999)
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the...
Morita, Y., Ishibashi, K., Hatsugai, Y.
Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon)...
Plateaux Transitions in the Pairing Model:Topology and Selection Rule (1999)
Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by...
Sum Rule of the Hall Conductance in Random Quantum Phase Transition (1999)
Hatsugai, Y., Ishibashi, K., Morita, Y.
The Hall conductance $\sigma_{xy}$ of two-dimensional {\it lattice} electrons with random potential is investigated. The change of $\sigma_{xy}$ due to randomness is focused on. It is a quantum phase...
Collapse of Charge Gap in Random Mott Insulators (1998)
Otsuka, Y., Morita, Y., Hatsugai, Y.
Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state...
Scaling near random criticality in two-dimensional Dirac fermions (1998)
Recently the existence of a random critical line in two dimensional Dirac fermions is confirmed. In this paper, we focus on its scaling properties, especially in the critical region. We treat Dirac...
Kimura, K., Hatsugai, Y., Kohmoto, M.
A one-parameter family of models that interpolates between the periodic Anderson model with infinite repulsion at half-filling and a model whose ground state is exactly the Resonating-Valence-Bond...
Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids (1997)
Wu, Y. S., Yu, Y., Hatsugai, Y., Kohmoto, M.
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several...
Simple Exactly Solvable Models of non-Fermi Liquids (1997)
Lidsky, D., Shiraishi, J., Hatsugai, Y., Kohmoto, M.
We generalize the model of Hatsugai and Kohmoto [J. Phys. Soc. Jpn, 61, 2056 (1992)] and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it...
Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field (1995)
The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A...
Exact Results on Superconductivity due to Interband Coupling (1995)
Morita, Y., Hatsugai, Y., Kohmoto, M.
We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the...
Hatsugai, Y., Kohmoto, M., Koma, T.
We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic...
Morita, Y., Hatsugai, Y., Kohmoto, M.
We study the correlations between eigenvalues of the large random matrices by a renormalization group approach. The results strongly support the universality of the correlations proposed by Br\'ezin...
Universal Behavior of Correlations between Eigenvalues of Random Matrices (1994)
Kobayakawa, T. S., Hatsugai, Y., Kohmoto, M., Zee, A.
The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although...
Phase diagram of the S=1/2 quantum spin chain with bond alternation (1993)
Yamanaka, M., Hatsugai, Y., Kohmoto, M.
We study the ground state properties of the bond alternating $S=1/2$ quantum spin chain whose Hamiltonian is H=\sum_j (S_{2j}^x S_{2j+1}^x +S_{2j}^y S_{2j+1}^y +\lambda S_{2j}^z S_{2j+1}^z ) +\beta...