Time-Reversal Symmetry in Non-Hermitian Systems

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde

Density Matrix Renormalization Group Study of the S=1/2 Anisotropic Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation

The low energy behavior of the S=1/2 antiferromagnetic XY-like XXZ chains with precious mean quasiperiodic exchange modulation is studied by the density matrix renormalization group method. It is found that the energy gap of the chain with length N scales as $\exp (-cN^{\omega})$ with nonuniversal exponent $\omega$ if the Ising component of the exhange coupling is antiferromagnetic. This behavior is expected to be the characteristic feature of the quantum spin chains with relevant aperiodicity. This is in contrast to the XY chain for which the precious mean exchange modulation is marginal and the gap scales as $N^{-z}$. On the contrary, it is also verified that the energy gap scales as $N^{-1}$ if the Ising component of the exhange coupling is ferromagnetic. Our results are not only consistent with the recent bosonization analysis of Vidal, Mouhanna and Giamarchi but also clarify the nature of the strong coupling regime which is inaccesssible by the bosonization approach.Comment: 8 pages, 15 figures, 1 table; Proceedings of the workshop 'Frontiers in Magnetism', Kyoto, Oct. 199

Exact Results on Superconductivity due to Interband Coupling

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 Hamiltonians were diagonalized explicitly. The zero-temperature phase diagrams and the thermodynamic properties are discussed. Several new properties are revealed which are different from those of the BCS-type superconductor

Adiabatic connection between the RVB State and the ground state of the half filled periodic Anderson model

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 state is studied. It is shown numerically that the excitation gap does not collapse. Therefore the ground states of the two models are adiabatically connected.Comment: 6 pages, 3 figures Revte

Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation

Ground state properties of the S=1/2 antiferromagnetic XXZ chain with Fibonacci exchange modulation are studied using the real space renormalization group method for strong modulation. The quantum dynamical critical behavior with a new universality class is predicted in the isotropic case. Combining our results with the weak coupling renormalization group results by Vidal et al., the ground state phase diagram is obtained.Comment: 9 pages, 9 figure

Quasiperiodic Hubbard chains

Low energy properties of half-filled Fibonacci Hubbard models are studied by weak coupling renormalization group and density matrix renormalization group method. In the case of diagonal modulation, weak Coulomb repulsion is irrelevant and the system behaves as a free Fibonacci chain, while for strong Coulomb repulsion, the charge sector is a Mott insulator and the spin sector behaves as a uniform Heisenberg antiferromagnetic chain. The off-diagonal modulation always drives the charge sector to a Mott insulator and the spin sector to a Fibonacci antiferromagnetic Heisenberg chain.Comment: 4 pages, 4 figures; Final version to appear in Phys. Rev. Let

Electronic energy spectra and wave functions on the square Fibonacci tiling

We study the electronic energy spectra and wave functions on the square Fibonacci tiling, using an off-diagonal tight-binding model, in order to determine the exact nature of the transitions between different spectral behaviors, as well as the scaling of the total bandwidth as it becomes finite. The macroscopic degeneracy of certain energy values in the spectrum is invoked as a possible mechanism for the emergence of extended electronic Bloch wave functions as the dimension changes from one to two

Transmission Resonance in an Infinite Strip of Phason-Defects of a Penrose Approximant Network

An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an infinite approximant network in analytical form; b) to determine, also analytically, the quantum resistance of a finite strip of a network under appropriate boundary conditions. As a result of a subtle interplay between topology and phase interferences, we find that a strip of phason-defects along a special symmetry direction of a low 2-d Penrose approximant, leads to the rigorous vanishing of the reflection coefficient for certain energies. A similar behavior appears in a low 3-d approximant. This type of ``resonance" is discussed in connection with the gap structure of the corresponding ordered (undefected) system.Comment: 18 pages special macros jnl.tex,reforder.tex, eqnorder.te

Temporal Oscillation of Conductances in Quantum Hall Effect of Bloch Electrons

We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with a very large frequencies due to quantum fluctuation.Comment: 8 pages, 4 figure

Quantum Hall Effect in Three-dimensional Field-Induced Spin Density Wave Phases with a Tilted Magnetic Field

The quantum Hall effect in the three-dimensional anisotropic tight-binding electrons is investigated in the field-induced spin density wave phases with a magnetic field tilted to any direction. The Hall conductivity, $\sigma_{xy}$ and $\sigma_{xz}$, are shown to be quantized as a function of the wave vector of FISDW, while $\sigma_{yz}$ stays zero, where $x$ is the most conducting direction and $y$ and $z$ are perpendicular to $x$.Comment: 18 pages, REVTeX 3.0, 1 figure is available upon request, to be published in Physical Review