Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength $\lambda$, in all models where this coupling depends only on phonon momentum $q$. In the SSH model the coupling also depends on the electron momentum $k$; we find it has a sharp transition, at a critical coupling strength $\lambda_c$, between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at $\lambda = \lambda_c$, except the average number of phonons in the polaronic cloud. This result is representative of all polarons with coupling depending on $k$ and $q$, and will have important experimental consequences (eg., in ARPES and conductivity experiments)

Quantum Dynamics of a Bose Superfluid Vortex

We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid, in the temperature regime where the normal fluid density $\rho_n(T)$ is small. The coupling between the vortex "zero mode" and the quasiparticles has no term linear in the quasiparticle variables -- the lowest-order coupling is quadratic. We find that as a function of the dimensionless frequency $\tilde \Omega = \hbar \Omega/k_BT$, the standard Hall-Vinen/Iordanskii equations are valid when $\tilde \Omega \ll 1$ (the "classical regime"), but elsewhere, the equations of motion become highly retarded, with significant experimental implications when $\tilde \Omega \gtrsim 1$.Comment: 12 pages (4 pages + supp info), 2 figures, accepted to PR

Charge-Spin Separation in 2D Fermi Systems: Singular Interactions as Modified Commutators, and Solution of 2D Hubbard Model in Bosonized Approximation

The general 2-dimensional fermion system with repulsive interactions (typified by the Hubbard Model) is bosonized, taking into account the finite on-shell forward scattering phase shift derived in earlier papers. By taking this phase shift into account in the bosonic commutation relations a consistent picture emerges showing the charge-spin separation and anomalous exponents of the Luttinger liquid.Comment: Latex file 14 pages. email: [email protected]

Quantum Relaxation of Magnetisation in Magnetic Particles

At temperatures below the magnetic anisotropy energy, monodomain magnetic systems (small particles, nanomagnetic devices, etc.) must relax quantum mechanically. This quantum relaxation must be mediated by the coupling to both nuclear spins and phonons (and electrons if either particle or substrate is conducting. We analyze the effect of each of these couplings, and then combine them. Conducting systems can be modelled by a "giant Kondo" Hamiltonian, with nuclear spins added in as well. At low temperatures, even microscopic particles on a conducting substrate (containing only $10-50$ spins) will have their magnetisation frozen over millenia by a combination of electronic dissipation and the "degeneracy blocking" caused by nuclear spins. Raising the temperature leads to a sudden unblocking of the spin dynamics at a well defined temperature. Insulating systems are quite different. The relaxation is strongly enhanced by the coupling to nuclear spins. At short times the magnetisation of an ensemble of particles relaxes logarithmically in time, after an initial very fast decay; this relaxation proceeds entirely via the nuclear spins. At longer times phonons take over, but the decay rate is still governed by the temperature-dependent nuclear bias field acting on the particles - decay may be exponential or power-law depending on the temperature. The most surprising feature of the results is the pivotal role played by the nuclear spins. The results are relevant to any experiments on magnetic particles in which interparticle dipolar interactions are unimportant. They are also relevant to future magnetic device technology.Comment: 30 pages, RevTex, e:mail , Submitted to J.Low Temp.Phys. on 1 Nov. 199

Suppression of tunneling by interference in half-integer--spin particles

Within a wide class of ferromagnetic and antiferromagnetic systems, quantum tunneling of magnetization direction is spin-parity dependent: it vanishes for magnetic particles with half-integer spin, but is allowed for integer spin. A coherent-state path integral calculation shows that this topological effect results from interference between tunneling paths.Comment: 14 pages (RevTeX), 2 postscript figures available upon reques

On the Stability and Single-Particle Properties of Bosonized Fermi Liquids

We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth non-singular Fermi liquid interactions we obtain Shankar's renormalization- group flows and reproduce well known results for quasi-particle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero sound modes and present a concise derivation of both the spin and the charge collective mode equations. Finally we discuss some aspects of singular Fermi liquid interactions.Comment: 13 pages plus three postscript figures appended; RevTex 3.0; BUP-JBM-

Quantum Walks, Quantum Gates and Quantum Computers

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between quantum walk Hamiltonians and Hamiltonians for qubit systems and quantum circuits; this is done for both a single- and multi-excitation coding, and for more general mappings. Specific examples of spin chains, as well as static and dynamic systems of qubits, are mapped to quantum walks, and walks on hyperlattices and hypercubes are mapped to various gate systems. We also show how to map a quantum circuit performing the quantum Fourier transform, the key element of Shor's algorithm, to a quantum walk system doing the same. The results herein are an essential preliminary to a Hamiltonian formulation of quantum walks in which coupling to a dynamic quantum environment is included.Comment: 17 pages, 10 figure

Macroscopic Quantum Tunneling of a Domain Wall in a Ferromagnetic Metal

The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic metal is studied based on the Hubbard model. It is found that the ohmic dissipation is present even at zero temperature due to the gapless Stoner excitation, which is the crucial difference from the case of the insulating magnet. The dissipative effect is calculated as a function of width of the wall and is shown to be effective in a thin wall and in a weak ferromagnet. The results are discussed in the light of recent experiments on ferromagnets with strong anisotropy. PACS numbers:75.60.Ch, 03.65.Sq, 75.10.LpComment: 13page

Quantum Thermoactivation of Nanoscale Magnets

The integral relaxation time describing the thermoactivated escape of a uniaxial quantum spin system interacting with a boson bath is calculated analytically in the whole temperature range. For temperatures T much less than the barrier height \Delta U, the level quantization near the top of the barrier and the strong frequency dependence of the one-boson transition probability can lead to the regularly spaced deep minima of the thermoactivation rate as a function of the magnetic field applied along the z axis.Comment: 4 pages, no figures, rejected from Phys. Rev. Let