Interactions and phase transitions on graphene's honeycomb lattice

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and of the magnetic field are discussed.Comment: four pages, one figure; few typos corrected, references adde

Chains of Quasi-Classical Informations for Bipartite Correlations and the Role of Twin Observables

Having the quantum correlations in a general bipartite state in mind, the information accessible by simultaneous measurement on both subsystems is shown never to exceed the information accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite- subsystem) observables are shown to be responsible both for the amount of quasi-classical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.Comment: 7 pages, Latex2e, selected for the December 2002 issue of the Virtual Journal of Quantum Informatio

Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene

We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive and negative energy eigenstates. Among other systems, the resulting Hamiltonian describes the s-wave superconducting vortex at the surface of the topological insulator, at a finite chemical potential, and in the presence of both Zeeman and orbital couplings to the external magnetic field. Here we find that the bound zero-mode exists only when the Zeeman term is below a critical value. Other physical realizations pertaining to graphene are considered, and some novel zero-energy wave functions are analytically computed.Comment: 6 revtex pages; typos corrected, published versio

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.Comment: RevTex, 4 pages, 1 ps figur

Superconducting zero temperature phase transition in two dimensions and in the magnetic field

We derive the Ginzburg-Landau-Wilson theory for the superconducting phase transition in two dimensions and in the magnetic field. Without disorder the theory describes a fluctuation induced first-order quantum phase transition into the Abrikosov lattice. We propose a phenomenological criterion for determining the transition field and discuss the qualitative effects of disorder. Comparison with recent experiments on MoGe films is discussed.Comment: 7 pages, 2 figure

QED_3 theory of underdoped high temperature superconductors II: the quantum critical point

We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to 3D XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields $N$, and we estimate the correlation length exponent (nu = 0.65) and the vortex field anomalous dimension(eta_Phi=-0.48) at the quantum critical point for the physical case N=2. The stable critical point in the theory disappears for the number of Dirac fermions N > N_c, with N_c ~ 3.4 in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.Comment: 13 pages including figures in tex

Derivation of the quantum probability law from minimal non-demolition measurement

One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as ideal measurement, implies the probability law in a simple way. Namely, the very requirement of minimal change of state, put in proper mathematical form, gives the well known Lueders formula, which contains the probability rule.Comment: 8 page

Finite temperature transport at the superconductor-insulator transition in disordered systems

I argue that the incoherent, zero-frequency limit of the universal crossover function in the temperature-dependent conductivity at the superconductor-insulator transition in disordered systems may be understood as an analytic function of dimensionality of system d, with a simple pole at d=1. Combining the exact result for the crossover function in d=1 with the recursion relations in d=1+\epsilon, the leading term in the Laurent series in the small parameter \epsilon for this quantity is computed for the systems of disordered bosons with short-range and Coulomb interactions. The universal, low-temperature, dc critical conductivity for the dirty boson system with Coulomb interaction in d=2 is estimated to be 0.69 (2e)^2 /h, in relatively good agreement with many experiments on thin films. The next order correction is likely to somewhat increase the result, possibly bringing it closer to the self-dual value.Comment: 9 pages, LaTex, no figure

Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping

We study the real time dynamics of the Bose Hubbard model in the presence of time-dependent hopping allowing for a finite temperature initial state. We use the Schwinger-Keldysh technique to find the real-time strong coupling action for the problem at both zero and finite temperature. This action allows for the description of both the superfluid and Mott insulating phases. We use this action to obtain dynamical equations for the superfluid order parameter as hopping is tuned in real time so that the system crosses the superfluid phase boundary. We find that under a quench in the hopping, the system generically enters a metastable state in which the superfluid order parameter has an oscillatory time dependence with a finite magnitude, but disappears when averaged over a period. We relate our results to recent cold atom experiments.Comment: 22 pages, 7 figure

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page