Correlated tunneling and the instability of the fractional quantum Hall edge

We consider a class of interaction terms that describes correlated tunneling of composite fermions between effective Landau levels. Despite being generic and of similar strength to that of the usual density-density couplings, these terms are not included in the accepted theory of the edges of fractional quantum Hall systems. Here we show that they may lead to an instability of the edge towards a new reconstructed state with additional channels, and thereby demonstrate the incompleteness of the traditional edge theory.Comment: Published versio

Quantum Monte Carlo study of a bilayer U(2)×U(2)U(2)\times U(2) symmetric Hubbard model

We carry out a sign-problem-free quantum Monte Carlo calculation of a bilayer model with a repulsive intra-layer Hubbard interaction and a ferromagnetic inter-layer interaction. The latter breaks the global $SU(2)$ spin rotational symmetry but preserves a $U(2)\times U(2)$ invariance under mixing of same-spin electrons between layers. We show that despite the difference in symmetry, the bilayer model exhibits the same qualitative features found in the single-layer Hubbard model. These include stripe phases, whose nature is sensitive to the presence of next-nearest-neighbor hopping, a maximum in the Knight shift that moves to lower temperatures with increasing hole doping, and lack of evidence for intra-layer $d$-wave superconductivity. Instead, we find a superconducting phase whose critical temperature traces a dome as a function of doping and is due to inter-layer spin-polarized pairing that is induced by the ferromagnetic interaction.Comment: 10 pages, 10 figure

Dynamical transitions from slow to fast relaxation in random open quantum systems

We explore the effects of spatial locality on the dynamics of random quantum systems subject to a Markovian noise. To this end, we study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose entries decay as power laws of distance, with distinct exponents $\alpha_H, \alpha_L$. The steady state is always featureless, but the rate at which it is approached exhibits three phases depending on $\alpha_H$ and $\alpha_L$: a phase where the approach is asymptotically exponential as a result of a gap in the spectrum of the Lindblad superoperator that generates the dynamics, and two gapless phases with subexponential relaxation, distinguished by the manner in which the gap decreases with system size. Within perturbation theory, the phase boundaries in the $(\alpha_H, \alpha_L)$ plane differ for weak and strong dissipation, suggesting phase transitions as a function of noise strength. We identify nonperturbative effects that prevent such phase transitions in the thermodynamic limit.Comment: 5+20 pages, 4+26 figure