Zoran Ristivojevic

Phase Transition of Interacting Disordered Bosons in One Dimension

Interacting bosons generically form a superfluid state. In the presence of disorder it can get converted into a compressible Bose glass state. Here we study such a transition in one dimension at moderate interaction using bosonization and renormalization group techniques. We derive the two-loop scaling equations and discuss the phase diagram. We find that the correlation functions at the transition are characterized by universal exponents in a finite region around the fixed point.

Excitation spectrum of the Lieb-Liniger model.

We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with the increase of momentum. At lowest momenta good quasiparticles are fermions, while at higher momenta they are Bogoliubov bosons, in accordance with recent studies. In the limit of strong interaction, we analyze the exact solution and find exact results for the spectrum in terms of the asymptotic series. Those results undoubtedly suggest that fermionic quasiparticle excitations actually exist at all momenta for moderate and strong interaction and also at lowest momenta for arbitrary interaction. Moreover, at strong interaction we find highly accurate analytical results for several relevant quantities of the Lieb-Liniger model.

Relaxation of weakly interacting electrons in one dimension

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.

Interaction-induced corrections to conductance and thermopower in quantum wires

We study transport properties of weakly interacting spinless electrons in one-dimensional single-channel quantum wires. The effects of interaction manifest as three-particle collisions due to the severe constraints imposed by the conservation laws on the two-body processes. We focus on short wires where the effects of equilibration on the distribution function can be neglected and the collision integral can be treated in perturbation theory. We find that interaction-induced corrections to conductance and thermopower rely on the scattering processes that change the number of right- and left-moving electrons. The latter requires transition at the bottom of the band which is exponentially suppressed at low temperatures. Our theory is based on the scattering approach that is beyond the Luttinger-liquid limit. We emphasize the crucial role of the exchange terms in the three-particle scattering amplitude that was not discussed in previous studies.

Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas

We study the relaxation of excitations in a system of one-dimensional weakly interacting bosons. Due to residual weak interactions, Bogoliubov quasiparticles in this system have finite lifetimes. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle is disintegration into three others. We focus on phonon quasiparticles and find that their decay rate is proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes.

Superfluid-Bose glass transition in one dimension

We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values.

Interaction effects on thermal transport in quantum wires

We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value.

Super-rough phase of the random-phase sine-Gordon model: Two-loop results

We consider the two-dimensional random-phase sine-Gordon and study the vicinity of its glass transition temperature Tc, in an expansion in small τ = (Tc − T )/Tc ,w hereT denotes the temperature. We derive renormalization group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature T< T c behaves at large distances as � [θ (x) − θ (0)]2 �= A ln 2 (|x|/a) + O[ln(|x|/a)], where the amplitude A is a universal function of temperature A = 2τ 2 − 2τ 3 + O(τ 4 ). This result differs at two-loop order, i.e., O(τ 3 ), from the prediction based on results from the “nearly conformal” field theory of a related fermion model. We also obtain the correction-to-scaling exponent.