Density of bosons in phase-space and the transition from particle to wave behavior

CHRISTOF WETTERICH

Functional renormalization yields a simple unified description of bosons at zero temperature, in arbitrary space dimension $d$ and for $M$ complex fields. We concentrate on nonrelativistic bosons and an action with a linear time derivative. The ordered phase can be associated with a nonzero density of (quasi)particles $n$. The behavior of observables and correlation functions in the ordered phase depends crucially on the momentum ${k}_{\mathit{ph}}$, which is characteristic for a given experiment. For the dilute regime ${k}_{\mathit{ph}}\ensuremath{\gtrsim}{n}^{1∕d}$, the quantum phase transition is simple, with the same ``mean field'' critical exponents for all $d$ and $M$. On the other hand, the dense regime ${k}_{\mathit{ph}}⪡{n}^{1∕d}$ reveals a rather rich spectrum of features, depending on $d$ and $M$. In this regime, one observes for $d\ensuremath{\leqslant}3$ a crossover to a relativistic action with second time derivatives. This admits order for $d>1$, whereas $d=1$ shows a behavior similar to the low temperature phase of the classical two-dimensional $\mathrm{O}(2M)$ models.

A. O. Bolivar

Fernanda M. Chaves, José Wadih Maluf, Ivan Ventura

Satoshi Ejima, Georg Hager, Holger Fehske

We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudosite density-matrix renormalization group technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate, besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge-structure factor, the Luttinger liquid charge exponent, and the single-particle excitation gap for a one-dimensional infinite system.

Peter B. Weichman

Santi Prestipino, Alessandro Sergi, Ezio Bruno

Abstract We study a system of penetrable bosons on a line, focusing on the high-density/weak-interaction regime, where the ground state is, to a good approximation, a condensate. Under compression, the system clusterizes at zero temperature, i.e. particles gather together in separate, equally populated bunches. We compare predictions from the Gross–Pitaevskii (GP) equation with those of two distinct variational approximations of the single-particle state, written as either a sum of Gaussians or the square root of it. Not only the wave functions in the three theories are similar, but also the phase-transition density is the same for all. In particular, clusterization occurs together with the softening of roton excitations in GP theory. Compared to the latter theory, Gaussian variational theory has the advantage that the mean-field energy functional is written in (almost) closed form, which enables us to extract the phase-transition and high-density behaviors in fully analytic terms. We also compute the superfluid fraction of the clustered system, uncovering its exact behavior close, as well as very far away from, the transition.