We present a Lattice Non-Perturbative Renormalization Group (NPRG) approach to quantum XY spin models by using a mapping onto hardcore bosons. The NPRG takes as initial condition of the renormalization group flow the (local) limit of decoupled sites,
allowing us to take into account the hardcore constraint exactly. The initial condition of the flow is equivalent to the large $S$ classical results of the corresponding spin system. Furthermore, the hardcore constraint is conserved along the RG flow, and we can describe both local and long-distance fluctuations in a non-trivial way. We discuss a simple approximation scheme, and solve the corresponding flow equations. We compute both the zero-temperature thermodynamics and the finite temperature phase diagram on the square and cubic lattices. The NPRG allows us to recover the correct critical physics at finite temperature in two and three dimensions. The results compare well with numerical simulations.
We address the physics of equilibration in ultracold atomic gases following a quench of the interaction parameter. We focus on the momentum distribution of the excitations, $n_{mathbf k}$, and observe that larger ${mathbf k}$ modes will equilibrate f
aster, as has been claimed in recent experimental work. We identify three time regimes. At short times $n_{mathbf k}$ exhibits oscillations; these are damped out at intermediate times where the system appears to be in a false-equilibrium. Finally, at longer times, full equilibration occurs. This false-equilibrium is associated with the necessarily slower relaxation of the condensate which sufficiently high ${mathbf k}$-states (of the excitation response) will then quasi-adiabatically follow. Our work bears on the recent literature focus on interaction quench experiments. We take issue with the fact that theories to date assume that the oscillatory regime is adequate for addressing experiments.
In this paper we compare Bose transport in normal phase atomic gases with its counterpart in Fermi gases, illustrating the non-universality of two dimensional bosonic transport associated with different dissipation mechanisms. Near the superfluid tra
nsition temperature $T_c$, a striking similarity between the fermionic and bosonic transport emerges because super-conducting(fluid) fluctuation transport for Fermi gases is dominated by the bosonic, Cooper pair component. As in fluctuation theory, one finds that the Seebeck coefficient changes sign at $T_c$ and the Lorenz number approaches zero at $T_c$. Our findings appear semi-quantitatively consistent with recent Bose gas experiments.
We derive the exact out-of-equilibrium Wigner function of a bosonic mode linearly coupled to a bosonic bath of arbitrary spectral density. Our solution does not rely on any master equation approach and it therefore also correctly describes a bosonic
mode which is initially entangled with its environment. It has been recently suggested that non-Markovian quantum effects lead to dissi- pationless dynamics in the case of a strong coupling to a bath whose spectral density has a support bounded from below. We show in this work that such a system undergoes a quantum phase transi- tion at some critical bath coupling strength. The apparent dissipationless dynamics then correspond to the relaxation towards the new ground-state.
In this paper we study the transient dynamics of a Bose superfluid subsequent to an interaction quench. Essential for equilibration is a source of dissipation which we include following the approach of Caldeira and Leggett. Here we solve the equation
s of motion exactly by integrating out an environmental bath. We thereby derive precisely the time dependent density correlation functions with the appropriate analytic and asymptotic properties. The resulting structure factor exhibits the expected damping and thereby differs from that of strict Bogoliubov theory. These damped sound modes, which reflect the physics beyond mean field approaches, are characterized and the structure factors are found to compare favorably with experiment.
We study the thermodynamics near the generic (density-driven) superfluid--Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy the physics is controlled by the G
aussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only {it via} two nonuniversal parameters, namely the effective mass $m^*$ and the scattering length $a^*$ of the elementary excitations at the quantum critical point between the superfluid and Mott-insulating phase. A notable exception is the condensate density in the superfluid phase which is proportional to the quasi-particle weight $Zqp$ of the elementary excitations. The universal regime is defined by $m^*a^*{}^2 Tll 1$ and $m^*a^*{}^2|deltamu|ll 1$, or equivalently $|bar n-bar n_c|a^*{}^3ll 1$, where $deltamu=mu-mu_c$ is the chemical potential shift from the quantum critical point $(mu=mu_c,T=0)$ and $bar n-bar n_c$ the doping with respect to the commensurate density $bar n_c$ of the T=0 Mott insulator. We compute $Zqp$, $m^*$ and $a^*$ and find that they vary strongly with both the ratio $t/U$ between hopping amplitude and on-site repulsion and the value of the (commensurate) density $bar n_c$. Finally, we discuss the experimental observation of universality and the measurement of $Zqp$, $m^*$ and $a^*$ in a cold atomic gas in an optical lattice.
We present a non-perturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial
way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the Ginzburg length as a crossover length between a weakly- and a strongly-correlated superfluid phase.
