Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System

We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\epsilon$ expansion near four spatial dimension. In dimension $d = 4 - \epsilon$, the chemical potential of Bose gases near resonances is shown to approach the universal value $\epsilon^{(2/(4-\epsilon))} \epsilon_F \sqrt...

Aiming for simplicity of explicit equations and at the same time controllable accuracy of the theory we present results for all thermodynamic quantities and correlation functions for the weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaev's diagrammatic technique. With a small symmetry breaking term Beliaev's diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present or...

We present a comprehensive analysis of quantum fluctuation effects in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The superfluid order parameter, and fluctuations thereof, are implemented by a bosonic Hubbard-Stratonovich field, which splits into two components corresponding to longitudinal and transverse (Goldstone) fluctuations. Physical properties of the system are computed from a set of ap...

The perturbative calculation of the effect of fluctuations in the nonzero frequency modes of a weakly interacting Bose gas on the condensation temperature is reviewed. These dynamic modes, discarded in most of the recent studies, have a temperature-induced energy gap that allows for a perturbative approach. The simple, yet powerful algorithm used to calculate the effect in a high-temperature expansion in conjunction with zeta function regularization of infrared divergences is...

As is well-known, in the conventional formulation of Bogoliubov's theory of an interacting Bose gas, the Hamiltonian $\hat{H}$ is written as a decoupled sum of contributions from different momenta of the form $\hat{H} = \sum_{k\neq 0}\hat{H}_{k}$. Then, each of the single-mode Hamiltonians $\hat{H}_{k}$ is diagonalized separately, and the resulting ground state wavefunction of the total Hamiltonian $\hat{H}$ is written as a simple product of the ground state wavefunctions of ...

Non-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal fixed points in a bosonic quantum many-body system by integrating out long-wave-length density fluctuations. The system consists of $N$ distinguishable spatially uniform Bose gases with $\mathrm{U}(N)$-symmetric interactions. The effective th...

We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/N. This is based on joint works with S. Petrat, P. Pickl, R. Seiringer and A. Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix.

We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose-Einstein employing the Keldysh-Schwinger approach a...

The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds to a renormalization of the two-point vertex function. By collecting the leading order logarithmic corrections we have derived the standard result for the density of states in the critical dimension, d=1. This method, which is shown to be id...

Understanding non-Fermi liquids in dimensions higher than one, has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Fermi liquid. In this work, we investigate the emergence of a novel non-Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with the Bose ...