# Tilman Enss | Many-body theory seminar

The research seminar of the Enss group takes place on Wednesdays at 14.00h in Philosophenweg 19 (seminar room).

#### Summer term 2018

- Wednesday 18 July 2018, 14.00h, SR Phil19

**TBA**

Dr. Richard Schmidt (Max-Planck Institute for Quantum Optics, Garching)

- Wednesday 6 June 2018, 14.00h, SR Phil19

**Dynamical Vertex Approximation for the attractive Hubbard model**

Dr. Lorenzo Del Re (SISSA, Trieste, and Technical University Vienna)

**Abstract:**In this seminar, I will present an extension of the formalism of the Dynamical Vertex Approximation (DΓA) [1], a diagrammatic approach including many-body correlations beyond the Dynamical Mean-Field Theory [2], to treat the case of attractive on-site interactions. I will first introduce the method from a theoretical point of view and briefly review some of the already published results for the repulsive case [3-5]. Then, I will derive the equations for the attractive case proving the validity of the derivation by showing, both analytically and numerically, that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models [6]. Furthermore, I will show an application of the extended algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, I will focus on the parameter region in the proximity of the second-order transition to the superconducting and charge-density wave phase, respectively, and show (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties. [1] A. Toschi et al., Phys. Rev. B 75, 045118 (2007); [2] A. Georges et al., Rev. Mod. Phys. 68, 13 (1996); [3] G. Rohringer et al., Phys. Rev. Lett. 107, 256402 (2011); [4] T. Schäfer et al., Phys. Rev. B 91, 125109 (2015); [5] G. Rohringer et al., arXiv:1705.00024 (2017); [6] L. Del Re, M. Capone, A. Toschi, in preparation (2018).

- Wednesday 23 May 2018, 14.00h, SR Phil19

**Dynamical critical scaling of long-range interacting quantum magnets**

Dr. Nicolò Defenu (Heidelberg University)

**Abstract:**Slow variations (quenches) of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In short-ranged systems the heat exhibits a universal power-law scaling as a function of the quench rate, known as Kibble-Zurek (KZ) scaling. Attempts to extend this hypothesis to long-range interacting systems have lead to seemingly contradicting results. In this work we analyse slow quenches of the magnetic field in the Lipkin-Meshkov-Glick model, which describes fully-connected quantum spins. We determine the quantum contribution to the residual heat as a function of the quench rate by means of a Bogoliubov expansion about the mean-field value and calculate the exact solution. For a quench which ends at the quantum critical point we identify two regimes: the adiabatic limit for finite-size chains, where the scaling is dominated by the Landau-Zener tunneling, and the Kibble-Zurek scaling. For a quench symmetric about the critical point, instead, there is no Kibble-Zurek scaling.

- Wednesday 16 May 2018, 14.00h, SR Phil19

**Bosonic mixtures in two dimensions**

Volker Karle (Heidelberg University)

**Abstract:**In this talk a two-component bosonic gas in two dimensions at low temperatures with zero-range repulsive interaction is considered. In our work we focus on the coexistence phase with superfluid behavior in both components, where a new phenomenon appears: The non-dissipative drag, also called Andreev-Bashkin effect, as a result of the interbosonic interactions, which leads to a modification of the usual BKT transition. Quantum fluctuations of the elementary excitations lead to further corrections of the phase boundary. We study the renormalization of the densities at finite temperatures using standard RG methods.

- Wednesday 09 May 2018,
**13.00h**, SR Phil19

**Journal club: Casimir interaction among heavy fermions in the BCS-BEC crossover**

Dr. Tilman Enss (Heidelberg University)**Abstract:**Journal club on Y. Nishida, Phys. Rev. A**79**, 013629 (2009).

- Wednesday 02 May 2018,
**13.00h, Phil12 gHS**

**SFB workshop**

- Wednesday 18 April 2018,
**16.00h, CQD lounge — jointly with Weidemüller group**

**The Efimov effect in Li-Cs mixtures**

Dr. Bing Zhu (Heidelberg University)

- Wednesday 11 April 2018, 13.30h, SR Phil19

**Scale invariance and the Quantum anomaly in the 2D Fermi gas**

Dr. Nicolò Defenu (Heidelberg University)

#### Winter term 2017/18

- Wednesday 17 January 2018, 14.00h, SR Phil19

**Multiply quantised vortices in fermionic superfluids: angular momentum, unpaired fermions, and spectral asymmetry**

Dr. Sergej Moroz (Technical University Munich)

**Abstract:**Quantized vortices are a hallmark of superfluids and superconductors. In this seminar I will talk about the orbital angular momentum L_{z}of an s-wave paired superfluid in the presence of an axisymmetric multiply quantised vortex. For vortices with winding number |k| > 1, I will argue that in the weak-pairing BCS regime, L_{z}is significantly reduced from its value L_{z}=ℏ N k/2 in the BEC regime, where N is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex sub-gap states.

- Wednesday 13 December 2017, 14.00h, SR Phil19

**Soliton friction and pairing in superfluids**

Dr. Johannes Hofmann (Cambridge University, UK)

**Abstract:**I shall discuss two examples of interaction effects in quantum gases.

First, I shall discuss the interaction of a collective quantum object - a soliton in a one-dimensional Bose gas - with its thermal environment. Intuitively, one could think of this object as a large pollen in a fluid, expecting Brownian motion to affect the soliton dynamics. Yet, because of the underlying integrability of the problem, it was long thought that such an interaction does not exist. It turns out, however, that there remains a more subtle interplay between soliton and thermal gas which gives rise to a damping force similar to the radiation force exerted on an accelerated charge in electrodynamics, called the Abraham-Lorentz force.

The second part of the talk will discuss interaction effects in mesoscopic Fermi gases relevant to ongoing experiments in Heidelberg as well as experiments on SrTiO_{3}nanostructures. While Fermi gases with a variable interaction typically realize a BEC-BCS crossover, finite particle number or confinement can give rise to additional fluctuation effects. I will introduce some aspects of mesoscopic superfluids and discuss how fluctuation effects show up in experiments.

- Wednesday 25 October 2017, 14.00h, SR Phil19

**Hard-core bosons in flat band systems**

Moritz Drescher (Heidelberg University)

- Wednesday 18 October 2017, 11.15h, SR Phil19

**Collective oscillations of a trapped atomic gas in low dimensions and thermodynamics of one-dimensional Bose gas**

Dr. Giulia De Rosi (University of Trento, Italy)

**Abstract:**Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity.

In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this talk, I will present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules.

I will discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a one-dimensional (1D) trapped Bose gas with repulsive contact interaction. I will show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. I will show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, I will discuss our research on a gas with a finite number N of atoms in a ring geometry at zero temperature. I will discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.