# 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).

#### Winter term 2018/2019

- Wednesday 6 February 2018, 14.00h, SR Phil19

**Second sound and superfluidity in ultracold quantum gases**

Dr. Vijay Singh (Hamburg University)

**Abstract:**

Ultracold atom systems are well-controlled and tunable quantum systems, and thereby enable us to explore quantum many-body effects, such as superfluidity, or second sound. In this talk, I will examine second sound and superfluidity in ultracold quantum gases using analytical and simulation techniques. I will report on the second sound measurements in the BEC-BCS crossover and provide a theoretical description of the second sound velocity on the BEC side of the system [1]. Here, I will demonstrate that the second sound velocity vanishes at the superfluid-thermal boundary, which is a defining feature of second sound. In the second part of this talk, I will investigate superfluidity of ultracold quantum gases via laser stirring. I will present the stirring experiments in the BEC- BCS crossover and provide a quantitative analysis of the breakdown of superfluidity [2]. I will then investigate superfluidity of 2D Bose gases across the Kosterlitz-Thouless transition and provide a quantitative understanding of the experiments performed in the Dalibard group [3]. I will also present the noise correlations of 2D Bose gases in short time of flight and use them to determine the superfluid phase of the recent experiments at Hamburg [4].

[1] D. Hoffmann, V. P. Singh, T. Paintner, W. Limmer, L. Mathey, and J. H. Denschlag, Second sound in the BEC-BCS crossover, forthcoming.

[2] W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, Phys. Rev. Lett. 114, 095301 (2015); V. P. Singh et al., Phys. Rev. A 93, 023634 (2016).

[3] V. P. Singh, C. Weitenberg, J. Dalibard, and L. Mathey, Phys. Rev. A 95, 043631 (2017).

[4] V. P. Singh and L. Mathey, Phys. Rev. A 89, 053612 (2014).

- Wednesday
**23 January 2018, 12.00h**, SR Phil19

**Quasiparticle origin of dynamical quantum phase transitions**

Dr. Jad Halimeh (MPIPKS Dresden and TU München)

**Abstract:**

We consider one- and two-dimensional Ising models with varying interaction ranges. Using matrix product state techniques, we study the dynamics of these systems and show a direct connection between the type of lowest-energy quasiparticles in the spectrum of the quench Hamiltonian and the type of nonanalyticities occuring in the Loschmidt return rate, a dynamical analog of the free energy. Our results also show a clear connection between the type of nonanalyticities and the phase of the long-time steady state in addition to how the order parameter decays at intermediate times. In particular, we discuss*anomalous*nonanalyticities that occur with no underlying local signature in the order parameter dynamics, unlike the traditional*regular*nonanalyticities that always correspond to zero crossings of the order parameter. Moreover, we demonstrate how dynamical quantum phase transitions can be used to extract the equilibrium physics of the model from short-time dynamics.

- Wednesday
**23 January 2018, 11.00h**, SR Phil19

**Quasi-localized excitations induced by confinement in translationally-invariant quantum chains**

Alessio Lerose (SISSA Trieste, Italy)

**Abstract:**

We show that quantum confinement can induce spatial quasi-localization of excitations and slow dynamics even in the absence of quenched disorder. By means of numerical computations based on matrix product states and exact diagonalization, we study the nonequilibrium evolution in quantum Ising chains with longitudinal fields, in long-range quantum Ising chains, and in U(1) lattice gauge theories in one dimension. We demonstrate the emergence of regimes characterized by quasi-many-body localization and long-lived excitations at high energy. We capture these anomalous nonequilibrium dynamics via effective analytical descriptions or via exact mappings to models exhibiting weak ergodicity breaking. These phenomena can be tested in quantum simulators with trapped ions and Rydberg atoms.

References: arXiv:1806.09674, arXiv:1811.05513, and work in preparation (Feb 2019).

- Wednesday 16 January 2019, 14.00h, SR Phil19

**Spectral functions in QCD: Calculation and Application**

Nicolas Wink (Heidelberg University)

- Wednesday 9 January 2019, 14.00h, SR Phil19

**Relaxation dynamics of disordered Heisenberg spins realized by Rydberg atoms**

Dr. Martin Gärttner (Heidelberg University)

- Wednesday 12 December 2018, 15.40h, INF 226 room 01.210 — jointly with Weidemüller group

**Boiling a Unitary Fermi Liquid**

Manuel Gerken (Heidelberg University)

**Abstract:**Journal club on S. Yan et al., arXiv:1811.00481. - Wednesday 28 November 2018, 14.00h, SR Phil19

**Deviations from off-diagonal long-range order and mesoscopic condensation in one-dimensional quantum systems**

Andrea Colcelli (SISSA Trieste, Italy)

**Abstract:**

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue λ_{0}of the one-body-density matrix scales as λ_{0}~ N, where N is the total number of particles. Putting λ_{0}~ N^{C}to define the scaling exponent C, then C=1 corresponds to ODLRO and C=0 to the single-particle occupation of the density matrix orbitals. When 0<C<1, C can be used to quantify deviations from ODLRO. In this talk I will present the study of the exponent C in a variety of one-dimensional bosonic and anyonic systems. - Wednesday 31 October 2018, 15.30h, INF 226
room 01.210 — jointly with Weidemüller group

**Real space dynamics of attractive and repulsive polarons in Bose-Einstein condensates**

Moritz Drescher (Heidelberg University)

**Abstract:**

We investigate the formation of a Bose polaron when a single impurity in a Bose-Einstein condensate is quenched from a non-interacting to an attractively interacting state in the vicinity of a Feshbach resonance. We use a beyond-Fröhlich Hamiltonian that is able to cover both sides of the resonance and the Lee-Low-Pines variational ansatz to compute the time-evolution of Boson density profiles in position space. We find that on the repulsive side of the Feshbach resonance, the system keeps oscillating with a characteristic frequency for which we derive an implicit equation and discuss to what extent this can be interpreted as a competition between a molecular and a repulsive polaron state. If the impurity is introduced at finite velocity, it is periodically slowed down or even arrested before speeding up again. - Wednesday 24 October 2018, 14.00h, SR Phil19

**Motion of an impurity particle in a boson superfluid**

Moritz Drescher (Heidelberg University)

**Abstract:**Journal club on Girardeau, Phys. Fluids**4**, 279 (1961).

- Wednesday 17 October 2018, 14.00h, SR Phil19

**Transport in strange metals**

Dr. Tilman Enss (Heidelberg University)

#### Summer term 2018

- Tuesday 02 October 2018, 14.15h, SR Phil19

**Universality in the epsilon expansion**

Dr. Alessandro Codello (CP3-Origins Odense and INFN Bologna)

**Abstract:**

After reviewing the Functional reformulation of the standard Perturbative RG (FPRG), I'll describe the classification of universality classes in arbitrary dimension within the epsilon-expansion and the relative determination of CFT data. In the single component case, universality classes are represented by renormalizable scalar QFTs with self-interacting potentials of highest monomial phi^m below their upper critical dimensions dc = 2m/(m-2). For even integers, m >= 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. An important outcome of this analysis is the realization of the existence of a new non-trivial family of d = 3 universality classes with upper critical dimension dc = 10/3. Subsequently, I will show how the FPRG formalism allows a straightforward generalization to the multicomponent case, with almost no need for additional computations. The classification of multicomponent universality classes is far from complete and I will discuss the present state of knowledge with few examples, including Potts and O(N) models.

- Tuesday 18 September 2018, 14.00h, SR Phil19

**RG induced inflation**

Dr. Nicolò Defenu (Heidelberg University)

- Tuesday 07 August 2018, 10.00h, SR Phil19

**Journal club: Dynamical formation of Bose polarons**

Dr. Tilman Enss (Heidelberg University)

**Abstract:**Journal club on K.K. Nielsen et al., arXiv:1806.09933.

- Thursday 19 July 2018, 15.00h, INF 226 room 01.106 (Glas Box)— jointly with Weidemüller group

**Composite, rotating impurities interacting with a many-body environment: analytical and numerical approaches**

Dr. Giacomo Bighin (IST Vienna, Austria)

**Abstract:**

The angulon quasiparticle formalizes the concept of a composite, rotating impurity in a quantum many-body environment and has proven useful in the description of several experimental settings, from ultracold molecules in a BEC to molecules in He nanodroplets. I introduce a diagrammatic formalism, merging Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, describing angular momentum redistribution in a many-body system. Then, motivated by recent experiments on laser-induced alignment of molecules in He nanodroplets, I introduce a finite-temperature variational approach to angulon dynamics, showing that the far-from-equilibrium dynamical response of molecular impurities can be rationalized in terms of angulons. - Tuesday 17 July 2018, 14.15h, SR Phil19

**Many-body physics with quantum impurities in cold atoms and beyond**

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

**Abstract:**

When an impurity is immersed into an environment, it changes its properties due to its interactions with the surrounding medium. The impurity is dressed by many-body excitations and forms a quasiparticle, the polaron. Depending on the character of the environment and the form of interactions, different types of polarons are created. In this talk, I will review recent experimental and theoretical progress on studying the many-body physics of polarons in ultracold atomic systems [1], and discuss related polaronic phenomena encountered in two-dimensional semiconductors [2] and the study of rotating molecules in superfluid Helium [3]. In the second part of the talk I will then focus on impurities interacting with bosonic quantum gases. Specifically, I will discuss progress on the theoretical description of Rydberg excitations coupled to Bose-Einstein condensates. In such systems the interaction between the Rydberg atom and the Bose gas is mediated by the Rydberg electron. This gives rise to a new polaronic dressing mechanisms, where instead of collective excitations, molecules of gigantic size dress the Rydberg impurity. We develop a functional determinant approach [4] to describe the dynamics of such Rydberg systems which incorporates atomic and many-body theory. Using this approach we predict the appearance of a superpolaronic state which has recently been observed in experiments [5,6].

[1] R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Rep. Prog. Phys. 81, 024401 (2018). [2] M. Sidler et al., Nature Physics 13, 255 (2017). [3] R. Schmidt, and M. Lemeshko, Phys. Rev. Lett. 114, 203001 (2015). [4] R. Schmidt, H. Sadeghpour, and E. Demler, Phys. Rev. Lett. 116, 105302 (2016). [5] F. Camargo et al., Phys. Rev. Lett. 120, 083401 (2018). [6] R. Schmidt et al., Phys. Rev. A 97, 022707 (2018).

- Wednesday 11 July 2018, 14.00h, SR Phil19

**Journal club: Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach**

Moritz Drescher (Heidelberg University)

**Abstract:**Journal club on Grusdt et al., Phys. Rev. A**97**, 033612 (2018).

- Wednesday 4 July 2018, 14.00h, SR Phil19

**Many-body properties from a few-body perspective**

Dr. Tilman Enss (Heidelberg University)

- Wednesday 27 June 2018, 14.00h, SR Phil19

**Journal club: Collisional Properties of a Polarized Fermi Gas with Resonant Interactions**

Hans Böhringer (Heidelberg University)

**Abstract:**Journal club on G.M. Bruun et al., Phys. Rev. Lett**100**, 240406 (2008).

- 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 30 May 2018, 14.00h, SR Phil19

**Journal club: Casimir interaction among heavy fermions in the BCS-BEC crossover (part 2)**

**Abstract:**Journal club on Y. Nishida, Phys. Rev. A**79**, 013629 (2009).

- 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.