## Quantum Matter Theory Group

Welcome to the homepage of our group! Our research is focused on ultracold gases in optical lattices, hybrid quantum simulators such as ion-atom systems, and strongly correlated electrons, e.g. in nanostructures. You can find descriptions of the individual research projects here. Below is a selection of recent publications.

## Research News

##### Topological invariant for 2D open systems

(arXiv:1710.03119)

We study the topology of 2D open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems and the equivalent descriptions through topological Hamiltonian and Berry curvature are developed separately. The invariant is well-defined iff all of the eigenvalues of the Green's function for imaginary frequency are finite nonzero numbers. Meanwhile, we define another topological invariant via the single particle density matrix, which works for general gapped systems and is equivalent to the former for the case of weak coupling to an environment. We also discuss two applications. For time-reversal invariant insulators, we explain the relation between the invariant for each spin-subsystem and the Z2 index of the full system. As a second application, we consider the interference effect when an ordinary insulator is coupled to a topological insulator. The bulk-boundary correspondence of the open system shows new features.

##### Non-thermalized Steady States and Resonant Tunneling in Time-Periodically Driven Systems with Interactions

(arXiv:1709.03021)

Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups address the relatively weakly-interacting regime so far, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study non-equilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the non-thermalized properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi's Golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve "photo-doping". For driven interactions, we find that the double occupancy is strongly modulated.

##### Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

(arXiv:1707.07037)

Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic and topological properties as a function of frustration using exact diagonalization and bosonic dynamical mean-field theory. We do find an emergent chiral spin state in the intermediate frustration regime. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but its Chern number is zero.

##### Phase transitions of the coherently coupled two-component Bose gas in a square optical lattice

(arXiv:1705.02833)

We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean field theory as well as bosonic dynamical mean field theory. We find that the interplay of strong inter-species repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.

##### Spectral functions of a time-periodically driven Falicov-Kimball model: real-space Floquet DMFT study

(arXiv:1704.03250, Phys. Rev. B 96, 075134(2017))

We present a systematic study of spectral functions of a time-periodically driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account interaction effects and contributions from higher Floquet bands in a non-perturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. However, as also illustrated by our results, one should bear in mind that Floquet DMFT describes a non-equilibrium steady state (NESS), while an effective static Hamiltonian describes an equilibrium state. We further demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry.

##### Breaking of SU(4) symmetry and interplay between strongly-correlated phases in the Hubbard model

(arXiv:1612.06258, Phys. Rev. B 95, 125108(2017))

We study thermodynamic properties of four-component fermionic mixtures described by the Hubbard model using the dynamical mean-field theory approach. Special attention is given to the system with SU(4)-symmetric interactions at half filling, where we analyze equilibrium many-body phases and their coexistence regions at nonzero temperature for the case of simple cubic lattice geometry. We also determine the evolution of observables in low-temperature phases while lowering the symmetry of the Hamiltonian towards the two-band Hubbard model. This is achieved by varying interflavor interactions or by introducing the spin-flip term (Hund's coupling). By calculating the entropy for different symmetries of the model we determine the optimal regimes for approaching the studied phases in experiments with ultracold alkali and alkaline-earth-like atoms in optical lattices.

##### The infinite occupation number basis of bosons - solving a numerical challenge

(arXiv:1611.10185, Phys. Rev. B 95, 224516(2017))

In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a novel truncation scheme to account for contributions from higher number states. By simply adding a single \textit{coherent-tail} state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

##### Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperaturel

(arXiv:1608.07235, Phys. Rev. B 94, 214305(2016))

We present a self-contained operator-based approach to derive the spectrum of trapped ions. This approach provides the complete normal form of the low-energy quadratic Hamiltonian in terms of bosonic phonons, as well as an effective free-particle degree of freedom for each spontaneously broken spatial symmetry. We demonstrate how this formalism can directly be used to characterize an ion chain both in the linear and the zigzag regimes. In particular, we compute, both for the ground state and finite temperature states, spatial correlations, heat capacity, and dynamical susceptibility. Last, for the ground state, which has quantum correlations, we analyze the amount of energy reduction compared to an uncorrelated state with minimum energy, thus highlighting how the system can lower its energy by correlations.

##### Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model

(arXiv:1606.09161, Phys. Rev. B 94, 115161(2016))

Interaction effects have been a subject of contemporary interest in topological phases of matter. But in the presence of interactions, the accurate determination of topological invariants in their general form is difficult due to their dependence on multiple integrals containing Green's functions and their derivatives. Here we employ the recently proposed "effective topological Hamiltonian" approach to explore interaction-induced topological phases in the time-reversal-invariant Hofstadter-Hubbard model. Within this approach, the zero-frequency part of the self-energy is sufficient to determine the correct topological invariant. We combine the topological Hamiltonian approach with the local self-energy approximation within Hartree-Fock and dynamical mean field theory (DMFT), and present the resulting phase diagram in the presence of many-body interactions. We investigate the emergence of quantum spin Hall (QSH) states for different interaction strengths by calculating the Z2 invariant. The interplay of strong correlations and a staggered potential also induces magnetic long-range order with an associated first order transition. We present results for the staggered magnetisation (m_{s}), staggered occupancy (n_{s}) and double occupancy across the transition.