My main interests are strongly correlated quantum systems in low dimensions, a setting where the appearance of astonishing many-body effects is typical. This results in collective excitations which have properties dramatically different from the original particles that one started with. Consider for example electrons in a one-dimensional wire. Each electron possesses spin and charge which, as the standard model of particle physics tells us, cannot be separated. In spite of this, if the electrons start to behave collectively, the spin and charge degrees of freedom become independent and can be individually observed in experiments [see, eg, Kim et al., Nature Phys. 2, 397 (2006)]. Thus electrons in one dimension form a state of matter which is completely different from the usual one in higher dimensions, a fact of utter importance for systems like quantum wires or carbon nanotubes

Similar many-body phenomena also exist in quantum dots. For example, the Kondo effect appears when a localised spin is coupled to itinerant electrons. At low energies the spins of the electrons collectively screen the localised spin, thus forming the so-called Kondo singlet. A fascinating consequence of this is the appearance of universal behaviour, ie, experimental measurements of, for example, the conductance becomes independent of the microscopic details of the experimental samples

My research focuses on systems dominated by such strong correlation effects. In particular, I am interested in the manifestations of the collective many-body behaviour in the time evolution and relaxation dynamics, transport properties as well as other observable quantities. Furthermore, I am interested in the underlying theoretical framework and in the development of methods to analyse strongly correlated systems. Below I will give a brief overview of the topics I have been working on in the past. For more details please check my publications.

We have studied an implementation of Kitaev's toy model [A Yu Kitaev, Phys.-Usp. 44, 131 (2001)] for Majorana wires in an array of superconducting islands. We showed [1] that a capacitive coupling between the islands leads to an effective interaction between the Majorana modes. Using a Jordan-Wigner transformation we mapped the system to the ANNNI model and studied its phase diagram in detail (see Fig 1). We demonstrated that although strong repulsive interactions will eventually drive the system into a Mott insulating state, the competition between the band insulator and the Mott insulator leads to an interjacent topological state for arbitrary strong interactions. Indeed we were able [2,3] to show that the exact ground states can even be obtained analytically when the on-site (chemical) potential is tuned to a particular function of the other parameters. Using these exact ground states we demonstrated explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalisation of Majorana edge zero modes. Furthermore we have investigated [4] the interplay of interactions and disorder in the chemical potential. We found that moderate disorder or repulsive interactions individually stabilise the topological order, which also remains valid for their combined effect. However, both repulsive and attractive interactions lead to a suppression of the topological phase at strong disorder.

As a further project in the currently very active research field of topological insulators we have investigated the scattering off dilute magnetic impurities placed on their surface [5]. The interaction between the impurity moment and the electrons of the surface metal leads to mutual spin flips, such that backscattering could be allowed although time-reversal symmetry remains unbroken. Since the time-reversal symmetry remains intact the scattering off the magnetic impurity does not open new scattering channels in momentum space. Still the spin-flip processes lead to a distinct energy dependence of the quasiparticle interference (QPI) patterns as recorded by scanning tunneling spectroscopy. The most dramatic effect shows up at low energies where the Kondo effect occurs, ie, the impurity moments are screened by the surface-state electrons, despite their exotic locking of spin and momentum (see Fig 2).

[1] F Hassler and D Schuricht, New J. Phys. 14, 125018 (2012).

[2] H Katsura, D Schuricht and M Takahashi, Phys Rev B 92, 115137 (2015).

[3] J Wouters, H Katsura and D Schuricht, Phys Rev B 98, 155119 (2018).

[4] N M Gergs, L Fritz and D Schuricht, Phys Rev B 93, 075129 (2016).

[5] A Mitchell, D Schuricht, M Vojta and L Fritz, Phys Rev B 87, 075430 (2013).

Fig 1: Phase diagram of the interacting Majorana chain [8]. Repulsive interactions facilitate the topological phase due to their competition with the on-site chemical potential. Inset: Gap along the blue dashed line.

Fig 2: Quasiparticle interference patterns for a dynamic magnetic impurity [11]. At low energies there is a strong enhancement due to the Kondo effect.

More recently we have considered parafermions, which constitute a direct generalisation of Majorana fermions discussed above [see, eg, P Fendley, J Stat Mech (2012) P11020]. We investigated the properties of two specific setups: (i) parafermions as generalisations of Majorana fermions, and (ii) Fock parafermions, which constitute the corresponding generalisation of ordinary Dirac fermions. For the parafermions, very recently we determined [6] the phase diagram of an extended parafermion chain (see Fig. 3). The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase. The phase diagram was obtained by the combination of numerical DMRG simulations and analytical approaches like bosonisation. We discussed a possible experimental realisation using hetero-nanostructures. In a second work [7], based on Witten's conjugation argument, we developed a general framework to derive frustration-free systems and their exact ground states. The approach allowed us to treat several frustration-free parafermion chains in a unified framework.

Regarding the second setup, we studies a tight binding model of Fock parafermions with single-particle and pair-hopping terms [8]. The phase diagram (see Fig. 4) has four different phases: a gapped phase, a gapless phase with central charge c=2, and two gapless phases with central charge c=1. We characterised each phase by analysing the energy gap, entanglement entropy and different correlation functions. The extensive numerical simulations were complemented by analytical arguments.

[6] J Wouters, F Hassler, H Katsura and D Schuricht, SciPost Phys. Core 5, 008 (2022).

[7] J Wouters, H Katsura and D Schuricht, SciPost Phys. Core 4, 027 (2021).

[8] I Mahyaeh, J Wouters and D Schuricht, SciPost Phys. Core 3, 011 (2020).

Fig 3: Phase diagram of an extended parafermion chain [6]. We observe several phases, including a topological phase and a Luttinger-liquid phase.

Fig 4: Phase diagram of a Fock parafermion chain [8] as a function of the pair hopping amplitude g and particle density n. We find four different phases: a gapped phase, a gapless phase with central charge c=2, and two gapless phases with central charge c=1.

The main focus of my current research is the investigation of the time evolution of low-dimensional systems after a quantum quench, ie, the sudden change of the system parameters. This has been a field of intensive research in recent years, which was triggered by enormous developments in experiments on ultra-cold atomic gases in optical traps, which now allow an almost full control over the system parameters and can thus be used to mimic various kinds of many-body systems well-known in condensed matter physics [see, eg, I Bloch, J Dalibard and P Zoller, Rev. Mod. Phys. 80, 885 (2008)].

My main interest in this context is the analysis of the time evolution of observables and correlation functions strongly correlated quantum systems. One prominent example is the sine-Gordon model, which constitutes the effective low-energy description of one-dimensional interacting bosons in a weak optical lattice or can be applied to describe the relative phase of split condensates. Our main result was that one-point functions of non-local observables will decay exponentially in time [9]; in the presence of breather modes one also finds additional oscillations [10]. Furthermore, by showing that the numerical simulations for the time evolution are consistent with field-theoretical predictions obtained for the Tomonaga-Luttinger model we showed that the quench dynamics possesses a degree of universality [11].

We have also studied [12] dynamical quantum phase transitions, ie, non-analytic features in the time evolution of the Loschmidt amplitude which appear when quenching across a quantum critical point. Using time-dependent DMRG we found that this behaviour does not only appear in the quantum chain [as previously investigated, see M Heyl, A Polkovnikov and S Kehrein, Phys. Rev. Lett. 110, 135704 (2013)] which is equivalent to free fermions, but also shows up for quenches in the transverse axial next-nearest-neighbour Ising (ANNNI) chain and a generalised Ising model in a longitudinal magnetic field (see Fig 5). Our results for these 'interacting theories' indicate that the non-analytic dynamics is a generic feature of sudden quenches across quantum critical points. However, a recent study in the three-state quantum Potts chain showed that the dynamical quantum phase transitions are not related to the universality class of the Potts model, ie, the non-analyticities in the Loschmidt amplitude do not show non-trivial power-law behaviour [13].

Recently we studies the time evolution in the Tomonaga-Luttinger model [14] and transverse-field Ising chain [15] subject to quantum quenches of finite duration, ie, a continuous change in the transverse magnetic field over a finite time. As our main result we showed that the light-cone picture describing two-point correlation functions remains applicable; however, the propagating front is delayed as compared to the sudden quench (see Fig. 6).

[9] B Bertini, D Schuricht and F H L Essler, J. Stat. Mech. (2014) P10035.

[10] A Cortés Cubero and D Schuricht, J. Stat. Mech. (2017) 103106.

[11] C Karrasch, J Rentrop, D Schuricht and V Meden, Phys. Rev. Lett. 109, 126406 (2012).

[12] C Karrasch and D Schuricht, Phys. Rev. B 87, 195104 (2013).

[13] C Karrasch and D Schuricht, Phys Rev B 95, 075143 (2017).

[14] P Chudzinski and D Schuricht, Phys Rev B 94, 075129 (2016).

[15] T Puškarov and D Schuricht, SciPost phys 1, 003 (2016).

Fig 5: Return amplitude for quenches from the paramagnetic phase to the ferromagnetic phase in the ANNNI model [12]. One observes non-analytic behaviour (see inset).

Fig 6: Logarithm of the fermionic Green function after a linear quench in the Tomonaga-Luttinger model [14]. The white line indicates the position of the light-cone horizon, while the black line shows the position of the horizon after a sudden quench of the same strength. We clearly observe a delay of the horizon in the linear quench setup.

In the past I have intensively studied the properties of one-dimensional electronic systems, in particular the local density of states (LDOS) of one-dimensional Mott insulators and charge density wave states [16]. Here the LDOS is of direct experimental relevance for scanning tunneling microscopy experiments on quasi-one-dimensional materials such as self-organised atomic gold chains [see, eg, C Blumenstein et al., Nature Phys. 7, 776 (2011)]. Our main result was that the spatial Fourier transform of the LDOS clearly shows signatures of spin-charge separation.

More recently I have studied [17] the spectral properties of spiral Luttinger liquids, which emerge in one-dimensional electron systems coupled to localised magnetic moments or quantum wires with spin-orbit interactions. I derived analytic results for the spectral function (see Fig 7), local density of states, and optical conductivity and identified various characteristic signatures for an experimental detection of these states. This study was also extended to transport properties in two-terminal setups [18] as well as the analysis of a microscopic model [19].

[16] D Schuricht, F H L Essler, A Jaefari and E Fradkin, Phys. Rev. Lett. 101, 086403 (2008).

[17] D Schuricht, Phys. Rev. B 85, 121101(R) (2012).

[18] T Meng, L Fritz, D Schuricht and D Loss, Phys Rev B 89, 045111(2014).

[19] G W Winkler, M Ganahl, D Schuricht, H G Evertz and S Andergassen, New J Phys 19, 063009 (2017).

Fig 7: Spectral function of a spiral Luttinger liquid state [17]. We observe a gap in the down-spin component only. Furthermore we see that the breather contributions are very weak.

Transport through quantum dots and nanostructures is currently a very active field of research. The basic setup consists of a small region, the quantum dot, which possesses discrete energy levels that can be influenced by the application of gate voltages, magnetic fields or the like. This dot region is coupled to at least two electronic leads (see Fig 8). If these are held at different chemical potentials this drives the system out of equilibrium and results in a current flowing through the quantum dot. The applied bias voltage introduces an additional energy scale which poses a big theoretical challenge, rendering a treatment via standard equilibrium methods impossible. Hence the development of new theoretical methods, in particular for systems with strong correlations, is required.

In the past I worked on the development and application of renormalisation group methods for the study of non-equilibrium transport through strongly correlated quantum dots. I have mainly studied two paradigmatic systems: quantum dots dominated by spin fluctuations (ie, Kondo dots, see eg, [20]) or charge fluctuations (interacting resonant level model [21]).

In this context I have recently started to work on thermotransport, ie, the study of electrical and heat currents driven by finite temperature differences between the leads. In Ref. [22] we analysed how charge fluctuation processes are crucial for the non-linear heat conductance through an interacting nanostructure, even far from a resonance. We illustrated this for an Anderson quantum dot, and identified energy-transport resonances in the Coulomb blockade regime which provide qualitative information about relaxation processes in the system, for instance, by a strong negative differential heat conductance relative to the heat current (see Fig 9).

[20] M Pletyukhov and D Schuricht, Phys. Rev. B 84, 041309(R) (2011).

[21] S Andergassen, M Pletyukhov, D Schuricht, H Schoeller and L Borda, Phys. Rev. B 83, 205103 (2011).

[22] N M Gergs, C B M Hörig, M R Wegewijs and D Schuricht, Phys. Rev. B 91, 201107(R) (2015).

Fig 8: Sketch of a quantum dot attached to two electronic leads held at chemical potentials μ_{L/R}=±*V*/2.

Fig 9: Differential charge and energy conductance through an Anderson quantum dot [22]. We observe several resonance features labelled by (i)-(vii) which contain information about the relaxation mechanisms on the quantum dot.

Beside the study of stationary quantities I am interested in the investigation of the time evolution and relaxation in quantum dots. In the past we have already studied the time evolution of spin and current in a Kondo quantum dot attached to leads with a bias voltage [23]. We showed that (i) the voltage is an important energy scale for the dynamics which shows up in oscillatory, power-law, and logarithmic behaviour, (ii) in the long-time limit one finds generically, ie, in all orders of perturbation theory, that all terms are exponentially decaying with one of the transport rates Γ_{i,} and that (iii) the exponential relaxation is accompanied by power-law decay and oscillatory behaviour

We have also investigated the influence of the hyperfine interaction between the spin on the quantum dot and the nuclear spins in the semiconductor material. To this end we studied the relaxation in the central spin model by applying the Algebraic Bethe Ansatz (ABA) together with a Monte Carlo sampling over the Hilbert space [24,25]. Using the ABA allowed us to study the whole crossover from the perturbative regime of strong Zeeman fields to the limit of zero field. In particular, we showed that for weak fields there exist long-lived slow oscillations (see Fig 10), while in the limit of vanishing field, an initial rapid decay is followed by the formation of a non-decaying coherent fraction whose amplitude and phase is in one-to-one correspondence with the initial state of the central spin. This lack of decay can be explained as a consequence of Bose-Einstein-condensate-like physics in the central spin model.

Very recently we studied how to manipulate spin currents through quantum-dot spin valves [26]. Such a spin-valve setup is obtained by replacing the electronic leads in Fig. 6 with ferromagnetic nano magnets. We showed that by changing the gate and bias voltages ε and *V* one can influence the angle θ between the ferromagnets (see Fig 11). In particular, one can see that the setup can be used as a switch for the relative magnetisation of the nano magnets, eg, the alignments can be tuned from parallel to antiparallel by changing the gate voltage ε applied to the quantum dots between them.

[23] M Pletyukhov, D Schuricht and H Schoeller, Phys. Rev. Lett. 104, 106801 (2010).

[24] A Faribault and D Schuricht, Phys. Rev. Lett. 110, 040405 (2013).

[25] A Faribault and D Schuricht, Phys. Rev. B 88, 085323 (2013).

[26] N M Gergs, S A Bender, R A Duine and D Schuricht, Phys Rev Lett 120, 017701 (2018).

Fig 10: Time evolution of the transverse central spin in the non-perturbative regime of the central spin model for various magnetic field strengths (increasing from top to bottom) [24]. One observes very slow oscillations and scaling behaviour.

Fig 11: Stationary angle θ between the ferromagnetic leads in a quantum-dot spin valve setup depending on the applied gate and bias voltages ε and *V* [26]. Inset: Time evolution of the angle for the parameters indicated by the symbols.

In the past I have intensively worked on spin chains with higher symmetry algebras (see, eg, [27]). Of particular interest are integrable systems, which possess infinitely many conservation laws and allow for an exact solution. In this context, we recently constructed [28] a novel solution to the Yang-Baxter equation, which may serve as a starting point for the construction of integrable spin chains with dissipation.

[27] D Schuricht and S Rachel, Phys. Rev. B 78, 014430 (2008).

[28] L Stronks, J van de Leur and D Schuricht, J Phys A 49, 444001 (2016).