New Trends in Nonequilibrium Many-Body Systems: Methods and Concepts

I will discuss recent results for correlated Mott systems out of equilibrium obtained by means of the so called Auxiliary Master Equation Approach [1,2,3], an efficient nonequilibrium impurity solver for Dynamical Mean Field theory [4,5]. The solver exploits an exponentially accurate mapping of the correlated impurity problem onto an auxiliary open quantum system including bath orbitals as well as a coupling to a Markovian environment. In particular, I will address the issue of dielectric breakdown taking place in Mott insulators at large electric fields and focus on the interplay between strong correlation and Joule dissipation provided by phonons around this transition [6]. Furthermore, I will discuss the effect of impact ionization in photoexcitation induced transport across a Mott insulating gap [5]. Finally, I will present a recent improvement of the nonequilibrium impurity solver based on a generalized configuration interaction for open quantum systems [7,8]. [1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013) [2] A. Dorda et al., Phys. Rev. B 89 165105 (2014) [3] A. Dorda et al., Phys. Rev. B 92, 125145 (2015) [4] I. Titvinidze et al., Phys. Rev. B 92, 245125 (2015) [5] M. Sorantin et al., Phys. Rev. B 97, 115113 (2018) [6] T. Mazzocchi at al., in preparation (2022). [7] A. A. Dzhioev et al, J. Phys. A 47, 095002 (2014). [8] D. Werner and E. Arrigoni in preparation (2022).

The study of systems under optical excitation receives tremendous attention because of both the recent rapid developments of ultrafast pump lasers and the discovery of striking phenomena not observable in equilibrium. Various numerical techniques have been applied to optically excited systems to study nonequilibrium dynamics, e.g., the time-dependent version of exact diagonalization technique or dynamical mean-field theory. Results for nonequilibrium dynamics based on tensor-network algorithms are still rare, however. In this study, we propose a direct numerical scheme in the matrix-product-states (MPS) representation for the computation of nonequilibrium dynamic response functions, which can be used for general (quasi-)one-dimensional systems. Using time-evolution techniques for (infinite) MPS, we calculate, directly in the thermodynamic limit, the time-dependent photoemission spectra and dynamic structure factors of the half-filled Hubbard chain after pulse irradiation. These quantities exhibit clear signatures of the photoinduced phase transition from insulator to metal that occurs because of the formation of so-called $\eta$ pairs. {\bf References}: - S. Ejima, T. Kaneko, F. Lange, S. Yunoki and H. Fehske, {\it Phys. Rev. Res.} {\bf 2}, 032008(R) (2020). - S. Ejima, F. Lange and H. Fehske, {\it Phys. Rev. Res.} {\bf 4}, L012012 (2022). - S.e Ejima, F. Lange and H. Fehske, arXiv:2204.09085.

Neural quantum states (NQS) are a variational ansatz in which a neural network is used to parametrize the quantum state of a many-body system. NQS-based methods can be applied to learning both ground states and dynamics of quantum many-body systems by optimizing the network weights as variational parameters. In this poster, we present our current efforts in applying NQS methods to simulating strongly correlated quantum systems in and out of equilibrium. In particular, we highlight our recent work on understanding the stability properties of time-evolution algorithms for NQS based on the time-dependent variational Monte Carlo method. Furthermore, we will present results of our ongoing research into the application of NQS for representing states in quantum spin liquid systems.

We present a new diagrammatic Monte Carlo impurity solver based on the strong-coupling expansion of the vertex functions. By directly sampling the four-point pseudo-particle vertex diagrams and applying the self-consistency equation at the level of the triangular vertex, we significantly improve the traditional schemes such as non-crossing and two-crossing approximations, and eventually achieve numerically exact results. We analyze the performance and the convergence rate of the impurity solver using exactly solvable models. As a proof-of-principle example, we discuss the physics of strong light-matter coupling in the spin-boson model representing an emitter in an optical waveguide.

Electron-hole pairs in organic photovoltaics dissociate efficiently despite their Coulomb-binding energy exceeding thermal energy at room temperature. The electronic states involved in charge separation couple to structured vibrational environments containing multiple underdamped modes. The non-perturbative simulations of such large, spatially extended electronic-vibrational (vibronic) systems remains an outstanding challenge. Current methods bypass this difficulty by considering effective one-dimensional Coulomb potentials or unstructured environments. Here we extend and apply a recently developed method for the non-perturbative simulation of open quantum systems to the dynamics of charge separation in one, two and three-dimensional donor-acceptor networks. This allows us to identify the precise conditions in which underdamped vibrational motion induces efficient long-range charge separation. Our analysis provides a comprehensive picture of ultrafast charge separation by showing how different mechanisms driven either by electronic or vibronic couplings are well differentiated for a wide range of driving forces and how entropic effects become apparent in large vibronic systems. These results allow us to quantify the relative importance of electronic and vibronic contributions in organic photovoltaics and provide a toolbox for the design of efficient charge separation pathways in artificial nanostructures.

Systems with spin orbit coupling (SOC) driven out of equilibrium give rise to interesting electron dynamics due to their coupling between the electron spin and momentum. Recent efforts have been made in order to understand the imprints of SOC on the high harmonic generation spectra of solids. In a parallel development, the field of non-equilibrium superconductivity in unconventional superconductors has lately attracted a lot of attention due to the prospect of Higgs-spectroscopy. We extend these studies by looking at the interplay of the spin related observables and collective excitations. Emphasis will be put on their non-linear signatures and thus relating the results to the already established normal state non-equilibrium dynamics.

The state of the art in simulating strongly correlated models out of equilibrium is to account for the dissipation of the energy injected into the system by means of auxiliary fermion baths known as Büttiker probes. In real compounds, however, Joule heat is carried away by lattice vibrations: including phonons in a coherent picture is then necessary to be able to predict the microscopic mechanisms governing heat transport in solids. To this purpose acoustic or optic phonon branches are treated within the non-self-consistent Migdal approximation. However, the latter scheme makes numerical calculations within the dynamical mean field theory approach very unstable, so there are actual limitations about reaching a steady-state solution without resorting to a coupling to a fermion bath. By means of the Floquet non-equilibrium Green's function approach we study the stability of the steady-state solution of a Hubbard model subject tot a static electric field - with phonons alone to provide dissipation - through the analysis of its spectral properties together with the frequency-resolved current and kinetic energy profiles.

Calculating the single-particle and two-particle correlations of interacting lattice systems in a consistent and con- serving manner is a challenging task. Nonlocal correlations play an important role in low-dimensional systems and in the vicinity of phase transitions and crossovers. We establish, use and implement the non-equilibrium framework of two methods that deal self-consistently with one-particle vertex corrections within the Hubbard model, namely the Two-Particle Self-Consistent approach (TPSC) and a variation of the latter (TPSC+GG). We employ them to study spin and charge susceptibilities upon quenching the system from 3 dimensions to 2, i.e from a cubic lattice to a square lattice. We also study interaction quenches in the vicinity of the renormalized classical regime.

Pump-probe spectroscopy measurements, such as time-resolved optical conductivity and time-resolved angle-resolved photoemission spectroscopy (trARPES), have been widely used to study the dynamical properties of strongly correlated electron systems. Especially, the ultrafast phenomena of one-dimensional (1D) Mott insulators, e.g., organic salt ET-F$_2$TCNQ [1,2] and halogen-bridged transition-metal compounds [3], have been intensively explored in experiments, since it was expected that the optical response is significantly affected by the formation of doublon-holon bound states induced by photoexcitation. Namely, the emergence of a light-induced in-gap state and metallization was reported by analyzing the time-resolved optical conductivity in the 1D half-filled extended Hubbard model (EHM) with nearest-neighbor Coulomb repulsion, using time-dependent exact diagonalization (ED) [4] and density-matrix renormalization group [5] techniques. These previous calculations have been carried out, however, with finite systems and therefore depend strongly on the system size. We calculate the nonequilibrium dynamics of the 1D EHM directly in the thermodynamic limit by imposing infinite boundary conditions (IBC) in the infinite matrix-product-states (iMPS) representation. Employing the (infinite) time-evolved block decimation technique [7], we perform time-evolution simulations to extract dynamical correlation functions. The time-resolved optical conductivity in the thermodynamic limit provides us with more precise information on the in-gap state. The other advantage of our numerical technique with IBC is that the momentum-dependent quantities, such as time-dependent photoemission spectra (PES), can also be computed with much higher resolution [8] than those by ED [9]. We will also demonstrate the numerical results of time-dependent PES in the 1D EHM after pulse irradiation, which are related to the trARPES experiments exhibiting gap collapse and reconstruction after photoexcitation. [1] H. Okamoto \textit{et al.}, Phys. Rev. Lett. 98, 037401 (2007). [2] S. Wall \textit{et al.}, Nat. Phys. 7, 114 (2011). [3] H. Matsuzaki \textit{et al.}, Phys. Rev. Lett. 113, 096403 (2014). [4] H. Lu, C. Shao, J. Bon\v{c}a, D. Manske, and T. Tohyama, Phys. Rev. B 91, 245117 (2015). [5] J. Rinc\'{o}n and A. E. Feiguin, Phys. Rev. B 104, 085122 (2021). [6] V. Zauner \textit{et al.}, J. Phys.: Condens. Matter 27, 425602 (2015). [7] G. Vidal, Phys. Rev. Lett. 98, 070201 (2007). [8] S. Ejima, F. Lange, and H. Fehske, Phys. Rev. Res. 4, L012012 (2022). [9] C. Shao, T. Tohyama, H. G. Luo, and H. Lu, Phys. Rev. B 101, 45128 (2020).

Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. While historically the focus has been on the equilibrium properties of the impurity-reservoir system, recent experiments with mesoscopic and cold-atomic systems enabled studies of highly non-equilibrium impurity models, which require novel theoretical techniques. In this talk, I will present an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF). The IF is a functional that encodes the dynamical influence of the bath on the impurity. The efficiency of its MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious “wave function” in the time domain. I will present some general features about TE and describe an efficient algorithm for converting the exact IF to MPS form for a certain family of reservoirs. Once the IF is encoded by a MPS, arbitrary temporal correlation functions of the interacting impurity can be efficiently computed, irrespective of its internal structure.

This work aims to increase the accuracy of the so called auxiliary master equation approach (AMEA). AMEA allows to simulate an impurity in contact with environments that have different chemical potentials and/or temperatures, i.e. a non-equilibrium system. This method is based on the Lindblad equation, which itself is only exact for completely filled or completely empty reservoirs, but here it is rather used to fit the hybridization function, where perfect fitting would reproduce the exact results for the respective environment. I.e. arbitrary reservoirs can be modeled. The more parameters one has, the better the model fits reality. Up to now the main method used to perform Dynamic Mean Field Theory calculations based on AMEA is Exact Diagonalisation, which means the computational power needed goes up exponentially with the number of sites used. Therefore, one can try to find the part of the Hilbert space which contributes most to the solution. A Matrix Product State (MPS) based approach lead to an immense increase in accuracy, but at the cost of high computation times. In this work we used the so called Configuration Interaction, which is well known for the equilibrium case. It has been adopted for usage in terms of the super fermion representation, and the results obtained so far look quite promising. Comparison with the MPS results showed good agreement, especially at higher voltages.