arXiv subjects

Marcus Kollar

Publications and source records attributed to Marcus Kollar.

At least 19 recordsLinked to original sources

arXiv2025

Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism

We investigate flat magnonic bands in a generalized sawtooth-chain model in which three sets of exchange parameters (symmetric Heisenberg exchange, axial Ising anisotropy, and antisymmetric Dzyaloshinskii-Moriya (DM) exchange) are assigned independently to each side of the triangular plaquette. If the effective Dzyaloshinskii-Moriya (DM) interaction parameters are generated via the Katsura-Nagaosa-Balatsky (KNB) mechanism of magnetoelectricity, they become explicit functions of the electric-field magnitude and direction, as well as of the lattice geometry, which in the present casen is characterized by two bond angles. We focus on the situation in which these two angles are unequal, corresponding to a distortion of the triangular plaquette. Several electric-field induced flat-band scenarios in the distorted sawtooth chain are analyzed, and expressions are derived for the electric-field strength required to drive the one-magnon excitations into a flat-band regime when the field is aligned along the lattice bonds. The saturation field and its dependence on the distortion angle are also examined. Finally, we establish a mapping between the flat-band solutions for a general DM interaction and its specific KNB-induced form. \\~ \emph{This article is dedicated to the memory of Johannes Richter.}

cond-mat.str-el↗

arXiv2025

On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain

We consider a generalization of the XXZ model on the sawtooth spin chain with Dzyaloshinskii-Moriya interactions in which all exchange constants (symmetric, antisymmetric, and axial anisotropy) are different for the three different bonds of each triangle. We derive and resolve algebraic constraints on the exchange constants ensuring the appearance of a flat band in the one-magnon spectrum. The properties of the corresponding flat magnon bands and localized magnon states are analyzed. We further construct the mapping of the flat-band conditions for the Dzyaloshinskii-Moriya constants onto the Katsura-Nagaosa-Balatsky parameters. Based on the mapping, the possibility of the electric-field-driven flat bands with the aid of the magnetoelectric coupling is examined.

cond-mat.str-el↗

arXiv2022

Photoinduced prethermalization phenomena in correlated metals

We study prethermalization phenomena in weakly interacting Hubbard systems after electric-field pump pulses with finite duration. We treat the Hubbard interaction up to second order, applying the prethermalization paradigm for time-dependent interaction protocols, and the electric field strength beyond linear order. A scaling behavior with pulse duration is observed for the absorbed energy as well as individual prethermalized momentum occupation numbers, which we attribute to the leading quadratic orders in interaction and electric field. We show that a pronounced non-thermal momentum distribution can be created with pump pulses of suitable resonance frequencies, and discuss how to distinguish them from thermal states.

cond-mat.str-el↗

arXiv2019

From Luttinger liquids to Luttinger droplets via higher-order bosonization identities

We derive generalized Kronig identities expressing quadratic fermionic terms including momentum transfer to bosonic operators and use them to obtain the exact solution for one-dimensional fermionic models with linear dispersion in the presence of position-dependent interactions and scattering potential. In these Luttinger droplets, which correspond to Luttinger liquids with spatial variations or constraints, the position dependences of the couplings break the translational invariance of correlation functions and modify the Luttinger-liquid interrelations between excitation velocities.

cond-mat.str-el↗

arXiv2017

Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.

cond-mat.dis-nn↗

arXiv2016

Stroboscopic prethermalization in weakly interacting periodically driven systems

Time-periodic driving provides a promising route to engineer non-trivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable systems can synchronize with the driving into a non-trivial periodic motion, generic non-integrable systems are expected to heat up until they display a trivial infinite-temperature behavior. In this paper we show that a quasi-periodic time evolution over many periods can also emerge in systems with weak integrability breaking, with a clear separation of the timescales for synchronization and the eventual approach of the infinite-temperature state. This behavior is the analogue of prethermalization in quenched systems. The synchronized state can be described using a macroscopic number of approximate constants of motion. We corroborate these findings with numerical simulations for the driven Hubbard model.

cond-mat.str-el↗

arXiv2014

Nonequilibrium dynamical mean-field theory and its applications

The study of nonequilibrium phenomena in correlated lattice systems has developed into an active and exciting branch of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultra-fast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultra-cold atoms in optical lattices provide a new way to control and measure the time-evolution of interacting lattice systems with a vastly different characteristic timescale compared to electron systems. A theoretical description of these phenomena is challenging because, firstly, we have to compute the quantum-mechanical time-evolution of many-body systems out of equilibrium, and secondly, deal with strong-correlation effects which can be of nonperturbative nature. In this review, we discuss the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. We summarize the insights gained into the properties of the infinite-dimensional Hubbard model under strong non-equilibrium conditions. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photo-doping, and collapse-and-revival oscillations in quenched systems.

cond-mat.str-el↗

arXiv2014

Integrability and weak diffraction in a two-particle Bose-Hubbard model

A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry can be obtained with a generalized Bethe ansatz if periodic boundary conditions are imposed. Furthermore, we provide numerical evidence that this holds true for open boundary conditions as well. The model exhibits backscattering at the impurity site -- which usually destroys integrability -- yet there exists an integrable subspace. We investigate the non-integrable even sector numerically and find a class of states which have almost the Bethe ansatz form. These weakly diffractive states correspond to a weak violation of the non-local Yang-Baxter relation which is satisfied in the odd sector. We bring up a method based on the Prony algorithm to check whether a numerically obtained wave function is in the Bethe form or not, and if so, to extract parameters from it. This technique is applicable to a wide variety of other lattice models.

quant-ph↗

arXiv2013

Magnetic instability of the orbital-selective Mott phase

We characterize the low-energy physics of the two-orbital Hubbard model in the orbital-selective Mott phase, in which one band is metallic and the other insulating. Using dynamical mean-field theory with the numerical renormalization group at zero temperature, we show that this phase has a ferromagnetic instability for any nonzero Hund's rule exchange interaction, which can be understood in terms of an effective spin-1 Kondo Hamiltonian. The metallic band therefore behaves as a singular Fermi liquid for which the self-energy has a logarithmic singularity at the Fermi energy.

cond-mat.str-el↗

arXiv2013

Optimal multi-configuration approximation of an N-fermion wave function

We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\geq N $ single-particle orbitals are sought iteratively so that the projection of the given wave function in the $C_M^N$-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.

quant-ph↗

arXiv2013

Kinetic description of thermalization dynamics in weakly interacting quantum systems

After a sudden disruption, weakly interacting quantum systems first relax to a prethermalized state that can be described by perturbation theory and a generalized Gibbs ensemble. Using these properties of the prethermalized state we perturbatively derive a kinetic equation which becomes a quantum Boltzmann equation in the scaling limit of vanishing interaction. Applying this to interaction quenches in the fermionic Hubbard model we find that the momentum distribution relaxes to the thermal prediction of statistical mechanics. For not too large interaction, this two-stage scenario provides a quantitative understanding of the time evolution leading from the initial pure via a metastable prethermal to the final thermal state.

cond-mat.str-el↗

arXiv2013

Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory

We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.

cond-mat.str-el↗

arXiv2013

Dynamical correlation functions and the quantum Rabi model

We study the quantum Rabi model within the framework of the analytical solution developed in Phys. Rev. Lett. 107,100401 (2011). In particular, through time-dependent correlation functions, we give a quantitative criterion for classifying two regions of the quantum Rabi model, involving the Jaynes-Cummings, the ultrastrong, and deep strong coupling regimes. In addition, we find a stationary qubit-field entangled basis that governs the whole dynamics as the coupling strength overcomes the mode frequency.

quant-ph↗

arXiv2012

Bound states in the one-dimensional two-particle Hubbard model with an impurity

We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V> 0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion H$^-$ problem. There are several different types of bound states in this system, each of which appears in a specific region. For given $V$, there exists a (positive) critical value $U_{c1}$ of $U$, below which the ground state is a bound state. Interestingly, close to the critical value ($U\lesssim U_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function, which was initially proposed for H$^-$. For $U>U_{c1}$, the ground state is no longer a bound state. However, there exists a second (larger) critical value $U_{c2}$ of $U$, above which a molecule-type bound state is established and stabilized by the repulsion. We have also tried to solve for the eigenstates of the model using the Bethe ansatz. The model possesses a global $\Zz_2$-symmetry (parity) which allows classification of all eigenstates into even and odd ones. It is found that all states with odd-parity have the Bethe form, but none of the states in the even-parity sector. This allows us to identify analytically two odd-parity bound states, which appear in the parameter regions $-2V<U<-V$ and $-V<U<0$, respectively. Remarkably, the latter one can be \textit{embedded} in the continuum spectrum with appropriate parameters. Moreover, in part of these regions, there exists an even-parity bound state accompanying the corresponding odd-parity bound state with almost the same energy.

cond-mat.quant-gas↗

arXiv2012

Emergence of a common energy scale close to the orbital-selective Mott transition

We calculate the spectra and spin susceptibilities of a Hubbard model with two bands having different bandwidths but the same on-site interaction, with parameters close to the orbital-selective Mott transition, using dynamical mean-field theory. If the Hund's rule coupling is sufficiently strong, one common energy scale emerges which characterizes both the location of kinks in the self-energy and extrema of the diagonal spin susceptibilities. A physical explanation of this energy scale is derived from a Kondo-type model. We infer that for multi-band systems local spin dynamics rather than spectral functions determine the location of kinks in the effective band structure.

cond-mat.str-el↗

arXiv2012

Exact real-time dynamics of the quantum Rabi model

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of <σ_x(t)> and <σ_z(t)> for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.

quant-ph↗

arXiv2012

DC conductivity of graphene with disorder

We model disorder in graphene by random impurities treated in a coherent-potential approximation. Using the analytically solvable Lloyd model for the disorder distribution, we show that the temperature dependence of the minimum conductivity as well as the temperature dependence of the resistivity at high densities and the density dependence of the respective slopes are consistently explained by a temperature dependent disorder strength $Γ$ consisting of a constant plus a $T$-linear contribution. This finding suggests that at least two contributions to scattering in graphene are important for its transport properties, and that one of the contributions is due to scattering of electrons from thermally induced excitations.

cond-mat.mes-hall↗

arXiv2011

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

A quantum many-body system which is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.

cond-mat.str-el↗