Dynamical mean field theory with the density matrix renormalization group

A new numerical method for the solution of the dynamical mean field theory's self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.     

Nonequilibrium photo dynamics of low-dimensional strongly correlated electron systems

One of the outstanding contemporary challenges in condensed matter physics is to understand the dynamics of interacting quantum systems exposed to an external perturbation. We theoretically examine nonequilibrium photo dynamics and its interplay of charge, spin, and lattice degrees of freedom on a Hubbard-Holstein chain in one dimension and a t-J-Holstein square lattice in two dimensions. In the chain, performing dynamical density-matrix renormalization group calculations, we find that many phonons generated dynamically after photo irradiation in Mott insulators cause initial relaxation process. On the other hand, in the square lattice with model parameters as relevant for cuprates, a Lanczos-type exact diagonalization calculation shows that the majority of absorbed energy flows into spin subsystem rather than phonon subsystem.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.     

Dynamically driven renormalization group

We present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.     

Formulation of statistical mechanics for chaotic systems

We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.      

Emergence of non-equilibrium superconductivity originated from repulsive interaction: Demonstration using optical lattices and implication to solid-state matter system

We study the dynamical properties of ultracold fermions in one-dimensional optical superlattices by using the adaptive time-dependent density matrix renormalization group method. The system is repulsive Hubbard model with an two-site periodic superlattice potential. Owing to superlattice structure, the ground-state states become the Mott-type insulating state at quarter-filling and band-type insulating state at half-filling, respectively. We clarify the dynamical properties of time evolution when the system is non-adiabatically changed to another lattice structure (i.e., the superlattice potential is suddenly changed to a normal one). In the case of Mott-type insulating state at quarter-filling, the time evolution exhibits a profile similar to that expected for single atom. On the other hand, we clarify the dynamical properties of a band-type insulating state at half-filling. The strongly-correlated interaction an unusual pairing of fermions induced the pair hopping process. We further address the robustness of pair hopping process and possibility of superconductivity by using sudden change from superlattice structure to normal one.     

Preparation and relaxation of very stable glassy states of a simulated liquid

We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose "fast" vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the "slow" structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.     

Quantum critical scenario from an effective classical renormalization group treatment close to and below four dimensions

We suggest a general procedure to analyze quantum criticality for a wide variety of quantum systems of topical interest, close and below four dimensions. The idea is to apply the Wilsonian renormalization group philosophy to an effective classical functional derived from a general quantum action by averaging over degrees of freedom with non-zero Matsubara frequencies. This allows us to describe, in an unified way, all crossovers expected close to a quantum critical point.     

Renormalization-group description of nonequilibrium critical short-time relaxation processes: A three-loop approximation

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ of the short time evolution of a system with an n-component order parameter is calculated within a dynamical dissipative model using the method of Σ-expansion in a three-loop approximation. Numerical values of θ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.     

Elimination of Fast Chaotic Degrees of Freedom: On the Accuracy of the Born Approximation

We apply standard projection operator techniques known from nonequilibrium statistical mechanics to eliminate fast chaotic degrees of freedom in a low-dimensional dynamical system. Through the usual perturbative approach we end up in second order with a stochastic system where the fast chaotic degrees of freedom are modelled by Gaussian white noise. The accuracy of the perturbation expansion is analysed in detail by the discussion of an exactly solvable model.     

Renormalization by continuous unitary transformations: one-dimensional spinless fermions

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the Hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension favorable results are obtained which agree well with the exact findings based on Bethe ansatz. Received 21 August 2002 / Received in final form 29 October 2002 Published online 31 December 2002     

Renormalization-group analysis for the transition to chaos in Hamiltonian systems

We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of invariant tori for Hamiltonian systems with two degrees of freedom. The analysis of this transformation indicates that the break-up of invariant tori is a universal mechanism. The properties of invariant tori are described by the renormalization flow. A trivial attractive set of the renormalization transformation characterizes the Hamiltonians that have a smooth invariant torus. The set of Hamiltonians that have a non-smooth invariant torus is a fractal surface. This critical surface is the stable manifold of a single strange set encompassing all irrational frequencies. This hyperbolic strange set characterizes the Hamiltonians that have an invariant torus at the threshold of the break-up. From the critical strange set, one can deduce the critical properties of the tori (self-similarity, universality classes).     

ρ-A1 mixing in pion induced reaction

The dynamical evolution of the heavy-ion collision is described by a transport equation of QMD type evolving nucleons, N* and Δ resonances, Λ′s and Σ baryons, furthermore, π′s, η′s, ρ′s, σ′s, ω′s and kaons with their isospin degrees of freedom. The input cross sections and resonance parameters of the model are fitted to the available nucleon-nucleon and pion-nucleon cross sections. One consequence of the chiral restoration is the mixing of parity partners. We look for a possible signature of the mixing of vector and axialvector mesons in heavy-ion collisions. We suggest an experimental method for its observation.     

Ising deconfinement transition between Feshbach-resonant superfluids

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.     

On the Validity of Linear Response Theory in High-Dimensional Deterministic Dynamical Systems

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory’s assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.