Interaction quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi-liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is, the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: (i) An initial buildup of correlations where the quasiparticles are formed. (ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. (iii) The long-time limit described by a quantum Boltzmann equation leading to thermalization of the momentum distribution function with a temperature T proportional, variantU.     

Artificial electric field in fermi liquids

Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasiparticle constrained within a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron dynamics with spin-orbit coupling, which has received much attention in recent years in noninteracting models. As is well known, the Berry curvature in momentum space modifies na?ve band dynamics via an "artificial magnetic field" in momentum space. Our Fermi liquid formulation completes the reinvention of modified band dynamics by introducing in addition an artificial electric field, related to Berry curvature in frequency and momentum space. We show explicitly how the artificial electric field affects the renormalization factor and transverse conductivity of interacting U(1) Fermi liquids with nondegenerate bands.     

Fermi surface reconstruction in strongly correlated Fermi systems as a first-order phase transition

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n(p), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T. The phase diagram in the vicinity of this transition has been constructed.     

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.     

Released momentum distribution of a Fermi gas in the BCS-BEC crossover

We develop a time-dependent mean-field theory to investigate the released momentum distribution and the released energy of an ultracold Fermi gas in the BCS-BEC crossover after the scattering length has been set to zero by a fast magnetic-field ramp. For a homogeneous gas we analyze the nonequilibrium dynamics of the system as a function of the interaction strength and of the ramp speed. For a trapped gas the theoretical predictions are compared with experimental results.     

Do we understand the role of incoherent interactions in many-body physics?

Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.     

Hubbard模型中的相位弦效应与交互Chern-Simons理论

费米子符号在费米液体理论中至关重要. 然而, 在Mott绝缘体中, 很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题. 本文首先回顾二分晶格上Hubbard模型的相位弦理论, 从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解. 在任意Coulomb作用强度U下, 我们首先导出Hubbard模型的严格的符号结构. 在小U极限下, 它回到通常的费米子符号; 在大U极限下, 它给出了t-J模型的相位弦符号. 在半满情形下, 我们构造了一种电子分数化的表象, 其中, 电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合. 由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图. 在弱关联区域, 费米液体的准粒子由电荷子与自旋子的束缚态构成, 其长程相位相干性取决于背景自旋的关联性质. 体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.     

Topological crossovers near a quantum critical point

We study the temperature evolution of the single-particle spectrum ε-(p) and quasiparticle momentum distribution n(p) of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid ³He.     

Many-body theory of nuclear matter

We combine the many-body theory and the low-density expansion developed by Brueckner, Bethe and others to investigate several properties of the ground state and of single-particle excited states of symmetric nuclear matter. We calculate the following quantities from Reid's hard core nucleon-nucleon interaction: strength, energy-dependence, nonlocality and density-dependence of the real and of the imaginary parts of the optical-model potential, momentum distribution in the interacting ground state, dependence on density and momentum of the norm of a quasiparticle and of the effective mass, spectral function for particle states, saturation density and average binding energy per nucleon. No free parameter is adjusted in the calculation; good agreement is obtained with empirical values. It is shown that the effective mass has a narrow maximum at the Fermi surface; this is investigated in the framework of analytical models.     

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. Received 19 December 2002 Published online 14 March 2003     

Nonequilibrium dynamics of Tonks-Girardeau gases on optical lattices

We summarize in the present work exact results obtained for Tonks-Girardeau gases on one-dimensional optical lattices both for the ground state and nonequilibrium dynamics. On the theoretical side, impenetrable bosons offer the opportunity to study strongly interacting systems in one-dimensional lattices exactly, by means of the Jordan-Wigner transformation, and hence contribute to the topic of strong correlations at the center of interest in both condensed matter physics and quantum gases. This motivation is further enhanced by recent experimental realizations of such systems with ultracold atoms. After having shown their universal properties in equilibrium, we concentrate on their nonequilibrium dynamics. It will be shown that, starting from a pure Fock state, quasi-long-range correlations develop dynamically and lead to the formation of quasicondensates with a momentum determined by the underlying lattice. We expect this effect to be relevant for atom lasers with full control of the wavelength. Then, we will show that the free evolution of an initially confined Tonks-Girardeau gas leads to a momentum distribution that approaches at long times that of the equivalent fermionic system, giving rise to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium. Remarkably, although the momentum distribution function of the Tonks-Girardeau gas becomes equal to the one of the fermions, no loss in coherence is observed in the system, as reflected by a large occupation of eigenstates of the one-particle density matrix.     

Geometric phase contribution to quantum nonequilibrium many-body dynamics

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum nonequilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, nonadiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. This interplay can lead to a nonequilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum-critical point.     

Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.     

Medium-dependent dynamics in Fermi systems from a pair-composite viewpoint

We examine the effects of medium dependence of the two-body dynamics on the many-body properties of Fermion systems, with approximation ultimately aimed at lower densities for all temperatures. The dynamics are initially treated in terms of a pair-composite formulation given previously, and the underlying single-Fermion nature of the pair constituents allows interpretation via more conventional thermal many-body formalism. This permits construction of coupled equations for composite amplitudes and bound states, single-particle energy and momentum distributions, and macroscopic thermodynamic properties. We explore differences between our results and those of traditional theories which incorporate two-body correlations in some fashion, and we display explicitly how correct limiting results are recovered from our equations when the density and/or coupling strength is decreased. Finally, we provide an interpretation of our results via a form of quasiparticle quantum cluster expansion analogous to the familiar particle quantum cluster expansion.     

Berry phase effects on the dynamics of quasiparticles in a superfluid with a vortex

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.     

The Symmetries of Fermion Fluids at Low Dimensions

We point out that the quasiparticle spectrum of the Landau Fermi liquid theory has an extra Z₂ symmetry, local in momentum space, which is not generic to the Hamiltonian with interactions. Thus the Fermi liquid is in this sense a (quantum) zero-temperature critical point.     

Nonequilibrium phase transition in a periodically driven XY spin chain

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-? chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.