Limit Of Weak Interactions Research Articles

Ferromagnetic instability for the single-band Hubbard model in the strong-coupling regime

We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubic and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the ferromagnetic order is more stable in the case that the noninteracting DOS exhibits a slower decay in the high-energy region. The present results suggest that, in the strong-coupling regime, the high-energy part of DOS plays an essential role for the emergence of the ferromagnetically ordered state, in contrast to the Stoner criterion justified in the weak interaction limit.

Describing many-body localized systems in thermal environments

In this work we formulate an efficient method for the description of fully many-body localized systems in weak contact with thermal environments at temperature T. The key idea is to exploit the representation of the system in terms of quasi-local integrals of motion (l-bits) to efficiently derive the generator for the quantum master equation in Born–Markov approximation. We, moreover, show how to compute the steady state of this equation efficiently by using quantum-jump Monte-Carlo techniques as well as by deriving approximate kinetic equations of motion. As an example, we consider a one-dimensional disordered extended Hubbard model for spinless fermions, for which we derive the l-bit representation approximately by employing a recently proposed method valid in the limit of strong disorder and weak interactions. Coupling the system to a global thermal bath, we study the transport between two leads with different chemical potentials at both of its ends. We find that the temperature-dependent current is captured by an interaction-dependent version of Mott’s law for variable range hopping, where transport is enhanced/lowered depending on whether the interactions are attractive or repulsive, respectively. We interpret these results in terms of spatio-energetic correlations between the l-bits.

Melting of ferromagnetic order on a trellis ladder

The ground state properties of a frustrated spin-1/2 system is studied on a trellis ladder which is composed of two zigzag ladders interacting through rung interactions. The presence of rung interaction between the zigzag ladders induces a non-magnetic ground state, although, each of zigzag ladders has ferromagnetic order in weak anti-ferromagnetic leg interaction limit. The rung interaction also generates rung dimers and opens spin gap which increases rapidly with rung interaction strength. The correlation between spins decreases exponentially with the distance between them.

Calibration of the Flory-Huggins interaction parameter in field-theoretic simulations.

Field-theoretic simulations (FTS) offer a versatile method of dealing with complicated block copolymer systems, but unfortunately they struggle to cope with the level of fluctuations typical of experiments. Although the main obstacle, an ultraviolet divergence, can be removed by renormalizing the Flory-Huggins χ parameter, this only works for unrealistically large invariant polymerization indexes, N¯. Here, we circumvent the problem by applying the Morse calibration, where a nonlinear relationship between the bare χb used in FTS and the effective χ corresponding to the standard Gaussian-chain model is obtained by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. This calibration brings the order-disorder transition obtained from FTS into agreement with the universal results of particle-based simulations for values of N¯ characteristic of the experiment. In the limit of weak interactions, the calibration reduces to a linear approximation, χ ≈ z∞χb, consistent with the previous renormalization of χ for large N¯.

Thermal conductivity of the degenerate one-dimensional Fermi gas

We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxation rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions.

Thermal power of heat flow through a qubit.

In this paper we consider the thermal power of a heat flow through a qubit between two baths. The baths are modeled as a set of harmonic oscillators initially at equilibrium, at two temperatures. Heat is defined as the change of energy of the cold bath, and thermal power is defined as expected heat per unit time, in the long-time limit. The qubit and the baths interact as in the spin-boson model, i.e., through qubit operator σ_{z}. We compute thermal power in an approximation analogous to a "noninteracting blip" (NIBA) and express it in the polaron picture as products of correlation functions of the two baths, and a time derivative of a correlation function of the cold bath. In the limit of weak interaction we recover known results in terms of a sum of correlation functions of the two baths, a correlation functions of the cold bath only, and the energy split.

Stacking tunable interlayer magnetism in bilayer CrI3

Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasi-bonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g. magnetism. Inspired by several recent experiments showing interlayer anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling results from a new stacking order with the C2/m space group symmetry, rather than the graphene-like one with R3 as previously believed. Moreover, we demonstrated that the intra- and inter-layer couplings in CrI3 bilayer are governed by two different mechanisms, namely ferromagnetic super-exchange and direct-exchange interactions, which are largely decoupled because of their significant difference in strength at the strong- and weak-interaction limits. This allows the much weaker interlayer magnetic coupling to be more feasibly tuned by stacking orders solely. Given the fact that interlayer magnetic properties can be altered by changing crystal structure with different stacking orders, our work opens a new paradigm for tuning interlayer magnetic properties with the freedom of stacking order in two dimensional layered materials.

Competition-induced increase of species abundance in mutualistic networks

Nutrients from a flowering plant are shared by its pollinators, giving rise to competition in the latter. Such exploitative competition of pollinators can limit their abundance and affect the global organization of the mutualistic partnership in the plant-pollinator mutualistic community. Here we investigate the effects of the exploitative competition between pollinators on the structure and the species abundance of the mutualistic networks which evolve by changing mutualistic partnership towards higher abundance of species. Simulations show different emergent network characteristics between plants and animals; hub plants connected to many pollinators are very rare while a few super-hub pollinators appear with the exploitative competition included, in contrast to equally many hubs of both types without the exploitative competition. More interestingly, the abundance of plant species increases with increasing the exploitative competition strength. We analyze the inverse of the generalized interaction matrix in the weak-interaction limit to identify the leading structural factors relevant to the species abundance, which are shown to be instrumental in optimizing the network structure to increase the mutualistic benefit and lower the cost of exploitative competition.

Schwinger effect by an SU(2) gauge field during inflation

Non-Abelian gauge fields may exist during inflation. We study the Schwinger effect by an SU(2) gauge field coupled to a charged scalar doublet in a (quasi) de Sitter background and the possible backreaction of the generated charged particles on the homogeneous dynamics. Contrary to the Abelian U(1) case, we find that both the Schwinger pair production and the induced current decrease as the interaction strength increases. The reason for this suppression is the isotropic vacuum expectation value of the SU(2) field which generates a (three times) greater effective mass for the scalar field than the U(1). In the weak interaction limit, the above effect is negligible and both the SU(2) and U(1) cases exhibit a linear increase of the current and a constant conductivity with the interaction strength. We conclude that the Schwinger effect does not pose a threat to the dynamics of inflationary models involving an SU(2) gauge field.

Fokker-Planck equation for lattice vibration: Stochastic dynamics and thermal conductivity

We propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas (PG) limit. Using the time-dependent, multiple state-variable probability function of a FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the thermal conductivity based on the Green-Kubo formalism. When the kinetic transport theories are valid, this FPE not only predicts a thermal conductivity that is identical to the one predicted by the phonon Boltzmann transport equation, but also provides additional microscopic details on the multiple-mode correlation functions. More importantly, when the kinetic theories become insufficient due to the breakdown of the PG approximation, this FPE theory remains valid to study the correlation functions among vibrational modes in highly anharmonic lattices with significant mode-mode interactions and/or in disordered lattices with strongly localized modes. At the limit of weak mode-mode interactions, we can adopt quantum perturbation theories to derive the drift/diffusion coefficients based on the anharmonicity data derived from first-principles methods. As temperature elevates to the classical regime, we can perform molecular dynamics simulations to directly compute the coefficients. Because these coefficients are defined as ensemble averages at the short time limit, we can implement massive parallel simulation algorithms to take full advantage of the paralleled high-performance computing platforms. A better understanding of the temperature-dependent coefficients up to melting temperatures will provide new insights on microscopic mechanisms that govern the heat conduction through anharmonic and/or disordered lattices beyond the PG model.

Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate

Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems, and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for weak impurity-boson interaction, if the transferred momentum/energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak coupling results. Using this, we show that the Landau effective interaction in general is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering, or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC. Finally, we show how the Landau effective interaction leads to a sizeable shift of the quasiparticle energy with increasing impurity concentration, which should be detectable with present day experimental techniques.

Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates

The lowest Landau level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our paper provides a controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multivortex solutions.

Coherent functional expansions in quantum field theory

A new formalism is introduced to treat problems in quantum field theory, using coherent functional expansions rather than path integrals. The basic results and identities of this approach are developed. In the case of a Bose gas with point-contact interactions, this leads to a soluble functional equation in the weak interaction limit, where the perturbing term is part of the kinetic energy. This approach has the potential to prevent the Dyson problem of divergence in perturbation theory.

Quantum dark solitons in a Bose gas confined in a hard-wall box

Schr\"odinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite square well potential. The corresponding eigenstates were constructed by M. Gaudin. We analyze weak interaction limit of Gaudin's solutions and identify parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of detection of particle's positions reveal dark solitons in the weak interaction regime and their quantum nature in the presence of strong interactions.

Probing Distance Dependent Charge-Transfer Character in Excimers of Extended Viologen Cyclophanes Using Femtosecond Vibrational Spectroscopy.

Facile exciton transport within ordered assemblies of π-stacked chromophores is essential for developing molecular photonic and electronic materials. Excimer states having variable charge transfer (CT) character are frequently implicated as promoting or inhibiting exciton mobility in such systems. However, determining the degree of CT character in excimers as a function of their structure has proven challenging. Herein, we report on a series of cyclophanes in which the interplanar distance between two phenyl-extended viologen (ExV2+) chromophores is varied systematically using a pair of o-, m-, or p-xylylene (o-, m-, or p-Xy) covalent linkers to produce o-ExBox4+ (3.5 Å), m-ExBox4+ (5.6 Å), and p-ExBox4+ (7.0 Å), respectively. The cyclophane structures are characterized using NMR spectroscopy in solution and single-crystal X-ray diffraction in the solid state. Femtosecond transient mid-IR and stimulated Raman spectroscopies show that the CT contribution to the excimer states formed in o-ExBox4+ and m-ExBox4+ depends on the distance between the chromophores within the cyclophanes, while in the weak interaction limit, as represented by p-ExBox4+ (7.0 Å), the lowest excited singlet state of ExV2+ exclusively photo-oxidizes the p-Xy spacer to give the p-Xy+•-ExV+• ion pair. Moreover, the vibrational spectra of the excimer state show that it assumes a geometry that is intermediate between that of the locally excited and CT states, approximately reflecting the degree of CT character.

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial and final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint Hamiltonian Hˆ0, induced by a time-dependent non-Hermitian interaction f(t)Hˆ1. In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be asymmetric for exchange of initial and final states. In particular, for a temporal shape f(t) of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form of Hˆ0 and Hˆ1. As an application of our results, we provide important physical insights into the asymmetric (chiral) behavior of dynamical encircling of an exceptional point in two- and three-level non-Hermitian systems.

Y junction of Luttinger liquid wires out of equilibrium

We calculate the conductances of a three-way junction of spinless Luttinger-liquid wires as functions of bias voltages applied to three independent Fermi-liquid reservoirs. In particular, we consider the setup that is characteristic of a tunneling experiment, in which the strength of electron-electron interactions in one of the arms of the junction ("tunneling tip") is different from that in the other two arms (which together form a "main wire"). The scaling dependence of the two independent conductances on bias voltages is determined within a fermionic renormalization-group approach in the limit of weak interactions. The solution shows that, in general, the conductances scale with the bias voltages in an essentially different way compared to their scaling with the temperature $T$. Specifically, unlike in the two-terminal setup, the nonlinear conductances cannot be generically obtained from the linear ones by simply replacing $T$ with the "corresponding" bias voltage or the largest one. Remarkably, a finite tunneling bias voltage prevents the interaction-induced breakup of the main wire into two disconnected pieces in the limit of zero $T$ and a zero source-drain voltage.

Stabilization of prethermal Floquet steady states in a periodically driven dissipative Bose-Hubbard model

We discuss the effect of dissipation on heating which occurs in periodically driven quantum many body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states appear. Our results demonstrate that periodically-driven systems can emit energy, which is absorbed from external drivings, to the reservoir so that they can avoid heating.

Distinct surface and bulk charge density waves in ultrathin 1T−TaS2

We employ low-frequency Raman spectroscopy to study the nearly commensurate (NC) to commensurate (C) charge density wave (CDW) transition in 1T-TaS2 ultrathin flakes protected from oxidation. We identify new modes originating from C phase CDW phonons that are distinct from those seen in bulk 1T-TaS2. We attribute these to CDW modes from the surface layers. By monitoring individual modes with temperature, we find that surfaces undergo a separate, low-hysteresis NC-C phase transition that is decoupled from the transition in the bulk layers. This indicates the activation of a secondary phase nucleation process in the limit of weak interlayer interaction, which can be understood from energy considerations.

Single-shot simulations of dynamics of quantum dark solitons

Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of non-interacting fermions but the wave-functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.