Infinite-range Interactions Research Articles

Helical metals and insulators: Sheet singularity of the inflated Berry monopole

We study the new phases of interacting Dirac matter that host novel Berry signatures. We predict a topological Lifshitz phase transition caused by the changes of a Dirac cone intersection from a semimetalic phase to helical insulating or metallic phases. These helical phases provide the examples of gapless topological phase where spectral gap is not required for a topological protection. To realize nodal helical phases one would need to consider isotropic infinite-range inter-particle interaction. This interaction could emerge because of a momentum conserving scattering of electron from a bosonic mode. For repulsive/attractive interactions in density/pseudospin channel system undergoes a transition to helical insulator phase. For an attractive density-density interaction, a new metallic phase forms that hosts {\it nodal circle} and {\it nodal sphere} in two and three dimensions, respectively. A {\it sheet singularity} of Berry curvature is highlighted as a peculiar feature of the nodal sphere phase in 3D and represent the extension of the Berry monopole singularities into inflated monopole. To illustrate the properties of these helical phases we investigate Landau levels in both metallic and insulating phases. Our study provides an extension of the paradigm in the interacting Dirac matter and makes an interesting connection to inflated topological singularities in cosmology.

Complete synchronization of chaotic maps under advection

We explore the emergence of complete synchronization under advection in a linear array of chaotic maps. The couplings decay algebraically with the distance between maps, covering from nearest-neighbor to infinite-range interactions, while the update protocol allows us to scan continuously from nondelayed to one-time-delayed dynamics. When the couplings are symmetric (diffusive) and the update is nondelayed, it is well known that chaotic orbits can synchronize if the range of interactions is long enough, while the inclusion of delays allows complete synchronization of a variety of other trajectories besides chaotic ones. Now we investigate through numerical simulations and theoretical analysis how the inclusion of antisymmetric couplings (advection) affects this scenario, showing the interplay among advection, the range of the interactions, and delay. In general, advection reduces the region in parameter space where completely synchronized states are stable, without affecting the nature of the orbits. The presence of delay can lessen the destabilizing effect of advection, such that synchronization is still possible even when couplings are short-range, for a suitable contribution of the delay, but globally coupled lattices are also affected when delayed responses predominate.

Bell correlations at finite temperature

We show that spin systems with infinite-range interactions can violate at thermal equilibrium a multipartite Bell inequality, up to a finite critical temperatureTc. Our framework can be applied to a wide class of spin systems and Bell inequalities, to study whether nonlocality occurs naturally in quantum many-body systems close to the ground state. Moreover, we also show that the low-energy spectrum of the Bell operator associated to such systems can be well approximated by the one of a quantum harmonic oscillator, and that spin-squeezed states are optimal in displaying Bell correlations for such Bell inequalities.

Effects of Interaction Range on the Behavior of Opinion Consensus

We have frequently encountered the rapid changes that prevalent opinion of the social community is toppled by a new and opposite opinion against the pre-exiting one. To understand this interesting process, mean-field model with infinite-interaction range has been mostly considered in previous studies S. A. Marvel et al., Phys. Rev. Lett. 110, 118702(2012). However, the mean-field interaction range is lack of reality in the sense that any individual cannot interact with all of the others in the community. Based on it, in the present work, we consider a simple model of opinion consensus so-called basic model on the low-dimensional lattices ($d$=1,2) with finite interaction range. The model consists of four types of subpopulations with different opinions: $A, B, AB$, and the zealot of $A$ denoted by $A_c$, following the basic model shown in the work by S. A. Marvel et al.. Comparing with their work, we consider the finite range of the interaction, and particularly reconstruct the lattice structure by adding new links when the two individuals have the distance $<\sigma$. We explore how the interaction range $\sigma$ affects the opinion consensus process on the reconstructed lattice structure. We find that the critical fraction of population for $A_c$ required for the opinion consensus on $A$ shows different behaviors in the small and large interaction ranges. Especially, the critical fraction for $A_c$ increases with the size of $\sigma$ in the region of small interaction range, which is counter-intuitive: When the interaction range is increased, not only the number of nodes affected by $A_c$ but also that affected by $B$ grows, which is believed to cause the increasing behavior of the critical fraction for $A_c$. We also present the difference of dynamic process to the opinion consensus between the regions of small and large interaction ranges.

Quantum optics in Maxwell's fish eye lens with single atoms and photons

We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model, where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of the entangling operation via dipole-dipole interaction. We derive our results analytically using perturbation theory and the Born-Markov approximation and then confirm their validity by numerical simulations. We also discuss how the two-dimensional Maxwell's fish eye lens could be realized experimentally using transformational plasmon optics.

Z2 fractionalized phases of a solvable disordered t−J model

We describe the phases of a solvable $t$-$J$ model of electrons with infinite-range, and random, hopping and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an `orthogonal metal', into a fermion $f$ which carries both the electron spin and charge, and a boson $\phi$. Both $f$ and $\phi$ carry emergent $\mathbb{Z}_2$ gauge charges. The model has a phase in which the $\phi$ bosons are gapped, and the $f$ fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates. The model also has an extended, critical, `quasi-Higgs' phase where both $\phi$ and $f$ are gapless, and the electron operator $\sim f \phi$ has a Fermi liquid-like $1/\tau$ propagator in imaginary time, $\tau$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by $\mathbb{Z}_2$ fractionalization and the anomalous exponents of the $f$ and $\phi$ excitations. This `quasi-Higgs' phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.

Validity and failure of the Boltzmann weight

The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics. The interactions between rotators decay with the distance rij like , where α → ∞ and respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas q-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to q-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on d and α through the ratio .

Temperature dependence of nonlinear susceptibilities in an infinite range interaction model

We present a model to probe metamagnetic properties in systems with a variable number of interacting spins. Thermodynamic properties such as the magnetization per particle , linear susceptibility , and nonlinear susceptibilities and were calculated. The model produces a different magnetic response for N particles when comparing to N − 1 particles for small . For an even number of particles, the susceptibilities show maxima in their temperature dependence. An odd number produces an additional free spin response that dominates at low temperatures. This free spin response also produces a step in the field-dependent magnetization per particle at B = 0 for odd N. The magnetization shows N/2 steps at with integer n for even N and additional steps at with integer n for odd N. Small clusters respond with metamagnetism in an otherwise isotropic spin space, while the large clusters show no metamagnetism.

Violent relaxation in quantum fluids with long-range interactions.

Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic XY model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.

Quantum Critical Metrology.

Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that under equilibrium conditions the management of quantum noise becomes extremely flexible around the quantum critical point of a quantum many-body system: this is due to the critical divergence of quantum fluctuations of the order parameter, which, via Heisenberg's inequalities, may lead to the critical suppression of the fluctuations in conjugate observables. Taking the quantum Ising model as the paradigmatic incarnation of quantum phase transitions, we show that it exhibits quantum critical squeezing of one spin component, providing a scaling for the precision of interferometric parameter estimation which, in dimensions d>2, lies in between the standard quantum limit and the Heisenberg limit. Quantum critical squeezing saturates the maximum metrological gain allowed by the quantum Fisher information in d=∞ (or with infinite-range interactions) at all temperatures, and it approaches closely the bound in a broad range of temperatures in d=2 and 3. This demonstrates the immediate metrological potential of equilibrium many-body states close to quantum criticality, which are accessible, e.g., to atomic quantum simulators via elementary adiabatic protocols.

Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.

Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.

Localization in Asymmetric Random Displacements Models with Infinite Range of Interaction

We consider a random displacements model in a Euclidean space with an infinite-range, polynomially decaying interaction potential, without assuming any symmetry properties of the latter, and give an elementary proof of eigenvalue concentration estimates without resorting to a more traditional Wegner-type analysis or explicit ground state energy minimization. In the strong disorder/semi-classical regime, we prove exponential spectral and dynamical localization, with sub-exponential decay of the eigenfunction correlators. Prior works focused on compactly supported interactions.

Traveling fronts for lattice neural field equations

We show existence and uniqueness of traveling front solutions to a class of neural field equations set on a lattice with infinite range interactions in the regime where the kinetics of each individual neuron is of bistable type. The existence proof relies on a regularization of the traveling wave problem allowing us to use well-known existence results for traveling front solutions of continuous neural field equations. We then show that the traveling front solutions which have nonzero wave speed are unique (up to translation) by constructing appropriate sub and super solutions. The spectral properties of the traveling fronts are also investigated via a careful study of the linear operator around a traveling front in co-moving frame where we crucially use Fredholm properties of nonlocal differential operators previously obtained by the author in an earlier work. For the spectral analysis, we need to impose an extra exponential localization condition on the interactions.

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions with infinite range interactions in $0+1$ dimensions. We have found that, close to the ground state $E \approx 0$, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite $N$, which we compute analytically and numerically, grows exponentially with $N$ for $E \approx 0$. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above $E \approx 0$, the spectral density grows exponential with the energy. Deep in the quantum regime, corresponding to the first $O(N)$ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for $E \approx 0$ is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalues separations smaller than the Thouless energy, which seems to scale linearly with $N$. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universality characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor $g(t)$, obtained from the connected two-level correlation function of the unfolded spectrum, decays as $1/t^2$ for times shorter but comparable to the Thouless time with $g(0)$ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Energy barriers between metastable states in first-order quantum phase transitions

A system of neutral atoms trapped in an optical lattice and dispersively coupled to the field of an optical cavity can realize a variation of the Bose-Hubbard model with infinite-range interactions. This model exhibits a first order quantum phase transition between a Mott insulator and a charge density wave, with spontaneous symmetry breaking between even and odd sites, as was recently observed experimentally [Landig \emph{et. al.}, Nature {\bf 532} (2016)]. In the present paper we approach the analysis of this transition using a variational model which allows us to establish the notion of an energy barrier separating the two phases. Using a discrete WKB method we then show that the local tunneling of atoms between adjacent sites lowers this energy barrier and hence facilitates the transition. Within our simplified description, we are thus able to increment the phase diagram of the model with information concerning the height of the barrier separating the metastable minima from the global minimum in each phase, which is an essential aspect for the understanding of the reconfiguration dynamics induced by a quench across a quantum critical point.

Correlated Dynamics in a Synthetic Lattice of Momentum States.

We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low-energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the added exchange energy between atoms in distinguishable momentum states leads to an effectively attractive, finite-ranged interaction between atoms in momentum space. In this Letter, we observe the onset of self-trapping driven by such interactions in a momentum-space double well, paving the way for more complex many-body studies in tailored MSLs. We consider the types of phenomena that may result from these interactions, including the formation of chiral solitons in zigzag flux lattices.

Theoretical exploration of competing phases of lattice Bose gases in a cavity

We consider bosonic atoms loaded into optical lattices with cavity-mediated infinite-range interactions. Competing short- and global-range interactions cultivates a rich phase diagram. With a systematic field-theoretical perspective, we present an $\emph{analytical}$ construction of global ground-state phase diagram. We find that the infinite-range interaction enhances the fluctuation of the number density. In the strong coupling regime, we find four branches of elementary excitations with two being "partilce-like" and two being "hole-like", and that the excitation gap becomes soft at the phase boundary between compressible phases and incompressible phases. We derive an effective theory describing compressible superfluid and supersolid states. To complement this perturbative study, we construct a self-consistent mean-field theory and find numerical results consistent with our theoretical analysis. We map out the phase diagram and find that a charge density wave may undergo a structure phase transition to a different charge density wave before it finally enters into the supersolid phase driven by increasing the hopping amplitude.

Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED

Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic position. Specifically, we experimentally show that the interference of near-degenerate cavity modes leads to both a strong and tunable-range interaction between Bose-Einstein condensates (BECs) trapped within the cavity. We exploit the symmetry of a confocal cavity to measure the interaction between real BECs and their virtual images without unwanted contributions arising from the merger of real BECs. Atom-atom coupling may be tuned from short range to long range. This capability paves the way toward future explorations of exotic, strongly correlated systems such as quantum liquid crystals and driven-dissipative spin glasses.

Super-radiance reveals infinite-range dipole interactions through a nanofiber

Atoms interact with each other through the electromagnetic field, creating collective states that can radiate faster or slower than a single atom, i.e., super- and sub-radiance. When the field is confined to one dimension it enables infinite-range atom–atom interactions. Here we present the first report of infinite-range interactions between macroscopically separated atomic dipoles mediated by an optical waveguide. We use cold 87Rb atoms in the vicinity of a single-mode optical nanofiber (ONF) that coherently exchange evanescently coupled photons through the ONF mode. In particular, we observe super-radiance of a few atoms separated by hundreds of resonant wavelengths. The same platform allows us to measure sub-radiance, a rarely observed effect, presenting a unique tool for quantum optics. This result constitutes a proof of principle for collective behavior of macroscopically delocalized atomic states, a crucial element for new proposals in quantum information and many-body physics.

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

We study the phase diagram of an elastic interaction model for spin crossover (SC) materials with antiferromagnetic-like short-range interactions. In this model, the interplay between the short-range interaction and the long-range interaction of elastic origin causes complex phase transitions. For relatively weak elastic interactions, the phase diagram is characterized by tricritical points, at which antiferromagnetic (AF) -like and ferromagnetic (F) -like spinodal lines and a critical line merge. On the other hand, for relatively strong elastic interactions, unusual ``horn structures,'' which are surrounded by the F-like spinodal lines, disorder (D) spinodal lines, and the critical line, are realized at higher temperatures. These structures are similar to those obtained in our previous study [Phys. Rev. B 93, 064109 (2016)] of an Ising antiferromagnet with infinite-range ferromagnetic interactions, and we find universal features caused by the interplay between the competing short-range and long-range interactions. The long-range interaction of elastic origin is irrelevant (inessential) for the critical line. In contrast, the AF-like, F-like, and D spinodal lines result from the long-range interaction of elastic origin. This difference causes qualitatively different features of domain formation or nucleation of the new phase: clustering occurs in the former case, while clustering is absent in the latter. Based on the phase diagrams, we discuss the patterns and clustering features of two-step SC transitions, in which the AF-like phase is realized in the intermediate temperature region.