Two-body Correlations Research Articles

Quantum Monte Carlo study of strongly interacting bosonic one-dimensional systems in periodic potentials

We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction $\rho_s/\rho_0$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for $\rho_s/\rho_0$ agree, but the LL model for scaling $\rho_s/\rho_0$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.

Manifestation of topological behaviors in interacting Weyl systems: One-body versus two-body correlations

Understanding correlation effects in topological phases of matter is at the forefront of current research in condensed matter physics. Here we try to clarify some subtleties in studying topological behaviors of interacting Weyl semimetals. It is well-known that there exist two topological invariants defined to identify their topological character. One is the many-body Chern number, which can be directly linked to the Hall conductivity and thus to the two-particle correlations. The other is the topological index constructed from the single-particle Green's functions. Because the information of Green's functions is easier to be achieved than the many-body wavefunctions, usually only the latter is employed in the literature. However, the approach based on the single-particle Green's function can break down in the strongly correlated phase. For illustration, an exactly solvable two-orbital model with momentum-local two-body interactions is discussed, in which both topological invariants can be calculated analytically. We find that the topological index calculated from the Green's function formalism can be nonzero even for a non-topological strongly correlated phase with vanishing many-body Chern number. In addition, we stress that the physical surface states implied by nonzero many-body Chern numbers should be the edge modes of particle-hole collective excitations, rather than those of quasiparticle nature derived from the Green's function formalism. Our observations thus demonstrate the limitation of the validity of Green's function formalism in the investigations of interacting topological materials.

Correlations in Ultra-relativistic Nuclear Collisions with Strings

While string models describe initial state radiation in ultra-relativistic nuclear collisions well, they mainly differ in their end-point positions of the strings in spatial rapidity. We present a generic model where wounded constituents are amended with strings whose both end-point positions fluctuate and analyze semi-analytically various scenarios of string-end-point fluctuations. In particular we constrain the different cases to experimental data on rapidity spectra from collisions at $\sqrt{s_{\rm NN}}=200$~GeV, and explore their respective two-body correlations, which allows to partially discriminate the possible solutions.

Momentum-Space Atom Correlations in a Mott Insulator

We report on the investigation of the three-dimensional single-atom-resolved distributions of bosonic Mott insulators in momentum-space. Firstly, we measure the two-body and three-body correlations deep in the Mott regime, finding a perfectly contrasted bunching whose periodicity reproduces the reciprocal lattice. In addition, we show that the two-body correlation length is inversely proportional to the in-trap size of the Mott state with a pre-factor in agreement with the prediction for an incoherent state occupying a uniformly filled lattice. Our findings indicate that the momentum-space correlations of a Mott insulator at small tunnelling is that of a many-body ground-state with Gaussian statistics. Secondly, in the Mott insulating regime with increasing tunnelling, we extract the spectral weight of the quasi-particles from the momentum density profiles. On approaching the transition towards a superfluid, the momentum spread of the spectral weight is found to decrease as a result of the increased mobility of the quasi-particles in the lattice. While the shapes of the observed spectral weight agree with the ones predicted by perturbative many-body calculations, the fitted mobilities are larger than the theoretical ones. This discrepancy is similar to that previously reported on the time-of-flight visibility.

Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wavefunction in both real and momentum space as well as the Tan contact unveiling the existence of short range two-body correlations. It is found that when the system is initialized in its bound state it is perturbed in the most efficient manner compared to any other initial configuration. Moreover, starting from an interacting ground state the two-boson response is enhanced for quenches towards the non-interacting limit.

Bell Correlations at Ising Quantum Critical Points.

When a collection of distant observers share an entangled quantum state, the statistical correlations among their measurements may violate a many-body Bell inequality, demonstrating a nonlocal behavior. Focusing on the Ising model in a transverse field with power-law (1/r^{α}) ferromagnetic interactions, we show that a permutationally invariant Bell inequality based on two-body correlations is violated in the vicinity of the quantum-critical point. This observation, obtained via analytical spin-wave calculations and numerical density-matrix renormalization group computations, is traced back to the squeezing of collective-spin fluctuations generated by quantum-critical correlations. We observe a maximal violation for infinite-range interactions (α=0), namely, when interactions and correlations are themselves permutationally invariant.

Equation of state and correlation functions of hypernuclear matter within the lowest order constrained variational method

The lowest order constrained variational method is reformulated to find the equation of state of hypernuclear matter. For the nucleon-nucleon interaction we employed the well-known Argonne V18 (AV18) interaction. The equation of state is calculated using two-body central potentials for $\mathrm{\ensuremath{\Lambda}}N$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ interactions that are determined in order to reproduce the experimental data on single- and double-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei. For the odd-state part of the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ interaction, which is not known due to the lack of experimental data, a proposed repulsive and attractive potential is employed to calculate the equation of state. It is shown that the presence of $\mathrm{\ensuremath{\Lambda}}$ in the hypernuclear matter produces a strong softening of the equation of state. The results are compared with similar calculations with another variational method. The state-dependent energy as well as central and tensor correlation functions are studied up to $J=2$ for each JLSTMT channel where related to total (J), orbital (L) and spin (S) angular momentum and isospin (T) and the third component of isospin (MT) respectively for $\mathrm{\ensuremath{\Lambda}}N$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ interactions. Furthermore, the effect of baryon density and hyperon density as well as the type of hyperon-hyperon interaction on the two-body correlation functions are investigated.

Fluid structure of 1D spinful Fermi gases with long-range interactions

We discuss the fluid structure in the quantum phases of a 1D spinful Fermi gas of atoms interacting via an infinitely long-range coupling, as it may result from a photon-mediated two-body coupling in optical cavities. The system reveals a rich physics, where the spin/charge-density wave and superfluid-like order compete with each other. Following our previous work based on a combined mean-field, exact diagonalization and bosonization analysis, we provide the phase diagram of the system and discuss the structure of the fluid, addressing the main features in momentum space of the order parameters, momentum distribution and two-body correlations. We highlight that the nesting of the Fermi surface in 1D ultimately drives the formation of periodic structures commensurate with the cavity-induced mean-field potential.

Dissipative correlated dynamics of a moving impurity immersed in a Bose–Einstein condensate

We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose–Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.

Optimization of device-independent witnesses of entanglement depth from two-body correlators

In a recent work [A. Aloy et al. arXiv:1807:06027 (2018)] we have considered the characterization of entanglement depth, from a device-independent perspective, in a quantum many-body system. We have shown that the inequalities introduced in [J. Tura et al. Science 344 1256 (2014)] can be used to obtain device-independent witnesses of entanglement depth and that they enjoy two key properties that allow to compute their $k$-producibility bounds more efficiently for larger system sizes, as well as yielding experimentally-friendlier device-independent witnesses of entanglement depth: they involve at most two-body correlators and they are permutationally invariant. While the main aim of our previous work was to illustrate the main ideas and applicability of the method, here we outline the details and complement its findings with detailed analysis and further case studies. Specifically, we consider the problem of finding the $k$-producible bounds of such DIWEDs under different assumptions. Not surprisingly, with the weakest assumptions, we can compute $k$-producible bounds only for relatively small number of parties; however we can still learn interesting features from these solutions that motivate the search on larger systems under the assumption that these features persist. This allows us to tackle the case where the system size eventually reaches the thermodynamic limit.

Device-Independent Witnesses of Entanglement Depth from Two-Body Correlators.

We consider the characterization of entanglement depth in a quantum many-body system from the device-independent perspective; that is, we aim at certifying how many particles are genuinely entangled without relying on assumptions on the system itself nor on the measurements performed. We obtain device-independent witnesses of entanglement depth (DIWEDs) using the Bell inequalities introduced in [J. Tura etal., Science 344, 1256 (2014)SCIEAS0036-807510.1126/science.1247715] and compute their k-producibility bounds. To this end, we exploit two complementary methods: first, a variational one, yielding a possibly optimal k-producible state; second, a certificate of optimality via a semidefinite program, based on a relaxation of the quantum marginal problem. Numerical results suggest a clear pattern on k-producible bounds for large system sizes, which we then tackle analytically in the thermodynamic limit. Contrary to existing DIWEDs, the ones we present here can be effectively measured by accessing only collective measurements and second moments thereof. These technical requirements are met in current experiments, which have already been performed in the context of detecting Bell correlations in quantum many-body systems of 5×10^{2}-5×10^{5} atoms.

Berezinskii-Kosterlitz-Thouless Paired Phase in Coupled XY Models.

We study the effect of a linear tunneling coupling between two-dimensional systems, each separately exhibiting the topological Berezinskii-Kosterlitz-Thouless (BKT) transition. In the uncoupled limit, there are two phases: one where the one-body correlation functions are algebraically decaying and the other with exponential decay. When the linear coupling is turned on, a third BKT-paired phase emerges, in which one-body correlations are exponentially decaying, while two-body correlation functions exhibit power-law decay. We perform numerical simulations in the paradigmatic case of two coupled XY models at finite temperature, finding evidences that for any finite value of the interlayer coupling, the BKT-paired phase is present. We provide a picture of the phase diagram using a renormalization group approach.

Universal relations for a spin-polarized Fermi gas in two dimensions

We derive the full set of universal relations for spin-polarized Fermi gases with p -wave interaction in two dimensions, simply using the short-range asymptotic behavior of fermion-pair wave functions. For p -wave interactions, an additional contact related to the effective range needs to be introduced, besides the one related to the scattering volume. Since the subleading tail (k−4) of the large-momentum distribution cannot fully be captured by the contacts defined by the adiabatic relations, an extra term resulted from the center-of-mass motions of the pairs gives rise to an additional divergence in the kinetic energy of the system, besides those related to the contacts defined. We show in Tan’s energy theorem that if only two-body correlations are taken into account, all these divergences are reasonably removed, leading to a finite internal energy of the system. In addition, we find that all the other universal relations, such as the high-frequency behavior of the radio-frequency response, short-range behavior of the pair correlation function, generalized virial theorem, and pressure relation, remain unaffected by the center-of-mass motions of the pairs, and are fully governed by the contacts defined by the adiabatic relations. Our results confirm the feasibility of generalizing the contact theory for higher-partial-wave scatterings, and could readily be confirmed in current experiments with ultracold 40K and 6Li atoms.

Clusterization and deformation of multi- Λ hypernuclei within a relativistic mean-field model

Deformed multi-$\Lambda$ hypernuclei are studied within a relativistic mean-field model. In this paper, we take some $N=Z$ "hyper isotope" chains, i.e., $^{8+n}_{\ \ n\Lambda}{\rm Be}$, $^{20+n}_{\ \ \ n\Lambda}{\rm Ne}$, and $^{28+n}_{\ \ \ n\Lambda}{\rm Si}$ systems where $n = 2$, $4$ for Be, and $n = 2$, $8$ for Ne and Si. A sign of two-$^6_{2\Lambda}$He cluster structure is observed in the two-body correlation in $^{12}_{4\Lambda}$Be. In the Ne hyper isotopes, the deformation is slightly reduced by addition of $\Lambda$ hyperons whereas it is significantly reduced or even disappears in the Si hyper isotopes.

Two-step production of resonant Bose-Einstein condensates

Producing a substantial and stable resonant Bose-Einstein condensate (BEC) has proven to be a challenging experimental task due to heating and three-body losses that may occur even before the gas comes to thermal equilibrium. In this paper, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths may not be the best way to prepare a resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between $0$ and $\infty$, which serves to maximize the transfer probability of $N$ bosons of mass $m$ in a harmonic trap with frequency $\omega$. We find that the intermediate scattering length should be $a\approx3.16N^{-2/3}\sqrt{\hbar/(m\omega)}$ to produce an optimum transition probability of $1.03N^{-1/6}$.

Forward-backward multiplicity fluctuations in ultrarelativistic nuclear collisions with wounded quarks and fluctuating strings

We analyze a generic model where wounded quarks are amended with strings in which both end-point positions fluctuate in spatial rapidity. With the assumption that the strings emit particles independently of one another and with a uniform distribution in rapidity, we are able to analyze the model semi-analytically, which allows for its detailed understanding. Using as a constraint the one-body string emission functions obtained from the experimental data for collisions at $\sqrt{s_{NN}}=200$ GeV, we explore the two-body correlations for various scenarios of string fluctuations. We find that the popular measures used to quantify the longitudinal fluctuations are limited with upper and lower bounds and assume close values for the most likely models of the end-point distributions, which may explain why various approaches yield here very similar results.

Charge density distributions and electron scattering form factors of 19F, 27Al and 25Mg nuclei

An effective two-body density operator for point nucleon system folded with two-body correlation functions, which take account of the effect of the strong short range repulsion and the strong tensor force in the nucleon-nucleon forces, is produced and used to derive an explicit form for ground state two-body charge density distributions (2BCDD's) and elastic electron scattering form factors F (q) for 19F, 27Al and 25Mg nuclei. It is found that the inclusion of the two-body short range correlations (SRC) has the feature of reducing the central part of the 2BCDD's significantly and increasing the tail part of them slightly, i.e. it tends to increase the probability of transferring the protons from the central region of the nucleus towards its surface and to increase the root mean square charge radius ˂ r 2˃ 1/2 of the nucleus and then makes the nucleus to be less rigid than the case when there is no (SRC). It is also found that the effects of two body tensor correlations (TCs) on 2BCDD's and ˂ r 2˃ 1/2 are in opposite direction to those of (SRC).

Phase-separation dynamics induced by an interaction quench of a correlated Fermi-Fermi mixture in a double well

We explore the interspecies interaction quench dynamics of ultracold spin-polarized few-body mass balanced Fermi-Fermi mixtures confined in a double-well with an emphasis on the beyond Hartree-Fock correlation effects. It is shown that the ground state of particle imbalanced mixtures exhibits a symmetry breaking of the single-particle density for strong interactions in the Hartree-Fock limit, which is altered within the many-body approach. Quenching the interspecies repulsion towards the strongly interacting regime the two species phase separate within the Hartree-Fock approximation while remaining miscible in the many-body treatment. Despite their miscible character on the one-body level the two species are found to be strongly correlated and exhibit a phase separation on the two-body level that suggests the anti-ferromagnetic like behavior of the few-body mixture. For particle balanced mixtures we show that an intrawell fragmentation (filamentation) of the density occurs both for the ground state as well as upon quenching from weak to strong interactions, a result that is exclusively caused by the presence of strong correlations. Inspecting the two-body correlations a phase separation of the two species is unveiled being a precursor towards an anti-ferromagnetic state. Finally, we simulate in-situ single-shot measurements and showcase how our findings can be retrieved by averaging over a sample of single-shot images.

Dissipation Dynamics of Nuclear Fusion Reactions

Based on both the time-dependent Hartree–Fock (TDHF) and the time-dependent density matrix (TDDM) methods, we adopt a macroscopic reduction procedure to investigate the dissipation dynamics of nuclear fusion reactions. The TDDM method is an extension of TDHF, in the sense that it goes beyond the mean-field concept and takes into account two-body correlations explicitly. To investigate the effect of correlations on dissipation, the collective trajectories as well as the friction coefficients for the reaction ¹⁶O + ¹⁶O →³²S are extracted. Our results suggest that two-body correlations play a relevant role in the fusion process.

Heavy Ion Charge Exchange Reactions as Probes for Beta–Decay

Peripheral heavy ion single and double charge reactions are described by fully quantum mechanical distorted wave methods. A special class of nuclear double charge exchange (DCE) reactions proceeding as a one-step reaction through a two-body process are shown to proceed by nuclear matrix elements of a diagrammatic structure as found also in 0ν2ß decay. These hadronic Majorana-type DCE reactions (MDCE) have to be distinguished from second order DCE reactions, given by double single charge exchange (DSCE) processes, resembling 2ν2ß decay. The theoretical concepts of MDCE are discussed. First results show that ion-ion DCE reactions are the ideal testing grounds for investigations of rare second order nuclear processes, giving insight into nuclear in-medium two-body correlation.