Finite-range Interaction Research Articles

Correlation-assisted quantized charge pumping

We investigate charge pumping in the vicinity of order-obstructed topological phases, i.e. symmetry protected topological phases masked by spontaneous symmetry breaking in the presence of strong correlations. To explore this, we study a prototypical Su-Schrieffer-Heeger model with finite-range interaction that gives rise to orbital charge density wave order, and characterize the impact of this order on the model's topological properties. In the ordered phase, where the many-body topological invariant loses quantization, we find that not only is quantized charge pumping still possible, but it is even assisted by the collective nature of the orbital charge density wave order. Remarkably, we show that the Thouless pump scenario may be used to uncover the underlying topology of order-obstructed phases.

Universal Dimerized Quantum Droplets in a One-Dimensional Lattice.

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.

Fermions with long and finite-range interactions on a quantum ring

Background: Idealised systems are commonly used in nuclear physics and condensed matter. For instance, the construction of nuclear energy density functionals involves properties of infinite matter, while neutron drops are used to test nuclear interactions and approximations to the nuclear many-body problem. In condensed matter, quantum rings are also used to study properties of electron systems. Purpose: To investigate the possibility to use quantum rings with systems of nucleons including many-body correlations. Methods: A quantum ring model of a finite number of same spin fermions is developed. Several attractive and repulsive interactions with finite and infinite ranges are considered. Quantum Monte Carlo calculations are used to provide exact ground-state energies. Comparisons with analytical Hartree-Fock solutions are used to get an insight into the role of correlations. Results: Hartree-Fock results with no breaking of space translational symmetry are able to describe many systems. However, additional spatial correlations are required in the case of dense systems with a strong short-range repulsion, or with attractive interactions in large rings. Conclusions: Self-bound systems of fermions with spatial correlations produced by basic features of the nuclear interactions can be described on a quantum ring, encouraging applications with realistic interactions, as well as investigations with higher dimensional geometries such as spherium.

Structure of 190-200Hg within the covariant density functional theory

We study in detail the chain of even - even mercury isotopes 190-200Hg using the relativistic point coupling model. A five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field (SCMF) calculations based on the relativistic density-dependent pointcoupling (DD-PC1) energy density functional, and a finite-range pairing interaction is used to calculate the low-energy excitation spectrum and the B(E2) transitions rates of even-even nuclei. The calculations suggest coexisting configurations in 190Hg, increased collectivity in the isotopes 192-198Hg and a more spherical structure in 200Hg.

Regularized pseudopotential for mean-field calculations

We present preliminary results obtained with a finite-range two-body pseudopotential complemented with zero-range spin-orbit and density-dependent terms. After discussing the penalty function used to adjust parameters, we discuss predictions for binding energies of spherical nuclei calculated at the mean-field level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction.

Three-body structure of B19 : Finite-range effects in two-neutron halo nuclei

The structure and $B(E1)$ transition strength of $^{19}$B are investigated in a $^{17}\text{B}+n+n$ model, triggered by a recent experiment showing that $^{19}$B exhibits a well pronounced two-neutron halo structure. Preliminary analysis of the experimental data was performed by employing contact $n$-$n$ interactions, which are known to underestimate the $s$-wave content in other halo nuclei such as $^{11}$Li. In the present work, the three-body hyperspherical formalism with finite-range two-body interactions is used to describe $^{19}$B. In particular, two different finite-range $n$-$n$ interactions will be used, as well as a simple central Gaussian potential whose range is progressively reduced. The purpose is to determine the main properties of the nucleus and investigate how they change when using contact-like $n$-$n$ potentials. Special attention is also paid to the dependence on the prescription used to account for three-body effects, i.e., a three-body force or a density-dependent $n$-$n$ potential. We have found that the three-body model plus finite-range potentials provide a description of $^{19}$B consistent with the experimental data. The results are essentially independent of the short-distance details of the two-body potentials, giving rise to an $(s_{1/2})^2$ content of about 55%, clearly larger than the initial estimates. Very little dependence has been found as well on the prescription used for the three-body effects. The total computed $B(E1)$ strength is compatible with the experimental result, although we slightly overestimate the data around the low-energy peak of the $dB(E1)/d\varepsilon$ distribution. Finally, we show that a reduction of the $n$-$n$ interaction range produces a significant reduction of the $s$-wave contribution, which then should be expected in calculations using contact interactions.

Revisiting the Θ Point

Using the first-order perturbation theory, we compute the osmotic second and third virial coefficients, the mean-square end-to-end distance ⟨Re2⟩, and the mean-square radius of gyration ⟨Rg2⟩ of a polymer near the Θ point. Our model is based on the discrete Gaussian chain model and includes a square-gradient term accounting for the finite-range interaction (characterized by κ), in addition to the usual monomer second and third virial coefficients (characterized by v and w, respectively). The use of the discrete model avoids the divergence problems encountered in previous studies using the continuous model. Our study identifies four special temperatures in the Θ regime: the temperature ΘN where the osmotic second virial coefficient vanishes, the critical temperature ΘNcr for phase separation, and two compensation temperatures ΘN(e) and ΘN(g) at which ⟨Re2⟩ and ⟨Rg2⟩ reach their respective ideal values. In the infinite chain-length limit N → ∞, all of these four temperatures approach Θ∞, the Θ temperature for the infinitely long chain. These temperatures differ from each other by terms of order N–1/2. In general, these temperatures follow the order ΘN > ΘNcr and ΘN > ΘN(e) > ΘN(g). Furthermore, ΘN > Θ∞, in agreement with the result obtained by Khokhlov some time ago. On the other hand, depending on the ratio w/κb, Θ∞ can be higher than ΘN(e) (for w/κb < 9.45), lower than ΘN(g) (for w/κb > 11.63), or in between ΘN(e) and ΘN(g) (for 9.45 < w/κb < 11.63). ΘNcr can be either higher or lower than Θ∞ depending on whether w/b6 is larger or smaller than 0.574. From the order of these temperatures, we conclude that the chain is mostly expanded relative to the ideal chain at its ΘN. However, at Θ∞, the chain can be either expanded or contracted, depending on the relative position of Θ∞ with respect to ΘN(e) and ΘN(g) and depending on whether the chain dimension is measured by ⟨Re2⟩ or ⟨Rg2⟩.

BCS-BEC Crossover Effects and Pseudogap in Neutron Matter

Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with the T-matrix theory used in the physics of ultracold atoms, which we generalize to the case of a non-separable finite-range interaction. A problem of the standard Nozières–Schmitt-Rink approach and different ways to solve it are discussed. It is shown that in the strong-coupling regime, the spectral function exhibits a pseudo-gap at temperatures above the critical temperature Tc. The effect of the correlated density on the density dependence of Tc is found to be rather weak, but a possibly important effect due to the reduced quasiparticle weight is identified.

Quantum Monte Carlo study of the hardcore bosons with finite-range interactions in one-dimensional optical lattices

Using Quantum Monte Carlo algorithm, we study the quantum behaviors of the hardcore bosons with finite-range interactions in one-dimensional optical lattices, such finite-range interactions were realized in Rydberg-dressed alkali atoms loaded into optical lattices. With the choice of the hardcore boson density ρ=0.75 and finite-interaction range rc=4, the ground-state of the system is expected to be degenerate due to the cluster formation. With the increase of interaction strength V/t, we find the system switches from the superfluid phase to supersolid phase and finally to CDW phase. The finite temperature effect and the finite size effect are also carefully examined.

A search for neutron magicity in the isotopic series of Z = 122, 128 superheavy nuclei

The superheavy nuclei have been examined systematically in the region 158 ⩽ N ⩽ 218, 162 ⩽ N ⩽ 212 for Z = 122 and 128, respectively. The explicit density-dependent meson-exchange (DD-ME) and point-coupling (DD-PC) models within the framework of covariant density functional theory (CDFT) have been used to study the structural and decay properties of the isotopic series which includes the separable form of a finite range of pairing interaction. From the potential energy curves, the ground state properties of nuclei are predicted. Due to the importance of the shell effect in the superheavy region, the Strutinsky shell correction method has been employed for a better understanding of the extra stability of nuclei. The results from neutron pairing energy, two-neutron separation energy (S 2n ), single-particle energy levels, and total shell-correction energy strongly support N = 168, 174, and 178 as deformed neutron-magic numbers from both the force parameter, in both the isotopic series. N = 172 and 184 are predicted as spherical magic with DD-ME2 interaction in the Z = 122 isotopic series. Using three different semi-empirical approaches named UNIV2, SemFIS2, and ImSahu, the α-decay properties are studied and compared with available experimental data, FRDM2012 and the WS4 mass model. The stability of synthesized superheavy nuclei can be determined by comparing spontaneous fission half-lives with α-decay half-lives.

Particles confined in arbitrary potentials with a class of finite-range repulsive interactions.

In this paper, we develop a large N field theory for a system of N classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, V_{ex}(x), and repel each other via a class of pairwise interaction potentials V_{int}(r) (where r is distance between a pair of particles) such that V_{int}∼|r|^{-k} when r→0. We consider the case where every particle is interacting with d (finite-range parameter) number of particles to its left and right. Due to the intricate interplay between external confinement, pairwise repulsion, and entropy, the density exhibits markedly distinct behavior in three regimes k>0,k→0, and k<0. From this field theory, we compute analytically the average density profile for large N in these regimes. We show that the contribution from interaction dominates the collective behavior for k>0 and the entropy contribution dominates for k<0, and both contribute equivalently in the k→0 limit (finite-range log-gas). Given the fact that this family of systems is of broad relevance, our analytical findings are of paramount importance. These results are in excellent agreement with brute-force Monte Carlo simulations.

Emergence of generalized hydrodynamics in the non-local Luttinger model

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

Tightening the Lieb-Robinson Bound in Locally Interacting Systems

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications. We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions. Most prominently, in systems with a large local Hilbert space dimension $D$, our method gives an LR velocity that grows much slower than previous bounds with $D$ as $D\to \infty$. For example, in the Heisenberg model with spin $S$, we find $v\leq$ const. compared to the previous $v\propto S$ which diverges at large $S$, and in multiorbital Hubbard models with $N$ orbitals, we find $v\propto \sqrt{N}$ instead of previous $v\propto N$, and similarly in the $N$-state truncated Bose-Hubbard model and Wen's quantum rotor model. Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the $d$-dimensional quantum Ising model and perturbed toric code models. Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.

A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site

We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also derive a limit estimate and an exponential estimate on the fluctuations of the position of the rightmost particle.

Domes of Tc in single-band and multiband superconductors with finite-range attractive interactions

The rise and fall of the superconducting transition temperature $T_c$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of $T_c$, we go beyond the prototypical attractive Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. By numerically solving the mean-field equations, as well as going beyond mean field theory using a functional renormalization group approach, we find that for a characteristic interaction range $\ell$, there exists a dome in $T_c$ around $k_F \ell \! \sim \! {\mathcal{O}}(1)$. For multiband systems, our mean field theory shows the presence of additional domes in the vicinity of Lifshitz transitions. Our results hold in both two and three dimensions and can be intuitively understood from the geometric relation between the Fermi surface and the interaction range. Our model may be relevant for domes of $T_c$ in dilute weakly coupled superconductors or in engineered cold atom systems.

Perfect sampling for Gibbs point processes using partial rejection sampling

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(\log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $\Theta(1/r^{d})$ parallel processor units are available.

Structure and composition of the inner crust of neutron stars from Gogny interactions

The detailed knowledge of the inner crust properties of neutron stars might be important to explain different phenomena such as pulsar glitches or the possibility of an {\it r-process} site in neutron star mergers. It has been shown in the literature that quantal effects like shell correction or pairing may play a relevant role to determine the composition of the inner crust of the neutron star. In this paper we construct the equation of state of the inner crust using the finite-range Gogny interactions, where the mean field and the pairing field are calculated with same interaction. We have used the semiclassical Variational Wigner-Kirkwood method along with shell and pairing corrections calculated with the Strutinsky integral method and the BCS approximation, respectively. Our results are compared with those of some popular models from the literature. We report a unified equation of state of the inner crust and core computed with the D1M* Gogny force, which was specifically fabricated for astrophysical calculations.

Microscopic description of the self-conjugate Xe108 and Te104 α -decay chain

A microscopic calculation of half-lives for the recently observed $^{108}\mathrm{Xe}\ensuremath{\rightarrow}^{104}\mathrm{Te}\ensuremath{\rightarrow}^{100}\mathrm{Sn}\ensuremath{\alpha}$-decay chain is performed by using a self-consistent framework based on energy density functionals. The relativistic density functional DD-PC1 and a separable pairing interaction of finite range are used to compute axially symmetric deformation-energy surfaces of $^{104}\mathrm{Te}$ and $^{108}\mathrm{Xe}$ as functions of quadrupole, octupole, and hexadecupole collective coordinates. Dynamic least-action paths are determined that trace the $\ensuremath{\alpha}$-particle emission from the equilibrium deformation to the point of scission. The calculated half-lives, 197 ns for $^{104}\mathrm{Te}$ and $50\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ for $^{108}\mathrm{Xe}$, are compared with recent experimental values of the half-lives of superallowed $\ensuremath{\alpha}$ decay of $^{104}\mathrm{Te}$: $&lt;18$ ns, and $^{108}\mathrm{Xe}$: ${58}_{\ensuremath{-}23}^{+106}\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$.

Kinetically constrained freezing transition in a dipole-conserving system

We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

Simplified and improved approach to tensor network operators in two dimensions

Matrix product states and matrix product operators (MPOs) are one-dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality and wide range of applicability of DMRG. However, current algorithms for two-dimensional (2D) tensor network states, known as projected entangled-pair states, rarely employ the associated 2D tensor network operators, projected entangled-pair operators (PEPOs), due to their computational cost and conceptual complexity. To lower these two barriers, we describe how to reformulate a PEPO into a set of tensor network operators that resemble MPOs by considering the different sets of local operators that are generated from sequential bipartitions of the 2D system. The expectation value of a PEPO can then be evaluated on the fly using only the action of MPOs and generalized MPOs at each step of the approximate contraction of the 2D tensor network. This technique allows for the simpler construction and more efficient energy evaluation of 2D Hamiltonians that contain finite-range interactions, and provides an improved strategy to encode long-range interactions that is orders of magnitude more accurate and efficient than existing schemes.