Critical Interaction Strength Research Articles

Suppression of polaron self-localization by correlations

We investigate self-localization of a polaron in a homogeneous Bose-Einstein condensate in one dimension. This effect, where an impurity is trapped by the deformation that it causes in the surrounding Bose gas, has been first predicted by mean-field calculations, but has not been seen in experiments. We study the system in one dimension, where, according to the mean-field approximation, the self-localization effect is particularly robust and present for arbitrarily weak impurity-boson interactions. We address the question whether self-localization is a real effect by developing a variational method which incorporates impurity-boson correlations nonperturbatively and solving the resulting inhomogeneous correlated polaron equations. We find that correlations inhibit self-localization except for very strongly repulsive or attractive impurity-boson interactions. Our prediction for the critical interaction strength for self-localization agrees with a sharp drop of the inverse effective mass found in quantum Monte Carlo simulations of polarons in one dimension. Published by the American Physical Society 2024

Kinetic relaxation and nucleation of Bose stars in self-interacting wave dark matter

We revisit kinetic relaxation and soliton/boson star nucleation in fuzzy scalar dark matter featuring short-ranged self-interactions Hint=−λ|ψ|4/2m2, alongside gravitational self-interactions. We map out the full curve of nucleation timescale for both repulsive (λ<0) and attractive (λ>0) short-ranged self-interaction strength and in doing so reveal two new points. Firstly, besides the two usual terms, ∝G2 and ∝λ2, in the total relaxation rate Γrelax, there is an additional cross term ∝Gλ arising due to interference between gravitational and short-ranged self-interaction scattering amplitudes. This yields a critical repulsive interaction strength λcr≃−2πGm2/v02, at which the relaxation rate is smallest and serves as the transition point between typical net attractive self-interaction (λ≳λcr) and net repulsive self-interaction (−λ≳−λcr). Secondly, while in the net attractive regime, nucleation timescale is similar to inverse relaxation timescale τnuc∼Γrelax−1; in the net repulsive regime, nucleation occurs at a delayed time τnuc∼(λ/λcr)Γrelax−1. We confirm our analytical understanding by performing 3D field simulations with varying average mass density ρ¯, box size L and grid size N. Published by the American Physical Society 2024

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

Highly Efficient Single-Exciton Strong Coupling with Plasmons by Lowering Critical Interaction Strength at an Exceptional Point.

The single-exciton strong coupling with the localized plasmon mode (LPM) at room temperature is highly desirable for exploiting quantum technology. However, its realization has been a very low probability event due to the harsh critical conditions, severely compromising its application. Here, we present a highly efficient approach for achieving such a strong coupling by reducing the critical interaction strength at the exceptional point based upon the damping inhibition and matching of the coupled system, instead of enhancing the coupling strength to overcome the system's large damping. Experimentally, we compress the LPM's damping linewidth from about 45nm to about 14nm using a leaky Fabry-Perot cavity, a good match to the excitonic linewidth of about 10nm. This method dramatically relaxes the harsh requirement in mode volume by more than an order of magnitude and allows a maximum direction angle of the exciton dipole relative to the mode field of up to around 71.9°, significantly improving the success rate of achieving the single-exciton strong coupling with LPMs from about 1% to about 80%.

Ferromagnetic domains in the large- U Hubbard model with a few holes: A full configuration interaction quantum Monte Carlo study

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.

Spectroscopy in the 2+1D Thirring model with N=1 domain wall fermions

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in $2+1+1$ dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\ensuremath{\rightarrow}\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$ symmetry breaking; we analyze the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}\ensuremath{\approx}3$ at the critical point, in stark contrast with the Gross-Neveu model in 3D and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalizable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation

We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a 1D bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the non-interacting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spin-like for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection we find that these edge excitations are quasiparticle-like as long as they remain within the bulk gap. Above a critical interaction strength of $U_c\approx 5 t$ these quasiparticles on the boundary loose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the non-trivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

Rabi Coupled Fermions in the BCS–BEC Crossover

We investigate the three-dimensional BCS–BEC crossover in the presence of a Rabi coupling, which strongly affects several properties of the system, such as the chemical potential, the pairing gap and the superfluid density. We determine the critical interaction strength, below which the system is normal also at zero temperature. Finally, we calculate the effect of the Rabi coupling on the critical temperature of the superfluid-to-normal phase transition by using different theoretical schemes.

The Kronig–Penney model in a quadratic channel with δ interactions: II. Scattering approach

The main purpose of the present paper is to introduce a scattering approach to the study of the Kronig–Penney model in a quadratic channel with δ interactions, which was discussed in full generality in the first paper of the present series. In particular, a secular equation whose zeros determine the spectrum will be written in terms of the scattering matrix from a single δ. The advantages of this approach will be demonstrated in addressing the domain with total energy E∈[0,12) , namely, the energy interval where, for under critical interaction strength, a discrete spectrum is known to exist for the single δ case. Extending this to the study of the periodic case reveals quite surprising behavior of the Floquet spectra and the corresponding spectral bands. The computation of these bands can be carried out numerically, and the main features can be qualitatively explained in terms of a semi-classical framework which is developed for the purpose.

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbour nonreciprocal hopping, in the presence of repulsive nearest-neighbour interactions. At half filling, we find two $\mathcal{PT}$ transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.

Spectral Transition for Dirac Operators with Electrostatic delta -Shell Potentials Supported on the Straight Line

In this note the two dimensional Dirac operator A_eta with an electrostatic delta -shell interaction of strength eta in {mathbb {R}} supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths eta =pm 2 the continuous spectrum of A_eta inside the spectral gap of the free Dirac operator A_0 collapses abruptly to a single point.

Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum MonteCarlo Study.

We perform large-scale quantum MonteCarlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with N=2 spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength U_{c}=7.28±0.02 in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding N=2 chiral Ising Gross-Neveu universality class: the inverse correlation length exponent ν^{-1}=1.19±0.03, the order parameter anomalous dimension η_{ϕ}=0.31±0.01, and the fermion anomalous dimension η_{ψ}=0.136±0.005.

Superfluid properties of bright solitons in a ring

We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.

Bose-Einstein condensate in an elliptical waveguide

We investigate the effects of spatial curvature for an atomic Bose-Einstein condensate confined in an elliptical waveguide. The system is well described by an effective 1D Gross-Pitaevskii equation with a quantum-curvature potential, which has the shape of a double-well but crucially depends on the eccentricity of the ellipse. The ground state of the system displays a quantum phase transition from a two-peak configuration to a one-peak configuration at a critical attractive interaction strength. In correspondence of this phase transition the superfluid fraction strongly reduces and goes to zero for a sufficiently attractive Bose-Bose interaction.

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.

Gapless excitations in non-Abelian Kitaev spin liquids with line defects

We show that line defects in a non-Abelian Kitaev spin liquid harbor gapless one-dimensional Majorana modes if the interaction across the defect falls below a critical value. Treating the weak interaction at the line defect within a mean-field approximation, we determine the critical interaction strength as a function of the external magnetic field. In the gapless regime, we use the low-energy effective field theory to calculate the spin-lattice relaxation rate for a nuclear spin near the defect and find a cubic temperature dependence that agrees with experiments in the Kitaev material $\alpha\text{-RuCl}_3$.

Generalized dynamical mean-field theory of two-sublattice systems with long-range interactions and its application to study charge and spin correlations in graphene

We investigate magnetic and charge correlations in graphene by using the formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. First, we map the average non-local interaction onto the effective static interaction between different sublattices, which is treated together with the local interaction within an effective "two-orbital" local model. The remaining part of the non-local interaction is considered by introducing an effective retarded interaction within the E-DMFT approach. The non-local susceptibilities in charge and spin channel are further evaluated in the ladder approximation. We verify the applicability of the proposed method to describe the effect of uniformly screened long-range Coulomb potential $\propto 1/r$, as well as screened realistic long-range electron interaction [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the developed approach describes a competition of semimetal, spin density wave (SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram is in a good agreement with recent results of functional renormalization group (fRG) for finite large graphene nanoflakes and scaling analysis of quantum Monte Carlo data on finite clusters. Similarly to the previously obtained results within the fRG approach, the realistic screening of Coulomb interaction by $\sigma$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential.

Magnetic, charge, and transport properties of graphene nanoflakes

We investigate magnetic, charge and transport properties of hexagonal graphene nanoflakes (GNFs) connected to two metallic leads by using the functional renormalization group (fRG) method. The interplay between the on-site and long-range interactions leads to a competition of semimetal (SM), spin density wave (SDW), and charge-density-wave (CDW) phases. The ground-state phase diagrams are presented for the GNF systems with screened realistic long-range electron interaction [T. O. Wehling, et. al., Phys. Rev. Lett. 106, 236805 (2011)], as well as uniformly screened long-range Coulomb potential $\propto 1/r$. We demonstrate that the realistic screening of Coulomb interaction by $\sigma$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential. This enhancement gives rise to a wide region of stability of the SM phase for realistic interaction, such that freely suspended GNFs are far from both SM-SDW and SM-CDW phase-transition boundaries and correspond to the SM phase. Close relation between the linear conductance and the magnetic or charge states of the systems is discussed. A comparison of the results with those of other studies on GNFs systems and infinite graphene sheet is presented.

Electron pairing with gapless excitations in mixed double layers

We study the interlayer pairing states in layered systems of two different 2d electronic subsystems, one with relativistic linear and the other with non-relativistic parabolic spectrum. The complex order parameter of the paired state has a two component structure. We investigate the pairing state formation on the mean-field level, determine the critical interaction strength and evaluate the effective potential. The anisotropic three-band spectrum of quasiparticles depends explicitly on the phase difference of the order parameter components, rotates in momentum space as it changes. It is subject to the strong band deformation due to the pairing. It leads to the fusion and hybridization of initially decoupled bands. The quasiparticle spectrum has the shape of deformed Dirac cones in the vicinity of the two touching points between neighboring bands. The density of states exhibits a number of specific features due to band deformation, such as a van Hove singularity.

Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

We apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction $U$ equals the bandwidth ${U}_{\mathrm{c}}=W$, where the single-particle gap opens linearly, $\mathrm{\ensuremath{\Delta}}(U\ensuremath{\ge}W)=U\ensuremath{-}W$. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution ${n}_{k}$ at the Fermi wave number ${k}_{\mathrm{F}}=0$ cannot be used to locate accurately ${U}_{\mathrm{c}}$ from finite-size systems. However, the slope of ${n}_{k}$ at the band edges ${k}_{\mathrm{B}}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$, reveals the formation of a single-particle bound state which can be used to determine ${U}_{\mathrm{c}}$ reliably from ${n}_{k}$ using accurate finite-size data.