Two-particle Bound State Research Articles

On the Bardeen–Cooper–Schrieffer interaction in quantum graphs

We introduce a real-space version of the Bardeen–Cooper–Schrieffer interaction allowing the investigation of the non-trivial interplay between many-body physics and particles confinement on a quantum graph. When the two-body problem is considered, we find that the two-particle wavefunction is solution of an integro-differential Schrödinger equation. The solution of the two-body eigenproblem shows the presence of a two-particle bound state whose stability is enhanced in graphs with peculiar topology. We demonstrate that the enhancement effect is robust against many-body effects, which can be studied by means of the Richardson exact solution of the many-body problem. These findings suggest that the effective pairing interaction can be enhanced in quantum graphs with appropriate connectivity. Experimental evidences in Josephson junctions arrays are also discussed in connection with the microscopic mechanism described in the present work.

Newtonian binding from lattice quantum gravity

We study scalar fields propagating on Euclidean dynamical triangulations (EDT). In this work we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and we study its dependence on the constituent particle mass in the non-relativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schr\"{o}dinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing non-trivial evidence that EDT is in fact a theory of gravity in four dimensions. Furthermore, this result allows us to determine the lattice spacing within an EDT calculation for the first time, and we find that the various lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. This lends further support to the asymptotic safety scenario for gravity.

High-field quantum disordered state in α−RuCl3 : Spin flips, bound states, and multiparticle continuum

Layered $\alpha$-RuCl3 has been discussed as a proximate Kitaev spin liquid compound. Raman and THz spectroscopy of magnetic excitations confirm that the low-temperature antiferromagnetic ordered phase features a broad Raman continuum, together with two magnon-like excitations at 2.7 and 3.6 meV, respectively. The continuum strength is maximized as long-range order is suppressed by an external magnetic field. The state above the field-induced quantum phase transition around 7.5 T is characterized by a gapped multi-particle continuum out of which a two-particle bound state emerges, together with a well-defined single-particle excitation at lower energy. Exact diagonalization calculations demonstrate that Kitaev and off-diagonal exchange terms in the Fleury-Loudon operator are crucial for the occurrence of these features in the Raman spectra. Our study firmly establishes the partially-polarized quantum disordered character of the high-field phase.

Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.

Higgs Mode of Planar Coupled Spin Ladders and its Observation in C9H18N2CuBr4

Polarized inelastic neutron scattering experiments recently identified the amplitude (Higgs) mode in C_{9}H_{18}N_{2}CuBr_{4}, a two-dimensional near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin structure factor of such planar coupled spin-ladder systems using large-scale quantum MonteCarlo simulations. This allows us to provide a quantitative account of the experimental neutron scattering data within a consistent quantum spin model. Moreover, we trace the details of the continuous evolution of the amplitude mode from a two-particle bound state of coupled ladders in the classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with fully restored SU(2) symmetry, where it gets overdamped by the two-magnon continuum in neutron scattering.

A Triplet Resonance in Superconducting Fe1.03Se0.4Te0.6☆☆Supported by the National Basic Research Program of China under Grant Nos 2012CB921700 and 2011CBA00112, the National Natural Science Foundation of China under Grant Nos 11034012 and 11190024, the National Science Foundation under Grant No DMR-0645305, the US DOE under Grant No DE-FG02-07ER46358, and the US Department of Energy, Office of Science, Office of Basic

From heavy fermion compounds and cuprates to iron pnictides and chalcogenides, a spin resonance at is a staple of nearly magnetic superconductors. Possible explanations include a two-particle bound state or loss of magnon damping in the superconducting state. While both scenarios suggest a central role for magnetic fluctuations, distinguishing them is important to identify the right theoretical framework to understand these types of unconventional superconductors. Using an inelastic neutron scattering technique, we show that the spin resonance in the optimally doped Fe1.03Se0.4Te0.6 superconductor splits into three peaks in a high magnetic field, a signature of a two-particle S = 1 triplet bound state.

Chiral liquid phase of simple quantum magnets

We study a $T=0$ quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin $S=1$ XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy plane single-ion anisotropy $D$. At the mean-field level, the system undergoes a direct transition at a critical $D = D_c$ between a paramagnetic state at $D > D_c$ and an ordered state with broken U(1) symmetry at $D < D_c$. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phase the Ising ($J_z$) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at $D > D_c$, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small $J_z$ because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of $D$ and transforms into the magnetically ordered state at some $D<D_c$. We corroborate our analytic treatment with numerical density matrix renormalization group calculations.

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to explicitly investigate the role of the three-particle force. Moreover, we discuss relaxing the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer.

On hydrogen-like bound states in mathcal{N} = 4 super Yang-Mills

Using relativistic quantum mechanics, we study the spectrum of a non-BPS two-particle bound state in the massive phase of mathcal{N} = 4 super Yang-Mills, in the limit when one of the particles is infinitely heavier than the other. We find that the spectrum shows the exact n2 degeneracy for each principal quantum number n, just as in the strict non-relativistic limit. This is in line with the findings of Caron-Huot and Henn, who studied the same system in the large N limit with the technique of integrability and the dual conformal symmetry.

Three-boson bound states in two dimensions

We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or dihalogenated materials). The bosons are classified in two species (a,b) such that a-a and b-b pairs repel each other and a-b attract each other, forming the two-particle bound state with binding energy $\epsilon_b^{(2)}$ (such as bi-exciton). We developed an efficient routine based on the proper choice of basis for analytic and numerical calculations. For zero-angular momentum we found the energies of the three-particle bound states $\epsilon^{(3)}_b$ for wide ranges of the scattering lengths, and found a universal curve of $\epsilon^{(3)}_b/\epsilon^{(2)}_b$ which depends only on the scattering lengths but not the microscopic details of the interactions, this is in contrast to the three-dimensional Efimov effect, where a non-universal three-body parameter is needed.

Floquet-Hubbard bound states in the continuum

We theoretically demonstrate that a type of robust two-particle bound state embedded in the continuum (BIC), which we call Floquet-Hubbard (FH) BIC, can be induced in a homogeneous (i.e., defect-free) Hubbard semilattice by an intense oscillating electric field. While single-particle BIC states are fragile states that exist solely for specially tailored potentials, FH BIC states are found in a wide range of parameter space, do not require fulfillment of resonance conditions, and are thresholdless. Analytical results are derived in the high-frequency limit of field modulation by a multiple-time-scale asymptotic analysis of the ac-driven Hubbard Hamiltonian in the two-particle sector. A FH BIC mode basically corresponds to a molecular state, in which the two particles bind together, undergoing correlated tunneling on the lattice. Localization of the molecular state is induced by the external oscillating field, which effectively attracts the molecular state at the edge of the semi-infinite lattice. Our results can pave the way for the study and interpretation of strong-field phenomena in correlated-particles physics.

Fermions in synthetic non-Abelian gauge potentials: rashbon condensates to novel Hamiltonians

Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin–orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin–orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose–Einstein condensate (RBEC) is a quite intriguing state with the rashbon–rashbon interactions being independent of the fermion–fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin–orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.

Bound states in the mirror TBA

AbstractThe spectrum of the light-cone AdS5×S5superstring contains states composed of particles with complex momenta including in particular those which turn into bound states in the decompactification limit. We propose the mirror TBA description for these states. We focus on a three-particle state which is a finite-size representative of a scattering state of a fundamental particle and a two-particle bound state and dual to an operator from the$ \mathfrak{s}\mathfrak{u}(2) $sector of$ \mathcal{N} = 4\;{\text{SYM}} $. We find that the analytic behavior of Y-functions differs drastically from the case of states with real momenta. Most importantly,YQ-functions exhibit poles in the analyticity strip which leads to the appearance of new terms in the formula for the energy of this state. In addition, the TBA equations are supplied by quantization conditions which involveY2. Considering yet another example of a three- particle state, we find that the corresponding quantization conditions do not even involveY1. Our treatment can be generalized to a wide class of states with complex momenta.

Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs

We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.

Fermi polaron in two dimensions: Importance of the two-body bound state

We investigate a single impurity interacting with a free two-dimensional atomic Fermi gas. The interaction between the impurity and the gas is characterized by an arbitrary attractive short-range potential, which, in two dimensions, always admits a two-particle bound state. We provide analytical expressions for the energy and the effective mass of the dressed impurity by including the two-body bound state, which is crucial for strong interactions, in the integral equation for the effective interaction. Using the same method we give also the results for the polaron parameters in one and three dimensions finding a pretty good agreement with previous known results. Thus our relations can be used as a simple way to estimate the polaron parameters once the two-body bound state of the interaction potential is known.

Microscopic Derivation of Hubbard Parameters for Cold Atomic Gases

We study the exact solution for two atomic particles in an optical lattice interacting via a Feshbach resonance. The analysis includes the influence of all higher bands, as well as the proper renormalization of molecular energy in the closed channel. This exact solution allows for the precise determination of the parameters in the Hubbard model and the two-particle bound state energy. We identify the regime, where a single band Hubbard model fails to describe the scattering properties of the atoms as well as the bound states energies.

Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results

Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.

Interactions of charged particles on surfaces

Charges of the same polarity bound to a surface with a large dielectric contrast exhibit an attractive long-range Coulomb interaction, which leads to a two-particle bound state. Ensembles of like charges experience a collective long-range interaction, which results in compacted structures with interparticle separations that can be orders of magnitude smaller than the equilibrium separation of the pair potential minimum. Simulations indicate that ensembles of surface bound nuclei, such as D or T, exhibit separations small enough to result in significant rates of fusion.

Spectral function of spinless fermions on a one-dimensional lattice

We study the spectral function of interacting one-dimensional fermions for an integrable lattice model away from half-filling. The divergent power-law singularity of the spectral function near the single-particle or single-hole energy is described by an effective x-ray edge type model. At low densities and for momentum near the zone boundary, we find a second divergent singularity at higher energies which is associated with a two-particle bound state. We use the Bethe ansatz solution of the model to calculate the exact singularity exponents for any momentum and for arbitrary values of chemical potential and interaction strength in the critical regime. We relate the singularities of the spectral function to the long-time decay of the fermion Green's function and compare our predictions with numerical results from the time-dependent density-matrix renormalization group (tDMRG). Our results show that the tDMRG method is able to provide accurate time decay exponents in the cases of power-law decay of the Green's function. Some implications for the line shape of the dynamical structure factor away from half-filling are also discussed. In addition, we show that 85% of the total spectral weight in the zero field Heisenberg model near wave-vector $q=\ensuremath{\pi}$ is given by the two-spinon contribution.

Pairing-Symmetry Selection in a Weakly Doped Canted Antiferromagnet on the Triangular Lattice

The mechanism of superconductivity generation by spin fluctuations in the electron doped canted antiferromagnet on the triangular lattice was analyzed. The underlying assumption is that the formation of the bound state is the prerequisite of pairing. The outcome of this analysis is also valid if an additional isotropic attraction is active but the anisotropic spin-fluctuation mediated force decides on the symmetry of the two-particle bound state. When the canted antiferromagnetic state is generated, the symmetry of the point group C6v for the triangular lattice is lowered to the symmetry of C3v. It is demonstrated that spin fluctuations definitely favor the p-wave bound state, which transforms according to the E representation of C3v. Since the inversion is not an element of C3v, the parity is not a good quantum number and thus the predicted paired state will be a mixture of singlet and triplet. Such a scenario may be relevant to physics of superconducting triangular cobaltates or organics.