Two-dimensional Boson Research Articles

Supervised learning of an interacting two-dimensional hardcore boson model of a weak topological insulator using correlation functions

Supervised learning of an interacting two-dimensional hardcore boson model of a weak topological insulator using correlation functions

Phases and dynamics of few fermionic impurities immersed in two-dimensional boson droplets

We unravel the ground state properties and emergent nonequilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is accompanied by the rise of induced fermion-fermion interactions mediated by the droplet. Additionally, for increasing attractive droplet-fermion coupling, undulations in the droplet density occur in the vicinity of the fermions manifesting the back-action of the latter. Following interaction quenches from strong to weaker attractive droplet-fermion couplings reveals the spontaneous nucleation of complex excitation patterns in the fermion density such as ring- and cross-shaped structures. These stem from the enhanced interference of the fermions that remain trapped within the droplet, which emulates, to a good degree, an effective potential for the fermions. The non-negligible back-action of the droplet manifests itself in the fact that the effective potential predictions are less accurate at the level of the many-body wave function. Our results provide a paradigm for physics beyond the reduced single-component droplet model, unveiling the role of back-action in droplets and the effect of induced mediated interactions. Published by the American Physical Society 2024

Density-wave-type supersolid of two-dimensional tilted dipolar bosons

Density-wave-type supersolid of two-dimensional tilted dipolar bosons

Searching for Unconventional Superfluid in Excitons of Monolayer Semiconductors.

It is well known that two-dimensional (2D) bosons in homogeneous space cannot undergo real Bose-Einstein condensation, and the superfluid to normal phase transition is Berezinskii-Kosterlitz-Thouless (BKT) type, associated with vortex-antivortex pair unbinding. Here we point out a 2D bosonic system whose low energy physics goes beyond conventional paradigm of 2D homogeneous bosons, i.e., intralayer excitons in monolayer transition metal dichalcogenides. With intrinsic valley-orbit coupling and valley Zeeman energy, exciton dispersion becomes linear at small momentum, giving rise to a series of novel features. The critical temperature of Bose-Einstein condensation of these excitons is nonzero, suggesting true long-range order in 2D homogeneous system. The dispersion of Goldstone mode at long wavelength has the form ϵ(q)∼sqrt[q], in contrast to conventional linear phonon spectrum. The vortex energy deviates from the usual logarithmic form with respect to system size, but instead has an additional linear term. Superfluid to normal phase transition is no longer BKT type for system size beyond a characteristic scale, without discontinuous jump in superfluid density. With the recent experimental progress on exciton fluid at thermal equilibrium in monolayer semiconductors, our work points out an experimentally accessible system to search for unconventional 2D superfluids beyond BKT paradigm.

Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential.

Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum MonteCarlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.

Gluon quasiparticles and the CGC density matrix

We revisit and extend the calculation of the density matrix and entanglement entropy of a color glass condensate (CGC) by including the leading saturation corrections in the calculation. We show that the density matrix is diagonal in the quasiparticle basis, where it has the Boltzmann form. The quasiparticles in a wide interval of momenta behave as massless two-dimensional bosons with the temperature proportional to the typical semihard scale $T={Q}_{s}/\sqrt{{\ensuremath{\alpha}}_{s}{N}_{c}}$. Thus, the semihard momentum region ${Q}_{s}<k<{Q}_{s}/\sqrt{{\ensuremath{\alpha}}_{s}{N}_{c}}$ arises as a well-defined intermediate regime between the perturbatively hard momenta and the nonperturbative soft momenta $k<{Q}_{s}$ in the CGC description of a hadronic wave function.

Erratum: Ground states of two-dimensional tilted dipolar bosons with density-induced hopping [Phys. Rev. A 103 , 043333 (2021)

Received 2 December 2021DOI:https://doi.org/10.1103/PhysRevA.105.019901©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesCold gases in optical latticesDipolar gasesAtomic, Molecular & Optical

Two-Dimensional Vector Boson Oscillator

We introduce two-dimensional vector boson oscillator (VBO) by using the generalized vector boson equation that derived as an excited state from the canonical quantization of classical spinning particle with Zitterbewegung. We write the relativistic vector boson equation (VBE) and introduce the oscillator coupling through non-minimal substitutions. This form of the equation is linear in both momentum and coordinate. The corresponding equation gives a set of coupled equations. By solving these equations we obtain an exact energy spectrum for two-dimensional VBO. This energy spectrum includes spin coupling and shows that the oscillator frequency depends on the spin of the vector boson. According to these results, we discuss several properties of the two-dimensional VBO.

Critical Temperatures of Hard-Core Boson Model on Square Lattice within Bethe Approximation

The short-range correlations are considered for a two-dimensional hard-core boson model on square lattice within Bethe approximation for the clusters consisting of two and four sites. Explicit equations are derived for the critical temperatures of charge and superfluid ordering and their solutions are considered for various ratios of the charge-charge correlation parameter to the transfer integral. It is shown that taking into account short-range correlations for the temperatures of charge ordering results in the appearance of the critical concentration of bosons, which restricts the existence domain of the solutions of charge ordering type. In the case of superfluid ordering with the assumption of short-range correlations, the critical temperature is reduced up to zero values at half-filling. A phase diagram of the hard-core boson model is constructed with the assumption of phase separation within Maxwell's construction and it is shown that taking into account short-range correlations within Bethe approximation quantitatively approximates the form of phase diagram to the results of the quantum Monte Carlo method.

Two-dimensional boson oscillator under a magnetic field in the presence of a minimal length in the non-commutative space

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The eigensolutions are found and the system is mapping to the well-known Schrodinger equation in a Pöschl-Teller potential.

Finite difference/Finite element simulation of the two-dimensional linear and nonlinear Higgs boson equation in the de Sitter space-time

Finite difference/Finite element simulation of the two-dimensional linear and nonlinear Higgs boson equation in the de Sitter space-time

Ground states of two-dimensional tilted dipolar bosons with density-induced hopping

Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study, by means of quantum Monte Carlo, the ground-state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the $xz$ plane. We present ground-state phase diagrams of the above system at different tilt angles. We find that as the dipolar interaction increases, the superfluid phase at half-filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle $\ensuremath{\theta}\ensuremath{\lesssim}{30}^{\ensuremath{\circ}}$ or $\ensuremath{\theta}\ensuremath{\gtrsim}{30}^{\ensuremath{\circ}}$, respectively. More interesting physics happens at tilt angles $\ensuremath{\theta}\ensuremath{\gtrsim}{58}^{\ensuremath{\circ}}$, where we find that as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.5. Moreover, unlike what is observed at lower tilt angles, we find that at half filling, a stripe supersolid intervenes between the superfluid and stripe solid phase.

SU(1,1) Echoes for Breathers in Quantum Gases

Though the celebrated spin echoes have been widely used to reverse quantum dynamics, they are not applicable to systems whose constituents are beyond the control of the su(2) algebra. Here, we design echoes to reverse quantum dynamics of breathers in three-dimensional unitary fermions and two-dimensional bosons and fermions with contact interactions, which are governed by an underlying su(1,1) algebra. Geometrically, SU(1,1) echoes produce closed trajectories on a single or multiple Poincaré disks and thus could recover any initial states without changing the sign of the Hamiltonian. In particular, the initial shape of a breather determines the superposition of trajectories on multiple Poincaré disks and whether the revival time has period multiplication. Our work provides physicists with a recipe to tailor collective excitations of interacting many-body systems.

Thermodynamics of two-dimensional bosons in the lowest Landau level

We study the thermodynamics of short-range interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.

Few-body bound states of two-dimensional bosons

We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

Tensor network approach to two-dimensional bosonization

We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for bosonization at the level of quantum states. Thus, we use the TNO to provide an explicit algorithm for bosonizing fermionic projected entangled pair states (fPEPs). A key step in the algorithm is to account for a choice of spin-structure, encoded in a set of bonds of the bosonized fPEPS. This enables our tensor network approach to bosonization to be applied to systems on arbitrary triangulations of orientable 2D manifolds.

Subsystem trace distance in low-lying states of (1 + 1)-dimensional conformal field theories

We report on a systematic replica approach to calculate the subsystem trace distance for a quantum field theory. This method has been recently introduced in [J. Zhang, P. Ruggiero and P. Calabrese, Phys. Rev. Lett.122 (2019) 141602], of which this work is a completion. The trace distance between two reduced density matrices ρA and σA is obtained from the moments tr(ρA− σA)n and taking the limit n → 1 of the traces of the even powers. We focus here on the case of a subsystem consisting of a single interval of length ℓ embedded in the low lying eigenstates of a one-dimensional critical system of length L, a situation that can be studied exploiting the path integral form of the reduced density matrices of two-dimensional conformal field theories. The trace distance turns out to be a scale invariant universal function of ℓ/L. Here we complete our previous work by providing detailed derivations of all results and further new formulas for the distances between several low-lying states in two-dimensional free massless compact boson and fermion theories. Remarkably, for one special case in the bosonic theory and for another in the fermionic one, we obtain the exact trace distance, as well as the Schatten n-distance, for an interval of arbitrary length, while in generic case we have a general form for the first term in the expansion in powers of ℓ/L. The analytical predictions in conformal field theories are tested against exact numerical calculations in XX and Ising spin chains, finding perfect agreement. As a byproduct, new results in two-dimensional CFT are also obtained for other entanglement-related quantities, such as the relative entropy and the fidelity.

Many-body localization in continuum systems: Two-dimensional bosons

We demonstrate that many-body localization of two-dimensional weakly interacting bosons in disorder remains stable in the thermodynamic limit at sufficiently low temperatures. Highly energetic particles destroy the localized state only above a critical temperature, which increases with the strength of the disorder. If the particle distribution is truncated at high energies, as it does for cold atom systems, the localization can be stable at any temperature.

Subsystem Trace Distance in Quantum Field Theory.

We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an adhoc replica trick. We then extensively apply this method to the calculation of the distance between reduced density matrices of one interval of length ℓ in eigenstates of conformal field theories. When the interval is short, using the operator product expansion of twist operators, we obtain a universal form for the leading order in ℓ of the trace distance. We compute the trace distances among the reduced density matrices of several low lying states in two-dimensional free massless boson and fermion theories. We compare our analytic conformal results with numerical calculations in XX and Ising spin chains finding perfect agreement.

Bosonization of Fermi liquids in a weak magnetic field

Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a {\em covariant Schwinger algebra}, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.