1D Bosons Research Articles

Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to free theory correlators

We develop a systematic method to constrain any n-point correlation function of spinning operators in Large N Slightly Broken Higher Spin (SBHS) theories. As an illustration of the methodology, we work out the three point functions which reproduce the previously known results. We then work out the four point functions of spinning operators. We show that the correlation functions of spinning operators in the interacting SBHS theory take a remarkably simple form and that they can be written just in terms of the free fermionic and critical bosonic theory correlators. They also interpolate nicely between the results in these two theories. When expressed in spinor-helicity variables we obtain an anyonic phase which nicely interpolates between the free fermionic and critical bosonic results which makes 3D bosonization manifest. Further, we also obtain a form for five and higher point functions as well by performing a similar analysis.

3D boson representation of affine Yangian of gl(1) and 3D cut-and-join operators

In this paper, we construct the 3D Bosonic Fock space, which is isomorphic to the vector space of 3D Young diagrams as graded vector spaces. Then we use 3D Bosons to represent the generators of the affine Yangian of gl(1) and show that the generators ψj in the affine Yangian of gl(1) are the 3D cut-and-join operators.

3D Bosons and W1+∞ algebra

In this paper, we consider 3D Young diagrams with at most N layers in z-axis direction, which can be constructed by N 2D Young diagrams on slice z = j, j = 1, 2, · · · , N from the Yang-Baxter equation. Using 2D Bosons {aj,m, m ∈ ℤ} associated to 2D Young diagrams on the slice z = j, we constructed 3D Bosons. Then we show the 3D Boson representation of W1+∞ algebra, and give the method to calculate the Littlewood-Richardson rule for 3-Jack polynomials.

Unusual fluid of one-dimensional disordered bosons at finite temperature

In previous important examinations by Aleiner et al. [Nat. Phys. 6, 900 (2010)] and Michal et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E4455 (2016)], the fluid insulator transition has been explored in one-dimensional (1D) disordered bosons by analytical methods. However, the nature of this ``fluid'' is still not quite understood. Here we shed more light on this ``fluid'' by studying its properties under changes in the average particle number $\ensuremath{\langle}N\ensuremath{\rangle}$ and temperature $T$ in the absence of superfluidity. For this purpose, the worm algorithm path-integral Monte Carlo method is utilized in the grand-canonical ensemble. A measure for the width of path fluctuations is introduced that we call ${\ensuremath{\sigma}}_{J}$. It is found that by increasing $\ensuremath{\langle}N\ensuremath{\rangle}$, ${\ensuremath{\sigma}}_{J}$ rises as the bosons become less repulsive and gain more mobility. The compressibility $\ensuremath{\chi}(\ensuremath{\mu})$, $\ensuremath{\mu}$ being the chemical potential, reveals fluid behavior at the lower $\ensuremath{\gamma}$ and a proposed Bose-glass phase at the larger $\ensuremath{\gamma}$ (the Lieb-Liniger interaction parameter). The kinetic energy ${E}_{K}$ versus $\ensuremath{\gamma}$ at various $T$ signals a transition by its convergence towards a common value. ${E}_{K}$ versus $\ensuremath{\mu}$ reveals a peculiar inversion as one goes from small to larger values of the speckle strength $\ensuremath{\langle}V\ensuremath{\rangle}$ demonstrating a complex influence of the disorder. A tipover of ${E}_{K}$ versus $\ensuremath{\gamma}$ from an increasing to a decreasing trend at the lower $\ensuremath{\gamma}$ also signals a transition. Further, Luttinger's liquid theory cannot be applied to describe 1D bosons in strong disorder at finite $T$ because of the absence of superfluidity. Moreover, $\ensuremath{\langle}V\ensuremath{\rangle}$ largely controls the behavior of $\ensuremath{\chi}(\ensuremath{\mu})$, the pair-correlation function at the origin ${g}_{2}(0)$, and ${E}_{K}$. Surprisingly, the diffusion constant ${D}_{0}$ does not obey the classical isomorphism as it rises with $T$. We also emphasize the importance of this work via its applicability to quantum wires.

Regularization of a strong–weak duality between pointlike interactions in one dimension

Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong–weak duality since the coupling constants in the bosonic and fermionic cases are inversely proportional to each other. We present a regularization of these pointlike interactions that preserves the strong–weak duality, contrary to previously known Hermitian regularizations. This is proven rigorously. This allows one to use this duality perturbatively and we illustrate it in the Lieb–Liniger model at strong coupling.

Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization

Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coupling λ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the λ expansions of the correlation functions. The λ expansions terminate at order λ2 and the solutions are exact in λ. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the 3D Chern-Simons vector models and their holographic duals in AdS4. Besides, we show that the same results can also be obtained rather simply from bosonization duality of 3D Chern-Simons vector models. The odd term at order O(λ) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the 3D bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.

Direct Methods for Pseudo-relativistic Schrödinger Operators

In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrodinger operators $$(-\Delta +m^{2})^{s}$$ with $$s\in (0,1)$$ and mass $$m>0$$ . As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators $$(-\Delta +m^{2})^{s}$$ in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrodinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When $$m=0$$ and $$s=1$$ , equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg–Landau functional associated to harmonic map.

Berry phase for a Bose gas on a one-dimensional ring

We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(\phi)=g \delta(\phi-\phi_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\Delta q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\Delta q/\hbar \oint \mathbf{A}\cdot d\mathbf{l}$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly-interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems.

New and old fermionic dualities from 3d bosonization

We construct novel fermion-fermion dualities in 2 + 1-dimensions using 3d bosonization dualities. This is achieved by relating two-node quiver theories using both the flavor-bounded and flavor-violated 3d bosonization dualities. Such quivers can be viewed as a generalization of the fermionic particle-vortex duality. A special case of these quivers exhibits a ℤ2 symmetry under interchange of the two nodes. Using orbifold techniques, we show that such dualities provide a novel way of deriving known 3d bosonization dualities with adjoint matter, thus unifying the non-Abelian bosonization dualities in an even larger duality web. We then use this construction to derive new dualities involving adjoint matter.

Exact results for the entanglement in 1D Hubbard models with spatial constraints

We investigate the entanglement in Hubbard models of hardcore bosons in 1D, with an additional hardcore interaction on nearest-neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor 1/2 due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.

Mathcal{N} = 1 dualities in 2+1 dimensions

We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared SU(N) ↔ U(k) duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the ε-expansion.

Scaling behavior of Tan's contact for trapped Lieb-Liniger bosons: From two to many

We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain N-boson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy.

Novel 3d bosonic dualities from bosonization and holography

We use 3d bosonization dualities to derive new non-supersymmetric dualities between bosonic quiver theories in 2 + 1 dimensions. It is shown that such dualities are a natural non-Abelian generalization of the bosonic particle-vortex duality. A special case of such dualities is applicable to Chern-Simons theories living on interfaces in 3 + 1 dimensional SU(N) Yang-Mills theory across which the theta angle jumps. We also analyze such interfaces in a holographic construction which provides further evidence for novel dualities between quiver gauge theories and gauge theories with adjoint scalars. These conjectured dualities pass some stringent consistency tests.

Mirror symmetry and bosonization in 2d and 3d

We study a supersymmetry breaking deformation of the mathcal{N}=left(2,2right) cigar = Liouville mirror pair, first introduced by Hori and Kapustin. We show that mirror symmetry flows in the infra-red to 2d bosonization, with the theories reducing to massive Thirring and Sine-Gordon respectively. The exact bosonization map emerges at one-loop. We further compactify non-supersymmetric 3d bosonization dualities on a circle and argue that these too flow to 2d bosonization at long distances.

Three-Body Problem Solved for 1D Boson Trio

Three-Body Problem Solved for 1D Boson Trio

Master 3d bosonization duality with boundaries

We establish the action of the three-dimensional non-Abelian bosonization dualities in the presence of a boundary, which supports a non-anomalous two-dimensional theory. In particular, we generalize a prescriptive method for assigning duality consistent boundary conditions used originally for Abelian dualities to dual non-Abelian Chern-Simons-matter theories with SU and U gauge groups and fundamental matter sectors. The cases of single species matter sectors and those with both scalars and fermions in the dual theories are considered. Generalization of our methods to SO and USp Chern-Simons theories is also discussed.

Phases of QCD3 from non-SUSY Seiberg duality and brane dynamics

We consider a non-supersymmetric USp Yang-Mills Chern-Simons gauge theory coupled to fundamental flavours. The theory is realised in type IIB string theory via an embedding in a Hanany-Witten brane configuration which includes an orientifold and anti-branes. We argue that the theory admits a magnetic Seiberg dual. Using the magnetic dual we identify dynamics in field theory and brane physics that correspond to various phases, obtaining a better understanding of 3d bosonization and dynamical breaking of flavour symmetry in USp QCD$_3$ theory. In field theory both phases correspond to magnetic 'squark' condensation. In string theory they correspond to open string tachyon condensation and brane reconnection. We also discuss other phases where the magnetic 'squark' is massive. Finally, we briefly comment on the case of unitary gauge groups.

Bosonizing three-dimensional quiver gauge theories

We start with the recently conjectured 3d bosonization dualities and gauge global symmetries to generate an infinite sequence of new dualities. These equate theories with non-Abelian product gauge groups and bifundamental matter. We uncover examples of Bose/Bose and Fermi/Fermi dualities, as well as a sequence of dualities between theories with scalar matter in two-index representations. Our conjectures are consistent with level/rank duality in massive phases.

On the higher-spin spectrum in large N Chern-Simons vector models

Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N . In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the ’t Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the ’t Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This logarithmic behavior disappears in the strong coupling limit, where the anomalous dimensions turn into those of the critical O(N ) or Gross-Neveu models, in agreement with the conjectured 3d bosonization duality.

Non-abelian 3D bosonization and quantum Hall states

Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the non-relativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.