1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules

Abstract

We study one dimensional fermionic and bosonic gases with repulsive power-law interactions $1/|x{|}^{\beta }$, with $\beta >1$, in the framework of Tomonaga-Luttinger liquid (LL) theory. We obtain an accurate analytical expression linking the LL parameter to the microscopic Hamiltonian, for arbitrary $\beta$ and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the LL unstable towards the formation of a cascade of lattice solids with fractional filling, thus forming a "Luttinger staircase". Several of these quantum phases and phase transitions are realized with groundstate polar molecules and weakly-bound magnetic Feshbach molecules.

arXiv comment4 pages, 3 figures, one table, updated discussions in Pag 2, 4

References in corpus (26)

• The physics of dipolar bosonic quantum gases
• Cold and Ultracold Molecules: Science, Technology, and Applications
• Bosonization and Strongly Correlated Systems
• Formation of ultracold polar molecules in the rovibrational ground state
• Dipolar collisions of polar molecules in the quantum regime
• Optical Production of Ultracold Polar Molecules
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Wigner Crystal in One Dimension
• Stabilizing a purely dipolar quantum gas against collapse
• Bosonizing one-dimensional cold atomic gases
• Quantum Phases of Cold Polar Molecules in 2D Optical Lattices
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Trapping ultracold dysprosium: a highly magnetic gas for dipolar physics
• Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases
• Photoassociative Production and Trapping of Ultracold KRb Molecules
• Commensurate-incommensurate transition of cold atoms in an optical lattice
• Repulsive shield between polar molecules
• Continuous loading of an electrostatic trap for polar molecules
• Universal rates for reactive ultracold polar molecules in reduced dimensions
• Formation of ultracold LiCs molecules
• Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
• Devil's staircases and supersolids in a one-dimensional dipolar Bose gas
• Electric field suppression of ultracold confined chemical rates
• Dipolar bosons in a planar array of one-dimensional tubes
• Quantum phase diagrams of fermionic dipolar gases for an arbitrary orientation of dipole moment in a planar array of 1D tubes
• Off-diagonal correlations in a one-dimensional gas of dipolar bosons

Cited by in corpus (55)

• A Strongly Dipolar Bose-Einstein Condensate of Dysprosium
• Condensed Matter Theory of Dipolar Quantum Gases
• Long-range interacting quantum systems
• Manipulation of Molecules with Electromagnetic Fields
• Entanglement entropy for the long range Ising chain
• Topological phases in ultracold polar-molecule quantum magnets
• Production of a dual-species Bose-Einstein condensate of Rb and Cs atoms
• Wigner Crystallization of Single Photons in Cold Rydberg Ensemble
• Dysprosium magneto-optical traps
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Chiral currents in one-dimensional fractional quantum Hall states
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Dislocation-mediated melting of one-dimensional Rydberg crystals
• Realization of a Rydberg-dressed Ramsey interferometer and electrometer
• Estimating Quasi-long-range Order via Renyi Entropies
• Random transverse-field Ising chain with long-range interactions
• Many-body physics of Rydberg dark-state polaritons in the strongly interacting regime
• Homogeneous and inhomogeneous magnetic phases of constrained dipolar bosons
• Trimer liquids and crystals of polar molecules in coupled wires
• Full counting statistics for interacting trapped fermions
• On the complexity of implementing Trotter steps
• Bosons with long range interactions on two-leg ladders in artificial magnetic fields
• Long-range random transverse-field Ising model in three dimensions
• Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
• Quantum spin models with long-range interactions and tunnelings: A quantum Monte Carlo study
• Bound states of Dipolar Bosons in One-dimensional Systems
• Quantum Phases of Dipolar Bosons in Bilayer Geometry
• Exotic Quantum Criticality in One-Dimensional Coupled Dipolar Bosons Tubes
• Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature
• Devil's staircases in synthetic dimensions and gauge fields
• Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint
• The Molecular Hubbard Hamiltonian: Field Regimes and Molecular Species
• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Spontaneous Peierls dimerization and emergent bond order in one-dimensional dipolar gases
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• Formation of classical crystals of dipolar particles in a helical geometry
• Dipolar Gases in Coupled One-Dimensional Lattices
• Topological Devil's staircase in atomic two-leg ladders
• Tuneable defect interactions and supersolidity in dipolar quantum gases on a lattice potential
• Quantum phases of a one-dimensional dipolar Fermi gas
• Polarization angle dependence of the breathing modes in confined one-dimensional dipolar bosons
• Quantum fluctuations in one-dimensional supersolids
• Dipoles on a Two-leg Ladder
• Phase-transitions of the random bond Potts chain with long-range interactions
• Quantum phases of quadrupolar Fermi gases in coupled one-dimensional systems
• Excitonic Tonks-Girardeau and charge-density wave phases in monolayer semiconductors
• Laser-painted cavity-mediated interactions in a quantum gas
• Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions
• Wigner crystal induced by dipole-dipole interaction in one-dimensional optical lattices
• Low energy quantum regimes of 1D dipolar Hubbard model with correlated hopping
• String order in dipole-blockaded quantum liquids
• Quantum frustrated Wigner chains
• Fractal ground state of ion chains in periodic potentials
• Ultracold and dense samples of ground-state molecules in lattice potentials
• Bose-Hubbard model with power-law hopping in one dimension