Quantum Simulation of the Hubbard Model: The Attractive Route

Abstract

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.

11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added references

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Cited by in corpus (54)

• Quantum Simulation
• Fermi-Hubbard physics with atoms in an optical lattice
• Band geometry, Berry curvature and superfluid weight
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Using Quantum Computers for Quantum Simulation
• Quantum gas microscopy of an attractive Fermi-Hubbard system
• Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice
• Optical Kagome lattice for ultra-cold atoms with nearest neighbor interactions
• Direct observation of non-local fermion pairing in an attractive Fermi-Hubbard gas
• Large atom number dual-species magneto-optical trap for fermionic 6Li and 40K atoms
• A dynamical mean-field theory study of stripe order and d-wave superconductivity in the two-dimensional Hubbard model
• Unruh effect for interacting particles with ultracold atoms
• Spin-orbit Coupling Effects on the Superfluidity of Fermi Gas in an Optical Lattice
• Temperature and doping induced instabilities of the repulsive Hubbard model on Lieb lattice
• Fulde-Ferrell-Larkin-Ovchinnikov pairing as leading instability on the square lattice
• Formation of stripes in a mixed-dimensional cold-atom Fermi-Hubbard system
• Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices
• Inhomogeneous BCS-BEC crossover for trapped cold atoms in optical lattices
• Controlled hole doping of a Mott insulator of ultracold fermionic atoms
• Proximity effects in cold atom artificial graphene
• A scalable numerical approach to the solution of the Dyson equation for the non-equilibrium single-particle Green's function
• Simulating a Mott insulator using attractive interaction
• Higher-Order Spin-Hole Correlations around a Localized Charge Impurity
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Charge-4$e$ Superconductivity in a Hubbard model
• Superfluidity of Dirac Fermions in a Tunable Honeycomb Lattice: Cooper Pairing, Collective Modes, and Critical Currents
• Mass-Imbalanced Ionic Hubbard Chain
• Interface and bulk superconductivity in superconducting heterostructures with enhanced critical temperatures
• Effective potential and quantum criticality for imbalanced Fermi mixtures
• Optical signatures of antiferromagnetic ordering of fermionic atoms in an optical lattice
• Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling
• Superfluidity of a dipolar Fermi gas in 2D optical lattices bilayer
• Superconductivity and charge order of confined Fermi systems
• Efficiently measuring $d$-wave pairing and beyond in quantum gas microscopes
• Orbital phases of fermions in an asymmetric optical ladder
• Dual Spectroscopy of Quantum Simulated Fermi-Hubbard Systems
• Ising Antiferromagnet in the 2D Hubbard Model with Mismatched Fermi Surfaces
• p-wave Superfluid Phases of Fermi Molecules in a Bilayer Lattice Array
• d-Wave Spin Density Wave phase in the Attractive Hubbard Model with Spin Polarization
• Unconventional superfluidity in quasi-one-dimensional systems
• Effects of forward disorder on quasi-1D superconductors
• Fermionic vs. bosonic two-site Hubbard models with a pair of interacting cold atoms
• Dynamical structure factor and a new method to measure the pairing gap in two-dimensional attractive Fermi-Hubbard model
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Sensitive linear response of an electron-hole superfluid in a periodic potential
• Frequency-Dependent Superconducting States From the Two-Time Linear Response Theory: Application To Sr${}_2$RuO${}_4$
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet
• Quantum simulation of the Hubbard model with ultracold fermions in optical lattices
• Superconductor-Insulator transition in a two-orbital attractive Hubbard model with Hund's exchange
• Quantum Effects In Low Temperature Bosonic Systems
• Feshbach resonant scattering of three fermions in one-dimensional wells
• Breakdown of electron-pairs in the presence of an electric field of a superconducting ring