Universal Hall Response in Synthetic Dimensions

Abstract

We theoretically study the Hall effect on interacting $M$-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on $SU(M)$ symmetric interacting bosons and fermions, as relevant for e.g. typical synthetic dimensional quantum gas experiments, we identify an extensive regime in which the Hall imbalance ${\Delta }_{\mathrm{H}}$ is universal and corresponds to a classical Hall resistivity $R_{\mathrm{H}}=-1/n$ for a large class of quantum phases. Away from this high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.

13 pages, 9 figures

References in corpus (56)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Synthetic gauge fields in synthetic dimensions
• Fidelity approach to quantum phase transitions
• Observation of the Meissner effect with ultracold atoms in bosonic ladders
• A one-dimensional liquid of fermions with tunable spin
• Change of carrier density at the pseudogap critical point of a cuprate superconductor
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Spin-orbit coupled fermions in an optical lattice clock
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Direct observation of chiral currents and magnetic reflection in atomic flux lattices
• Meissner effect in a bosonic ladder
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Bose Hubbard Model in a Strong Effective Magnetic Field: Emergence of a Chiral Mott Insulator Ground State
• Chiral Mott insulator with staggered loop currents in the fully frustrated Bose Hubbard model
• Bosonic Mott Insulator with Meissner Currents
• Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide
• Correlated dynamics in a synthetic lattice of momentum states
• Interacting atomic quantum fluids on momentum-space lattices
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Theory of Bosons in two-leg ladders with large magnetic fields
• Spinless Fermionic ladders in a magnetic field: Phase Diagram
• Synthetic gauge fields in synthetic dimensions: Interactions and chiral edge modes
• Chiral currents in one-dimensional fractional quantum Hall states
• Precursor of Laughlin state of hard core bosons on a two leg ladder
• Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux
• Mott transition in a two-leg Bose-Hubbard ladder under an artificial magnetic field
• Phases of Josephson Junction Ladders
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Vortex lattice melting in a boson-ladder in artificial gauge field
• The Hall Number of Strongly Correlated Metals
• Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux
• Josephson Junction Ladders: Ground State and Relaxation Phenomena
• Topological Transitions for Lattice Bosons in a Magnetic Field
• Phases of Attractive Fermi Gases in Synthetic Dimensions
• Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
• Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field
• Hall effect and inter-chain magneto-optical properties of coupled Luttinger liquids
• Reactive Hall response
• Memory function approach to the Hall constant in strongly correlated electron systems
• Hall effect in strongly correlated low dimensional systems
• Sign Reversal of the Hall Response in a Crystalline Superconductor
• Controlled parity switch of persistent currents in quantum ladders

Cited by in corpus (23)

• Generic transport formula for a system driven by Markovian reservoirs
• Observation of Universal Hall Response in Strongly Interacting Fermions
• Bose-Hubbard triangular ladder in an artificial gauge field
• Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics
• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• Probing the Hall Voltage in Synthetic Quantum Systems
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Ballistic-to-diffusive transition in spin chains with broken integrability
• Vanishing Hall Response of Charged Fermions in a Transverse Magnetic Field
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials
• Exploring helical phases of matter in bosonic ladders
• Drude weight increase by orbital and repulsive interactions in fermionic ladders
• Hall response in interacting bosonic and fermionic ladders
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Measuring Hall voltage and Hall resistance in an atom-based quantum simulator
• Hall response of locally correlated two-dimensional electrons at low density
• Interaction dependence of the Hall response for the Bose-Hubbard triangular ladder
• Exploring Frustration Effects of Strongly Interacting Bosons via the Hall Response
• Universal low-density power laws of the dc conductivity and Hall constant in the self-consistent Born approximation
• Dissipative Generation of Currents by Nonreciprocal Local and Global Environments