SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations

Abstract

We investigate one dimensional SU$(N)$ Hubbard chains at zero temperature, which can be emulated with ultracold alkaline earth atoms, by using the density matrix renormalization group (DMRG), Bethe ansatz (BA), and bosonization. We compute experimental observables and use the DMRG to benchmark the accuracy of the Bethe ansatz for $N>2$ where the BA is only approximate. In the worst case, we find a relative error $\epsilon \lesssim 4$ in the BA ground state energy for $N\le 4$ at filling 1/N, which is due to the fact that BA improperly treats the triply and higher occupied states. Using the DMRG for $N\le 4$ and the BA for large $N$, we determine the regimes of validity of strong- and weak-coupling perturbation theory for all values of $N$ and in particular, the parameter range in which the system is well described by a SU$(N)$ Heisenberg model at filling 1/N. We find this depends only weakly on $N$. We investigate the Berezinskii-Kosterlitz-Thouless phase transition from a Luttinger liquid to a Mott-insulator by computing the fidelity susceptibility and the Luttinger parameter $K_{\rho }$ at 1/N filling. The numerical findings give strong evidence that the fidelity susceptibility develops a minimum at a critical interaction strength which is found to occur at a finite positive value for $N>2$.

19 pages, 13 figures and 2 tables; slightly revised version as published in Phys. Rev. A

References in corpus (52)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Single-Spin Addressing in an Atomic Mott Insulator
• Sr lattice clock at 1x10^{-16} fractional uncertainty by remote optical evaluation with a Ca clock
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• From density-matrix renormalization group to matrix product states
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Quantum computing with alkaline earth atoms
• Imaging the Mott Insulator Shells using Atomic Clock Shifts
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Nuclear Spin Effects in Optical Lattice Clocks
• Bragg spectroscopy of a strongly interacting Fermi gas
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Competing orders in one dimensional spin 3/2 fermionic systems
• Optical atomic coherence at the one-second time scale
• Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Ground-state fidelity in one-dimensional gapless model
• Controlling and Detecting Spin Correlations of Ultracold Atoms in Optical lattices
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Resonating plaquette phases in large spin cold atom systems
• Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
• A Mott Insulator of Ultracold Alkaline-Earth-Like Atoms
• Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• The fidelity approach to the Hubbard model
• SU(N) quantum spin models: A variational wavefunction study
• DMRG studies of critical SU(N) spin chains
• Ground States of the SU(N) Heisenberg Model
• Three-Component Fermi Gas in a one-dimensional Optical Lattice
• Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field
• The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice
• Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain
• Three-Component Fermionic Atoms with Repulsive Interaction in Optical Lattices
• Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain
• Mott Transitions of Three-Component Fermionic Atoms with Repulsive Interaction in Optical Lattices
• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Exact diagonalization study of the trionic crossover and the trion liquid in the attractive three-component Hubbard model
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension
• Color Superfluid and Trionic State of Attractive Three-Component Lattice Fermionic Atoms at Finite Temperatures
• Exact models for trimerization and tetramerization in spin chains

Cited by in corpus (72)

• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Atomtronic circuits: from many-body physics to quantum technologies
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Production of quantum degenerate strontium gases: Larger, better, faster, colder
• Coherent and dissipative dynamics at quantum phase transitions
• Magnetic crystals and helical liquids in alkaline-earth fermionic gases
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Synthetic gauge fields in synthetic dimensions: Interactions and chiral edge modes
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Pomeranchuk cooling of the SU($2N$) ultra-cold fermions in optical lattices
• Ground-state fidelity at first-order quantum transitions
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Entanglement patterns and generalized correlation functions in quantum many body systems
• Synthetic gauge fields stabilize a chiral spin liquid phase
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz
• Selective insulators and anomalous responses in correlated fermions with synthetic extra dimensions
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders
• Massless renormalization group flow in SU(N)${}_k$ perturbed conformal field theory
• SU(3) Fermions on the Honeycomb Lattice at 1/3-Filling
• Interaction effects with varying $N$ in SU($N$) symmetric fermion lattice systems
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Collective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Two-leg SU(2n) spin ladder: A low-energy effective field theory approach
• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
• Fidelity and entanglement entropy for infinite-order phase transitions
• Quantum phase transition by employing trace distance along with the density matrix renormalization group
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Interplay between exotic superfluidity and magnetism in a chain of four-component ultracold atoms
• Quantum spiral spin-tensor magnetism
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Quantum liquid with strong orbital fluctuations: the case of a pyroxene family
• Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Emergence of Quintet Superfluidity in the Chain of Partially Polarized Spin-3/2 Ultracold Atom
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Competing superconducting instabilities in the one-dimensional p-band degenerate cold fermionic system
• Ground state separability and criticality in interacting many-particle systems
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study
• Persistent Current of SU(N) Fermions
• Finite temperature dynamical properties of SU($N$) fermionic Hubbard models in the spin-incoherent regime
• Momentum classification of SU($n$) spin chains using extended Young Tableaux
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Ground State Phase Diagram of $\text{SU}(3)$ $t$-$J$ Chain
• Phase diagram of the SU$(3)$ Fermi-Hubbard model with next-neighbor interactions
• Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas