Universal thermodynamics of an SU($N$) Fermi-Hubbard Model

Abstract

The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit $U/t\gg 1$, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU($N$) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on $N$. This raises the question of what -- if any -- are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU($N$) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant Quantum Monte Carlo and Numerical Linked Cluster Expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of $N$. Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site calculations.

arXiv comment22 pages, 15 figures

References in corpus (93)

• Colossal Magnetoresistant Materials: The Key Role of Phase Separation
• Electronic Properties of Graphene in a Strong Magnetic Field
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Quantum Simulators: Architectures and Opportunities
• Tools for quantum simulation with ultracold atoms in optical lattices
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• The Hubbard model: A computational perspective
• Short-range quantum magnetism of ultracold fermions in an optical lattice
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Bad metallic transport in a cold atom Fermi-Hubbard system
• SU(4) Theory for Spin Systems with Orbital Degeneracy
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Observation of canted antiferromagnetism with ultracold fermions in an optical lattice
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Phase diagram of the half-filled two-dimensional SU(N) Hubbard-Heisenberg model: a quantum Monte Carlo study
• Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid
• An ytterbium quantum gas microscope with narrow-line laser cooling
• Exploration of doped quantum magnets with ultracold atoms
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Characteristic Crossing Points in Specific Heat Curves of Correlated Systems
• SU(4) spin-orbit critical state in one dimension
• A Short Introduction to Numerical Linked-Cluster Expansions
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Antiferromagnetic spin correlation of SU($\mathcal{N}$) Fermi gas in an optical super-lattice
• Volume-Collapse Transitions in the Rare Earth Metals
• Geometry Dependence of the Sign Problem
• Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Metal-insulator transition in the one-dimensional SU(N) Hubbard model
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Thermodynamics of strongly interacting fermions in two-dimensional optical lattices
• Robust Bilayer Charge-Pumping for Spin- and Density-Resolved Quantum Gas Microscopy
• Signatures of Spin and Charge Energy Scales in the Local Moment and Specific Heat of the Two-Dimensional Hubbard Model
• SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
• Exact Diagonalization of Heisenberg SU(N) models
• Coupling a mobile hole to an antiferromagnetic spin background: Transient dynamics of a magnetic polaron
• Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
• Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
• Isosbestic Points: Theory and Applications
• Specific Heat of the 2D Hubbard Model
• Universal Thermometry for Quantum Simulation
• High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Mott transition and dimerization in the one-dimensional SU$(n)$ Hubbard model
• SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: implications for twistronics and Mott insulators
• Magnetism and domain formation in SU(3)-symmetric multi-species Fermi mixtures
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Synthetic gauge fields stabilize a chiral spin liquid phase
• Magnetic ordering of three-component ultracold fermionic mixtures in optical lattices
• Correlated Insulating Phases in the Twisted Bilayer Graphene
• Degenerate quantum gases of strontium
• Nearly universal crossing point of the specific heat curves of Hubbard models
• The fermion sign problem: A new decoupling transformation, and a new simulation algorithm
• Critical entropies and magnetic-phase-diagram analysis of ultracold three-component fermionic mixtures in optical lattices
• Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice
• SU(4) symmetry in twisted bilayer graphene - an itinerant perspective
• Artificial $SU(3)$ Spin-Orbit Coupling and Exotic Mott Insulators
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Interaction effects with varying $N$ in SU($N$) symmetric fermion lattice systems
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Emergent Fermi surface in a triangular-lattice SU(4) quantum antiferromagnet
• SU(3) Dirac electrons in the 1/5-depleted square-lattice Hubbard model at 1/4 filling
• Interaction-driven topological phase transitions in fermionic SU($3$) systems
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Ferromagnetic ground state of SU(3) Hubbard model on the Lieb lattice
• Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU($2N$) Dirac fermions
• Filling-driven Mott transition in SU(N) Hubbard models
• Slater and Mott insulating states in the SU(6) Hubbard model
• Breaking of SU(4) symmetry and interplay between strongly correlated phases in the Hubbard model
• Experimental Determination of Bose-Hubbard Energies
• Competing Charge and Magnetic Order in Fermionic Multi-Component Systems
• SU(4)-symmetric Hubbard model at quarter filling: Insights from the dynamical mean-field approach
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Flavor Degeneracy and Effects of Disorder in Ultracold Atom Systems
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• SU(2)-spin Invariant Auxiliary Field Quantum Monte Carlo Algorithm for Hubbard models

Cited by in corpus (31)

• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
• Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Sign Problem in Quantum Monte Carlo Simulation
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure
• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• SU(4)-symmetric Hubbard model at quarter filling: Insights from the dynamical mean-field approach
• Itinerant ferromagnetism in dilute SU(N) Fermi gases
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Effects of lattice geometry on thermopower properties of the repulsive Hubbard model
• Beyond universality in repulsive SU(N) Fermi gases
• On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Spectroscopic evidence for engineered hadron formation in repulsive fermionic $\text{SU}(N)$ Hubbard Models
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Solving the SU($N$) Orbital Hatsugai-Kohmoto Model
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice
• Thermodynamics of a Modified Fermi-Hubbard Model
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model
• Onset of charge incompressibility and Mott gaps in the Honeycomb-Lattice SU(4) Hubbard Model: Lessons for Twisted Bilayer Graphene systems