Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction

Abstract

Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective $J_1-J_2-$type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model.

8 + 6 pages

References in corpus (49)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Time-evolution methods for matrix-product states
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Fermi-Hubbard physics with atoms in an optical lattice
• The Hubbard Model
• Tools for quantum simulation with ultracold atoms in optical lattices
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• A Quantum Gas Microscope for Fermionic Atoms
• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• String patterns in the doped Hubbard model
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Learning a local Hamiltonian from local measurements
• Quantum Graphical Models and Belief Propagation
• Determining a local Hamiltonian from a single eigenstate
• Perfect Sampling with Unitary Tensor Networks
• Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid
• Quantum Hamiltonian identification from measurement time traces
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Exploration of doped quantum magnets with ultracold atoms
• Sample-efficient learning of quantum many-body systems
• Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Equation of state of the two-dimensional Hubbard model
• Hamiltonian tomography in an access-limited setting without state initialization
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Magnetically mediated hole pairing in fermionic ladders of ultracold atoms
• Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
• Stripe order enhanced superconductivity in the Hubbard model
• Microscopic spinon-chargon theory of magnetic polarons in the t-J model
• Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators
• From the pseudogap metal to the Fermi liquid using ancilla qubits
• Spectral properties of a spin-incoherent Luttinger Liquid
• Meson formation in mixed-dimensional t-J models
• Symmetry Conserving Purification of Quantum States within the Density Matrix Renormalization Group
• Enhanced Superexchange in a Tilted Mott Insulator
• Stripes and Superconductivity in Cuprates
• Z2 parton phases in the mixed-dimensional $t-J_z$ model
• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

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• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
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• Optimized Gutzwiller Projected States for Doped Antiferromagnets in Fermi-Hubbard Simulators