Exact sign structure of the $t$-$J$ chain and the single hole ground state

Abstract

Injecting a single hole into a one-dimensional Heisenberg spin chain is probably the simplest case of doping a Mott insulator. The motion of such a single hole will generally induce a many-body phase shift, which can be identified by an exact sign structure of the model known as the phase string. We show that the sign structure is nontrivial even in this simplest problem, which is responsible for the essential properties of Mott physics. We find that the characteristic momentum structure, the Luttinger liquid behavior, and the quantum phase interference of the hole under a periodic boundary condition, can all be attributed to it. We use the density matrix renormalization group (DMRG) numerical simulation to make a comparative study of the $t$-$J$ chain and a model in which the sign structure is switched off. We further show that the key DMRG results can be reproduced by a variational wave function with incorporating the correct sign structure. Physical implications of the sign structure for doped Mott insulators in general are also discussed.

16+5 pages, 8 figures

References in corpus (3)

• On the sign structure of doped Mott insulators
• One hole in the two-leg t-J ladder and adiabatic continuity to the non-interacting limit
• Properties of holons in the Quantum Dimer Model

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• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• Critical role of the sign structure in the doped Mott insulator: Superconductivity vs. Fermi liquid
• Two-Hole Ground State: Dichotomy in Pairing Symmetry
• Hidden spin current in doped Mott antiferromagnets
• Breakdown of the Bloch-wave behavior for a single hole in a gapped antiferromagnet
• Intrinsic translational symmetry breaking in a doped Mott insulator
• Single-hole wave function in two dimensions: A case study of the doped Mott insulator
• Proposal for asymmetric photoemission and tunneling spectroscopies in quantum simulators of the triangular-lattice Fermi-Hubbard model
• The spectral function of Mott-insulating Hubbard ladders: From fractionalized excitations to coherent quasi-particles
• Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped $t$-$J$ loop
• Mottness, Phase String, and High-$T_c$ Superconductivity
• Continuous transition from a Landau quasiparticle to a neutral spinon
• Fractionalized Kohn-Sham Scheme for Strongly Correlated Electrons
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination