Abstract
We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t-J_{z} model can be understood in terms of spinless chargons coupled to a Z_{2} lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z_{2} electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum MonteCarlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J_{z}, i.e., well within reach of current experiments.
Highlights
The phase diagram of this mixed-dimensional t − Jz model can be understood in terms of spinless chargons coupled to a Z2 lattice gauge field
Introduction.—Ultracold atoms in optical lattices provide an excellent platform to perform analog quantum simulations: they can mimic the behavior of tunable model Hamiltonians that are difficult or impossible to solve with current numerics
Significant steps have been taken towards simulating the Hubbard model, including the observation of long-range [1] and canted [2] antiferromagnetism (AFM), bad metallic [3] and spin [4] transport, magnetic polarons [5,6], string patterns [7,8], and in 1D spin-charge separation [9,10] and incommensurate magnetism [11]
Summary
Introduction.—Ultracold atoms in optical lattices provide an excellent platform to perform analog quantum simulations: they can mimic the behavior of tunable model Hamiltonians that are difficult or impossible to solve with current numerics. The phase diagram of this mixed-dimensional t − Jz model can be understood in terms of spinless chargons coupled to a Z2 lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z2 electric field lines which, in turn, lead to a robust stripe phase at low temperatures.
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