Recent advances in numerical analytic continuation with physics-motivated constraints now allow spectral functions with sharp features, such as peaks and edges, to be extracted from imaginary-time correlation functions computed by quantum Monte Carlo (QMC) simulations. Here, we test these approaches on various one-dimensional $S=1/2$ spin systems with a single ejected fermion, i.e., extracting the single-hole momentum ($k$) and energy ($\omega$)-dependent spectral function $A(k,\omega )$. We compute the distance ($r$)- and imaginary time ($\tau$)-dependent Green's function $G(r,\tau )$ via Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] of the fermionic Hamiltonian, implementing it for stochastic series expansion QMC simulations. Our calculations of $A(k,\omega )$ focus on the different characteristics of systems with spin-charge separation and those in which a spin polaron forms instead because of effectively attractive interactions between the spin and the charge. Spin-charge separation is well established in the conventional $t\text{−}J$ chain, which we confirm here as a demonstration of the method. Turning on a multispin interaction $Q$ that eventually drives the system into a spontaneously dimerized (valence-bond solid, VBS) state, we can observe the features of spin-charge separation until the VBS transition takes place. While generally good agreement is found with the conventional analytical spin-charge separation ansatz, we point out the formation of a gap between two holon bands that in the ansatz are degenerate (crossing each other versus the momentum) at $k=0$ and $k=\pi$. Inside the VBS phase, effectively attractive interactions may lead to the binding of the spinon and holon, for which we find evidence at large $Q/J$. In the statically dimerized $t\text{−}J$ chain (i.e., with alternating strengths of the model parameters), we find equally spaced spin-polaron bands corresponding to increasingly large bound states with two internal spin-polaron modes—even and odd with respect to parton permutation. Our results overall demonstrate the power of modern analytic continuation tools in combination with large-scale quantum Monte Carlo simulations.

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• Inverse problems
• Quasiparticles & collective excitations
• 1-dimensional systems
• Magnetic systems
• Strongly correlated systems
• Exact solutions for many-body systems
• Mean field theory
• Quantum Monte Carlo
• t-J model