Single-hole spectral functions in one-dimensional quantum magnets with different ground states

Abstract

Recent advances in numerical analytic continuation with physics-motivated constraints allow sharp spectral features to be extracted from imaginary-time quantum Monte Carlo (QMC) data. We apply these methods to one-dimensional $S=1/2$ spin systems with a single ejected fermion, computing the momentum- and energy-dependent single-hole spectral function $A(k,\omega)$. The real-space Green's function $G(r,\tau)$ is evaluated using Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] implemented within stochastic series expansion QMC, and $A(k,\omega)$ is obtained by constrained stochastic analytic continuation. We contrast systems exhibiting spin-charge separation with those forming a spin polaron through effective spin-charge attraction. For the conventional $t$-$J$ chain, we recover the established signatures of spin-charge separation. Adding a multispin interaction $Q$ drives the system into a spontaneously dimerized valence-bond-solid (VBS) state; spin-charge-separation features persist up to the transition. Although the spectra generally agree with the conventional analytical ansatz, we find a gap between two holon bands that the ansatz predicts to be degenerate at $k=0$ and $k=\pi$. Deep in the VBS phase, the spectra provide evidence for spinon-holon binding at large $Q/J$. In a statically dimerized $t$-$J$ chain, we observe equally spaced spin-polaron bands associated with increasingly large bound states and two internal modes, even and odd under parton permutation. These results demonstrate the power of constrained analytic continuation combined with large-scale QMC for resolving sharp spectral features and distinguishing fractionalized from bound excitations.