Single-hole spectral functions in 1D quantum magnets with different ground states

TL;DR

This paper employs advanced numerical analytic continuation methods with quantum Monte Carlo simulations to analyze single-hole spectral functions in 1D quantum magnets, revealing insights into spin-charge separation, spin polaron formation, and effects of dimerization.

Contribution

It introduces and tests improved analytic continuation techniques on QMC data for 1D spin systems, exploring the transition from spin-charge separation to bound states in dimerized phases.

Findings

Confirmed spin-charge separation in the $t$-$J$ chain.

Observed a gap between holon bands in the VBS phase.

Identified bound states of spinons and holons at large $Q/J$.

Abstract

Thanks to improved methods for numerical analytic continuation with constraints, spectral functions with sharp features can now be extracted from imaginary-time correlation functions computed by quantum Monte Carlo (QMC) simulations. Here we test these new approaches on various one-dimensional $S=1/2$ spin systems with a single ejected fermion, i.e., extracting the single-hole spectral function $A(k,\omega)$. We compute the Green's function $G(r,\tau)$ via a canonical transformation 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 due to effectively attractive interactions between the spin and the charge. Spin-charge separation is well established in the conventional $t$-$J$ chain, which we confirm here as a demonstration of the method. Turning on a multi-spin 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 at $k=0$ and $k=\pi$. Inside the VBS phase, effectively attractive interactions may lead to the binding of the spinon and holon, of which we find evidence at large $Q/J$. In the statically dimerized $t$-$J$ chain, 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 QMC simulations.