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arXiv:2511.20447 · Physical review. B./Physical review. B

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

Anonymous, Gabe Schumm, Bowen Zhao, Anders W. Sandvik

Published Jul 13, 2026• 0 citations
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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 $A(k,ω)$. The real-space Green's function $G(r,τ)$ is evaluated using Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] implemented within stochastic series expansion QMC, and $A(k,ω)$ 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 $k=π$. 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.

DOI
10.1103/y3sq-8knz

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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=1/2S=1/2S=1/2 spin systems with a single ejected fermion, computing the momentum- and energy-dependent single-hole spectral function A(k,ω)A(k,ω)A(k,ω). The real-space Green's function G(r,τ)G(r,τ)G(r,τ) is evaluated using Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] implemented within stochastic series expansion QMC, and A(k,ω)A(k,ω)A(k,ω) 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 ttt-JJJ chain, we recover the established signatures of spin-charge separation. Adding a multispin interaction QQQ 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=0k=0k=0 and k=πk=πk=π. Deep in the VBS phase, the spectra provide evidence for spinon-holon binding at large Q/JQ/JQ/J. In a statically dimerized ttt-JJJ 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.
Using quantum Monte Carlo and numerical analytic continuation methods, we study the dynamic spin structure factor and the single-hole spectral function of a two-dimensional quantum magnet (JJJ-QQQ model) at its quantum phase transition separating Néel antiferromagnetic and spontaneously dimerized ground states. At this putative deconfined quantum-critical point, we find a broad continuum of spinon excitations that can be accounted for by the fermionic πππ-flux state; a known mean-field model for deconfined quantum criticality. We find that the best description of the two-spinon continuum is with a version of the model with a 2×22\times 22×2 unit cell, reflecting non-trivial mutual statistics of spinons and anti-spinons. The single-hole spectral function can be described by the same spinon dispersion relation and an independently propagating holon. Thus, the system exhibits spin-charge separation and will likely evolve into an extended holon metal phase at finite doping.
Observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many-body physics. Here, we further explore a computational scheme [Y. Tang and A. W. Sandvik, Phys. Rev. Lett. 107, 157201 (2011)] based on valence-bond quantum Monte Carlo simulations of quantum spin systems. Using several different one-dimensional models, we characterize S=12S=\frac{1}{2}S=21​ spinon excitations using the intrinsic spinon size $\ensuremath{\lambda}$ and confinement length $\mathrm{\ensuremath{\Lambda}}$ (the size of a bound state). The spinons have finite size in valence-bond-solid states, infinite size in the critical region (with overlaps characterized by power laws), and become ill defined (completely unlocalizable) in the N\'eel state (which we stabilize in one dimension by introducing long-range interactions). We also verify that pairs of spinons are deconfined in uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths (dimerization) or coupling two chains (forming a ladder). In the dimerized system, an individual spinon can be small when the confinement length is large; this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence-bond solid (where the spinons are deconfined). Based on our numerical results, we argue that a system with $\ensuremath{\lambda}\ensuremath{\ll}\mathrm{\ensuremath{\Lambda}}$ is associated with weak repulsive short-range spinon-spinon interactions. In principle, both the length scales $\ensuremath{\lambda}$ and $\mathrm{\ensuremath{\Lambda}}$ can still be individually tuned from small to infinite (with $\ensuremath{\lambda}\ensuremath{\le}\mathrm{\ensuremath{\Lambda}}$) by varying model parameters. In contrast, in the ladder system the two lengths are always similar, and this is the case also in the weakly dimerized systems when the corresponding uniform chain is in the critical phase. In these systems, the effective spinon-spinon interactions are purely attractive and there is only a single large length scale close to criticality, which is reflected in the standard spin correlations as well as in the spinon characteristics.
By utilizing the twisted boundary conditions in the exact diagonalization method, we investigate the single-particle spectral function of the extended Peierls-Hubbard model at both half-filling and quarter filling. In one-dimensional (1D) interacting systems, the spin-charge separation can typically be identified in the single-particle spectral function by observing the distinct spinon and holon bands. At half filling, starting from the pure 1D Hubbard model with the on-site interaction U=10U=10U=10, we observe that the band structure indicative of the spin-charge separation gradually transitions to four individual bands as the Peierls instability δδδ increases. At U=10U=10U=10 and δ=0.2δ=0.2δ=0.2 where the spin-charge separation is still observable, increasing the nearest-neighbor interaction VVV can drive the system to a charge-density-wave (CDW) state when V≳U/2V\gtrsim U/2V≳U/2, without the obeservation of spinon and holon bands. At quarter-filling, on the other hand, the ground state of Peierls-Hubbard model manifests an antiferromagnetic Mott insulator in units of dimers. Increasing UUU results in only a very small gap in the single-particle spectrum because even for U=+∞U=+\inftyU=+∞, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability δδδ remains small. Conversely, increasing VVV can effectively open the single-particle gap and make the spinon and holon bands more prominent.
We study the effect of varying the boundary condition on the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow---which spans the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.
We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.
By utilizing the twisted boundary conditions in the exact diagonalization method, we investigate the single-particle spectral function of the extended Peierls-Hubbard model at both half-filling and quarter-filling. In one-dimensional (1D) interacting systems, the spin-charge separation can typically be identified in the single-particle spectral function by observing the distinct spinon and holon bands. At half-filling, starting from the pure 1D Hubbard model with the on-site interaction U=10U=10U=10, we observe that the band structure indicative of the spin-charge separation gradually transitions to four individual bands as the Peierls instability $\ensuremath{\delta}$ increases. At U=10U=10U=10 and $\ensuremath{\delta}=0.2$ where the spin-charge separation is still observable, increasing the nearest-neighbor interaction VVV can drive the system to a charge-density-wave state when $V\ensuremath{\gtrsim}U/2$. At quarter-filling, on the other hand, the ground state of Peierls-Hubbard model manifests an antiferromagnetic Mott insulator in units of dimers. Increasing UUU results in only a very small gap in the single-particle spectrum because even for $U=+\ensuremath{\infty}$, with the model transforming into a noninteracting half-filled dimerized tight-binding model, its gap determined by the Peierls instability $\ensuremath{\delta}$ remains small. Conversely, increasing VVV can effectively open the single-particle gap and make the spinon and holon bands more prominent.