arXiv subjects

Sibin Yang

Publications and source records attributed to Sibin Yang.

7 recordsLinked to original sources

arXiv2026

Imaginary-time correlations in time-sliced stochastic series expansion

Combined with numerical analytic continuation techniques, quantum Monte Carlo (QMC) methods enable the extraction of real-frequency dynamical properties from imaginary-time correlation functions. However, the efficient computation of imaginary-time correlation functions by QMC simulations can (depending on the particular model used) be challenging, particularly for operators that are off-diagonal in the computational basis. In this work, we present an efficient and general algorithm within the stochastic series expansion (SSE) framework for evaluating imaginary-time correlation functions of both diagonal and off-diagonal operators. The algorithm builds on a discrete imaginary-time slicing of the SSE operator string, which provides correlation functions on a grid of well-defined imaginary-time points with no discretization error. For off-diagonal operators, we derive estimators that integrate directly into the existing SSE directed-loop or cluster updating schemes, introducing only minimal computational overhead. We benchmark the method on the one-dimensional transverse-field Ising model (sampling with cluster updates) and XXZ spin chain (using directed-loop sampling), demonstrating excellent agreement (with only statistical errors) with exact diagonalization of small systems. We also study larger systems to demonstrate efficiency.

cond-mat.str-el↗

arXiv2025

Spinons and Spin-Charge Separation at the Deconfined Quantum Critical Point

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 ($J$-$Q$ model) at its quantum phase transition separating N\'eel 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 $\pi$-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 $2\times 2$ 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.

cond-mat.str-el↗

arXiv2025

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

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.

cond-mat.str-el↗

arXiv2024

Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions

We study the dynamic structure factor $S(k,\omega)$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign alternating) Heisenberg interactions $J_r \sim (-1)^{r-1} r^{-\alpha}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo calculations. We do so in both the long-range antiferromagnetic (AFM, for $\alpha \lesssim 2.23$) and quasi-long-range-ordered (QLRO, for $\alpha \gtrsim 2.23$) ground-state phases, employing different SAC parametrizations of $S(k,\omega)$ to resolve sharp edges characteristic of fractional quasi-particles and sharp peaks expected with conventional quasi-particles. In order to identify the most statistically accurate parametrization, we apply a newly developed cross-validation method as a ``model selection'' tool. We confirm that the spectral function contains a power-law divergent edge in the QLRO phase and a very sharp (likely $\delta$-function) magnon peak in the AFM phase. From our SAC results, we extract the dispersion relation in the different regimes of the model, and in the AFM phase we extract the weight of the magnon pole. In the limit where the model reduces to the conventional Heisenberg chain with nearest-neighbor interactions, our $S(k,\omega)$ agrees well with known Bethe ansatz results. In the AFM phase the low-energy dispersion relation is known to be nonlinear, $\omega_k \sim k^z$, and we extract the corresponding dynamic exponent $z(\alpha)$, which in general is somewhat above the form obtained in linear spin-wave theory. We also find a significant continuum above the magnon peak. This study serves as a benchmark for SAC/QMC studies of systems with a transition from conventional to fractionalized quasi-particles.

cond-mat.str-el↗

arXiv2024

Cross Validation in Stochastic Analytic Continuation

Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g. narrow peaks and divergent edges, to be resolved with unprecedented fidelity. Often times, it is not known what exact sharp features, if any, are present \textit{a priori}, and, due to the ill-posed nature of the analytic continuation problem, multiple spectral representations may be acceptable. In this work, we borrow from the machine learning and statistics literature and implement a cross validation technique to provide an unbiased method to identify the most likely spectrum amongst a set obtained with different spectral parameterizations and imposed constraints. We demonstrate the power of this method with examples using imaginary-time data generated by QMC simulations and synthetic data generated from artificial spectra. Our procedure, which can be considered a form of model selection, can be applied to a variety of numerical analytic continuation methods, beyond just SAC.

cond-mat.str-el↗

arXiv2020

Deconfined quantum criticality in spin-1/2 chains with long-range interactions

We study spin-$1/2$ chains with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange $J_r \propto r^{-α}$ and multi-spin interactions $Q$ favoring a valence-bond solid (VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum states and phase transitions in the $(α,Q)$ plane. For weak $Q$ and sufficiently slowly decaying Heisenberg interactions (small $α$), the system has a long-range-ordered antiferromagnetic (AFM) ground state, and upon increasing $α$ there is a continuous transition into a quasi long-range ordered (QLRO) critical state of the type in the standard Heisenberg chain. For rapidly decaying long-range interactions, there is transition between QLRO and VBS ground states of the same kind as in the frustrated $J_1$-$J_2$ Heisenberg chain. Our most important finding is a direct continuous quantum phase transition between the AFM and VBS states - a close analogy to the 2D deconfined quantum-critical point. In previous 1D analogies the ordered phases both have gapped fractional excitations, and the critical point is a conventional Luttinger Liquid. In our model the excitations fractionalize upon transitioning from the AFM state, changing from spin waves to deconfined spinons. We extract critical exponents at the AFM-VBS transition and use order-parameter distributions to study emergent symmetries. We find emergent O($4$) symmetry of the O($3$) AFM and scalar VBS order parameters. Thus, the order parameter fluctuations exhibit the covariance of a uniaxially deformed O($4$) sphere (an "elliptical" symmetry). This unusual quantum phase transition does not yet have any known field theory description, and our detailed results can serve to guide its construction. We discuss possible experimental realizations.

physics.comp-ph↗

arXiv2019

The AKLT model on a hexagonal chain is gapped

In 1987, Affleck, Kennedy, Lieb, and Tasaki introduced the AKLT spin chain and proved that it has a spectral gap above the ground state. Their concurrent conjecture that the two-dimensional AKLT model on the hexagonal lattice is also gapped remains open. In this paper, we show that the AKLT Hamiltonian restricted to an arbitrarily long chain of hexagons is gapped. The argument is based on explicitly verifying a finite-size criterion which is tailor-made for the system at hand. We also discuss generalizations of the method to the full hexagonal lattice.

quant-ph↗