Quantum Monte Carlo studies of spinons in one-dimensional spin systems

Abstract

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 = 1/2 spinon excitations using the intrinsic spinon size λ and confinement length Λ (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 Néel 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 λ Λ is associated with weak repulsive short-range spinon-spinon interactions. In principle both the length-scales λ and Λ can still be individually tuned from small to infinite (with λ ≤ Λ) 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.

Heterostructural one-unit-cell FeSe/SrTiO3: from high-temperature superconductivity to topological states

“…Some scanning-tunneling-spectroscopy (STS) experiments reported the absence of sharp in-gap bound states on nonmagnetic impurities on/in 1-UC FeSe [figures 3(d1)-(e2)], including Zn, Ag, K adatoms [70] and Fe vacancy [73]. In combination with the robust local superconductivity of 1-UC FeSe against severe K-adatom disorders [74], plain s ++ -wave is suggested by these investigations likely as the pairing symmetry of 1-UC FeSe.…”

Controlling ultracold p -wave collisions with nonresonant light: Predictions of an asymptotic model

“…Therefore, the van der Waals interaction is almost negligible, and the dipole-dipole interaction governs the dynamics. Table II also presents homonuclear pairs of atoms, bosonic or fermionic, with a large total angular momentum J and therefore a large permanent magnetic moment: pairs of the transition metal atom Cr, with atomic ground level 3d 5 4s 7 S 3 [43,44], pairs of the lanthanide atoms Dy [45,46] and Er [47,48], with respective atomic ground levels 4f 10 6s 2 5 I 8 and 4f 12 6s 2 6 H 6 . In their lowest state 2S+1 L J |M J |=J, with Landé factor g J , these atoms possess a large permanent magnetic dipole moment m=µ B g J J, and two collision partners strongly interact via magnetic dipole-dipole interaction.…”

Magnetic Field Effects in Low-Dimensional Quantum Magnets

“…Carlo, the most reliable method for large-scale simulations [2,3]. The J-Q model has been extensively studied at zero field, where the Q term drives a quantum phase transition from a Néel antiferromagnet (AFM) state to a valence-bond solid (VBS, a non-magnetic state consisting of a long-range-ordered arrangement of local singlet bonds between sites) [2,[4][5][6][7][8][9][10][11]. I extend previous work on the J-Q model by adding an external magnetic field, producing the J-Q-h model.…”

“…There is no closed-form solution for the motion of the comet that can account for the gravitational influence of all the planets. Instead, Alexis-Claude Clairaut set out to predict its position numerically (a controversial proposal), dividing the work between himself and two friends: Mr. Joseph Lalande 9 and Ms. Nicole-Reine Lepaute 10 [23, p. 16]. With the benefit of hindsight we know they had little hope of producing an accurate prediction, not due to any flaws in their approach, but due to missing information.…”