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. {\bf 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 spinon size and confinement length (the size of a bound state). The spinons have finite size in valence-bond-solid states, infinite size in the critical region, and become ill-defined in the Néel state. We also verify that pairs of spinons are deconfined in these 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 the situation $\lambda \ll \Lambda$ is associated with weak repulsive short-range spinon-spinon interactions. In principle both the length-scales can be individually tuned from small to infinite (with $\lambda \le \Lambda$) by varying model parameters. In the ladder system the two lengths are always similar, and this is the case also in the 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.

15 pages, 15 figures

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• Correlated valence-bond states
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• Monte Carlo based techniques for quantum magnets with long-range interactions
• Field-driven quantum phase transitions in $S=1/2$ spin chains
• Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions
• Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation
• Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point
• Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain
• The fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism
• Microscopic bosonization of band structures: X-ray processes beyond the Fermi edge
• From deconfined spinons to coherent magnons in an antiferromagnetic Heisenberg chain with long range interactions
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions