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Register a new userQuantum Monte Carlo studies of spinons in one-dimensional spin systems
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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 Neel 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.
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Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent progress made by QMC simulations. We focus on the cases of spin density wave and Ising nematic criticality. We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
We have measured the thermal conductivity along different directions of the S = 1/2 one-dimensional (1D) spin system Sr2V3O9 in magnetic fields up to 14 T. It has been found that the thermal conductivity along the [10-1] direction, k{appa}[10-1], is large and markedly suppressed by the application of magnetic field, indicating that there is a large contribution of spinons to k{appa}[10-1] and that the spin chains run along the [10-1] direction. The maximum value of the thermal conductivity due to spinons is ~14 W/Km along the [10-1] direction, supporting the empirical law that the magnitude of the thermal conductivity due to spinons is roughly proportional to the antiferromagnetic interaction between the nearest neighboring spins.
We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond basis enable calculations of quantities that are difficult to obtain with the standard basis of Sz eigenstates. In particular, we discuss quantities involving finite-momentum states in the triplet sector, such as the dispersion relation and the spectral weight of the lowest triplet.
We have measured the thermal conductivity along the c-axis parallel to the spin-chains, kappa_c, of the one-dimensional antiferromagnetic spin system SrCuO_2, using as-grown and O_2-annealed single-crystals grown from raw materials with 99.9% (3N) and 99.99% (4N) purity. The value of kappa_c around 50K, where large contribution of the thermal conductivity due to spinons, kappa_spinon, is observed, is markedly enhanced by both the increase of the purity of raw materials and the O_2-annealing. Therefore, the increase of kappa_c implies that kappa_spinon is enhanced due to the decrease of spin defects caused by impurities in raw materials and by oxygen defects. The mean free path of spinons is as large as about 24000 angstrom at low temperatures in the O_2-annealed single-crystal grown from raw materials with 4N purity.
We calculate the effect of the emergent photon on threshold production of spinons in $U(1)$ Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross-section dramatically, changing the weak turn-on expected from the density of states to an abrupt onset reflecting the basic coupling parameters. The slow photon typical in existing lattice models and materials suppresses the intensity at finite momentum and allows profuse Cerenkov radiation beyond a critical momentum. These features are broadly consistent with recent numerical and experimental results.
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