Fermi-Liquid Theory of Linear Antiferromagnetic Chains

Yamada, Tomoji

doi:10.1143/ptp.41.880

Cited by 94 publications

(64 citation statements)

References 8 publications

(6 reference statements)

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“…Since the spinons are deconfined and typically are further away from each other than the single-spinon length-scale λ, one would expect that P * AA (r) contains essentially the same information as the single-spinon function P AA (r) for the S = 1/2 state, defined in Eq. (17). This is indeed the case in the VBS phase, as demonstrated in Fig.…”

Section: Two Spinons In States With Total Spinsupporting

confidence: 70%

“…(17) to study the size of spinons in the VBS phase at dif- ) shows that the spinon is marginally defined at the critical point, with the overlap decaying as a power-law with exponent α = 0.500(2) (with a fitted line to the even-r points shown for N = 1025). The even-odd oscillations are due to the frustration caused by the single-spinon defect in a periodic chain (with the odd-r contributions only possible in a non-bipartite system).…”

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confidence: 99%

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

Tang

Sandvik

2015

Phys. Rev. B

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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. 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.

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Section: Two Spinons In States With Total Spinsupporting

confidence: 70%

mentioning

confidence: 99%

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

Tang

Sandvik

2015

Phys. Rev. B

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“…The particle-hole continuum of the Jordan-Wigner fermions, displayed in Fig. 1, is very similar to the two-spinon continuum 26 . The upper cutoff of the Jordan-Wigner particle-hole continuum is at (2 + 4 π )J ≈ 3.27J and therefore close to πJ which is the maximum energy for two spinons.…”

Section: Jordan-wigner Transformation For the 1d Spin Chainmentioning

confidence: 63%

Jordan-Wigner approach to dynamic correlations in spin ladders

Nunner

Kopp

2004

Phys. Rev. B

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We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended RPA-scheme we calculate the correlation function of neighboring spin flips which well approximates the optical conductivity of Sr2CuO3. We extend this approach to the two-leg S = 1 2 -ladder by numbering the spin operators in a meander-like sequence. We obtain good agreement with the optical conductivity of the spin ladder compound (La,Ca)14Cu24O41 for polarization along the rungs. For polarization along the legs higher order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4-and 6-fermion processes.

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“…If the spin is a half-integer, the spinons are unbound and there is no Haldane gap. Spin 1/2 compounds are even more interesting in that the spectrum is not simply given by a definite dispersion relation and indeed, analytic [17] and finite chain [18] calculations showed that it is actually a continuum of excitations confined to first approximation, for a given k, between a lower bound ω l (k) and an upper bound ω u (k) such that:…”

Section: Introductionmentioning

confidence: 99%

Sum rules for four-spinon dynamic structure factor in XXX model

Lakhal¹,

Abada²

2005

Physica B: Condensed Matter

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In the context of the antiferromagnetic spin 1/2 Heisenberg quantum spin chain (XXX model), we estimate the contribution of the exact four-spinon dynamic structure factor S 4 by calculating a number of sum rules the total dynamic structure factor S is known to satisfy exactly. These sum rules are: the static susceptibility, the integrated intensity, the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that the contribution of S 4 is between 1% and 2.5%, depending on the sum rule, whereas the contribution of the exact two-spinon dynamic structure factor S 2 is between 70% and 75%. This is consistent with the expected scattering weight of states from outside the spin-wave continuum. The calculations are numerical and Monte Carlo based. Good statistics are obtained.

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Fermi-Liquid Theory of Linear Antiferromagnetic Chains

Cited by 94 publications

References 8 publications

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

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

Jordan-Wigner approach to dynamic correlations in spin ladders

Sum rules for four-spinon dynamic structure factor in XXX model

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