Critical behaviour of spin-s Heisenberg antiferromagnetic chains: analytic and numerical results

Affleck, Ian; Gepner, Doron; Schulz, H. J.; Ziman, Timothy

doi:10.1088/0305-4470/22/5/015

Cited by 457 publications

(555 citation statements)

References 29 publications

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“…confirming the field theoretical prediction in [28] about the amplitude of the 1/(log T ) 3 correction which was argued to be universal however in disagreement with Bethe ansatz calculations in [27]. The reason for the "failure" of the treatment in [27] (instead of [12,13,14] were still plagued by higher order logarithmic contributions leading to erroneous conclusions with respect to the analysis of the specific heat.…”

Section: Asymptotics Of the Specific Heatsupporting

confidence: 59%

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The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

1998

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We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T /J = 10 −24 ) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.

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Section: Asymptotics Of the Specific Heatsupporting

confidence: 59%

“…In our case and vanishing external field we have x = 1/2 and b = 3/2 [28] such that m 0 ≃ δ 2/3 /(log δ) 1/2 .…”

Section: Perturbations Of the Pure Systemmentioning

confidence: 99%

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

1998

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“…Furthermore, we expect the marginally irrelevant κ L,R operators to give rise to logarithmic corrections to edge singularities for SU (2) symmetric models, similarly to the effect in equaltime correlation functions. 60 Logarithmic corrections are known to exist at the lower edge of the two-spinon contribution to the spin DSF for the Heisenberg model, 61 but we do not pursue that calculation here.…”

Section: Discussionmentioning

confidence: 99%

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

et al. 2012

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We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U → ∞ and a subset of the two-holontwo-spinon continuum that reconstructs the electron-hole continuum in the limit U → 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and η-spin SU (2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a Van Hove singularity that persists as a consequence of integrability.

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“…From the theory of spin-1/2 chains it is known that a perturbation consisting of nearest-neighbor spin-spin interactions with alternating sign is relevant. 32 From this discussion, it is natural to expect that even for U > 0 the system is gapped for all δt except δt = 0, where a quantum phase transition occurs. This parallels the case without interactions.…”

Section: One-dimensional Peierls-hubbard Modelmentioning

confidence: 99%

Topological invariants and interacting one-dimensional fermionic systems

et al. 2012

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We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model, and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the existence of topologically protected, zero-energy states at the boundaries of these systems can be tied to the value of the topological invariant, just like when working with the conventional, noninteracting topological insulators. We use a combination of analytical methods and the numerical density matrix renormalization group method to calculate the values of the topological invariant throughout the phase diagrams of these systems, thus deducing when topologically protected boundary states are present. We are also able to study topological states in spin systems because, deep in the Mott insulating regime, these fermionic systems reduce to spin chains. In this way, we associate the zero-energy states at the end of an antiferromagnetic spin-one Heisenberg chain with a topological invariant equal to 2.

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Critical behaviour of spin-s Heisenberg antiferromagnetic chains: analytic and numerical results

Cited by 457 publications

References 29 publications

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

Topological invariants and interacting one-dimensional fermionic systems

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