Analytical approach to dimerized and frustrated Heisenberg chains

Abstract

We present a self-consistent quantum-theoretical analysis of the ground-state energy and low-energy excitation spectrum of a dimerized and frustrated Heisenberg chain by the bosonization representation in the continuum-limit approach. The frustration effects on the ground-state energy and energy gap are investigated for α>αc where α is the frustration parameter and αc is its critical value, above which a frustration-induced energy gap is opened. It is shown that as α increases, the ground-state energy decreases and the energy gap increases. We find that the dimerization dependence of the ground-state energy and energy gap for small dimerization obeys the Cross-Fisher power law only at α = αc, but departs significantly from it when α>αc. The present results are in good agreement with numerical analyses from the density-matrix renormalization-group and exact diagonalization methods. The relevance of our calculated results to recent experiments on the spin-Peierls compounds CuGeO3 is also discussed.

An Approach to Temperature Dependence of the Magnetic Excitation in the Spin–Peierls Chain with Frustration

“…À =Þ, and D ¼ Jð2aÞ À1 ð1 À 3Þ with a, a short distance cutoff or lattice spacing. If we make rescaling of the field operator and its conjugate momentum the Hamiltonian (2) can be transformed further into the standard form of the doublefrequency SG representation as, 28)…”

Theory for low-lying excitations in the spin-Peierls systemCuGeO3

“…We also point out that there exists a power-law behavior as ⌬ 1 ϰ␦ 2/3 , so-called Cross-Fisher's law, 28 for small ␦ at ␣ϭ␣ c in the frustrated and dimerized Heisenberg chain model. 25 With ␣ increased the derivation from power-law behavior becomes large. Here we wish to compare the present theoretical results with experimental data.…”

“…͑3͒ are less than unity when the dimerization parameter is restricted within a relatively small region. Furthermore, in our previous work 25 we investigated the ground-state energy and the elementary excitation of a dimerized and frustrated Heisenberg chain by present theory. The calculated results are in agreement with numerical analyses from the exact-diagonalization method.…”

“…Recently, a self-consistent quantum theory 24 was developed to discuss the single-frequency SG model, by which the infrared divergence can be effectively treated and the energy gap in the spectrum can be obtained self-consistently. In a recent work, 25 we have applied this approach to the quantum double-frequency SG model and studied the properties of the ground state and the one-magnon excited state in a dimerized and frustrated Heisenberg chain. Here this approach is extended to the study of the singlet two-magnon bound state.…”

Quantum phase transition in a dimerized chain with hexameric distortion

“…The critical gapless phases emerging on the border lines separating two gapped phases in low‐dimensional spin systems have been the subject of studies for decades. The spin S = 1/2 Heisenberg chain with dimerization and frustration is a primary and well‐studied example of such a system, which shows a gapless phase in the ground state phase Diagram 1–4. After the seminal paper by Martin‐Delgado et al 5, great attention has been focused on the studies of the same phenomena in other wide classes of low‐dimensional magnets such as spin ladders 6–14 Recently, the gapless phases on the border of different massive phases have been discussed in two‐dimensional spin systems 15–17.…”