Fractal valence bond loops in a long-range Heisenberg model at criticality (original) (raw)
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Tentative structural features of a gapped RVB state in the anisotropic triangular lattice
The self-consistency equations for the independent order parameters as well as the free energy expression for the mean-field RVB model of the spin-1/2 Heisenberg Hamiltonian on the anisotropic triangular lattice is considered in the quasi-one-dimensional approximation. The solutions of the self-consistency equations in the zero-temperature limit are in fair agreement with the previous numerical analysis of the same model by other authors. In particular, the transition from the ungapped 1D-RVB state to the gapped 2D-RVB state occurs at an arbitrarily weak transversal exchange (J 2 → 0) although the amount of the gap is exponentially small: 12J 1 π exp − 2J 1 J 2 , where J 1 is the longitudinal exchange parameter. The structural consequences of the formation of the 2D-RVB state are formulated by extending the famous bond order vs. bond length relation known for polyenes (onedimensional Hubbard chains). Analytical estimates of this effect are given.
Ground state of a Heisenberg chain with next-nearest-neighbor bond alternation
Physical Review B, 2003
We investigate the ground-state properties of the spin-half J1−J2 Heisenberg chain with a nextnearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen, we find that for small frustration (J2/J1) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.
Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
SciPost Physics, 2019
We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J_1-J_2J1−J2 frustrated Heisenberg model. For J_2/J_1\sim 0.55J2/J1∼0.55 we show the emergence of critical (algebraic) dimer-dimer correlations – typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices – while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.
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Physical Review Letters, 2008
Exact formulas for the singularities of the dynamical structure factor, S zz (q, ω), of the S = 1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long time asymptotics of the self-correlation function 0|S z j (t)S z j (0)|0 . Utilizing these results to supplement very accurate time-dependent Density Matrix Renormalization Group (DMRG) for short to moderate times, we calculate S zz (q, ω) to very high precision. PACS numbers: 75.10.Pq, 71.10.Pm
Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
Journal of Statistical Mechanics: Theory and Experiment, 2005
Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, d ≥ 2 but exhibit only quasi long range order, with power law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude λ, as well as an adjustable power-law 1/|x| α , using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear σ model, and renormalization group methods. We map out the phase diagram in the λ-α plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z < 1.
Journal of Magnetism and Magnetic Materials, 2021
The spin-1/2 chain with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neighbors, respectively, has both gapless and gapped (∆(α) > 0) quantum phases at frustration 0 ≤ α ≤ 3/4. The ground state instability of regular (δ = 0) chains to dimerization (δ > 0) drives a spin-Peierls transition at TSP (α) that varies with α in these strongly correlated systems. The thermodynamic limit of correlated states is obtained by exact treatment of short chains followed by density matrix renormalization calculations of progressively longer chains. The doubly degenerate ground states of the gapped regular phase are bond order waves (BOWs) with long-range bondbond correlations and electronic dimerization δe(α). The T dependence of δe(T, α) is found using four-spin correlation functions and contrasted to structural dimerization δ(T, α) at T ≤ TSP (α). The relation between TSP (α) and the T = 0 gap ∆(δ(0), α) varies with frustration in both gapless and gapped phases. The magnetic susceptibility χ(T, α) at T > TSP can be used to identify physical realizations of spin-Peierls systems. The α = 1/2 chain illustrates the characteristic BOW features of a regular chain with a large singlet-triplet gap and electronic dimerization.
Criticality in coupled quantum spin-chains with competing ladder-like and two-dimensional couplings
2003
Motivated by the geometry of spins in the material CaCu$_2$O$_3$, we study a two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings J and \alpha*J along the two axes in the plane and a coupling J_\perp perpendicular to the planes. We study these class of models using the Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite temperatures and series expansion methods at T=0. The critical value of the interlayer coupling, J_\perp^c, separating the N{\'e}el ordered and disordered ground states, is found to follow very closely a square root dependence on alpha\alphaalpha. Both T=0 and finite-temperature properties of the model are presented.