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physica status solidi (b)

Low energy properties of even‐legged d ‐dimensional quantum spin systems: a variational approach

J. Richert, Otfried Gühne

Published May 9, 2008• 2 citations
Publisher

Abstract

Abstract We develop a variational formalism in order to study the gap structure in the spectrum of frustrated quantum spin systems. We introduce a trial wave function of a two‐leg ladder with one spin 1/2 on each site. The domains in which the wave function behaves realistically are determined. In these domains the spectra show a finite energy gap between the ground state and excited states. Under some approximations which are discussed the result can be extended to 2d and higher dimensional systems with an even number of rows. The gap vanishes for specific values of the coupling strengths which correspond to the location of phase transitions. In a second step we introduce quantitative estimates of the relevance of the variational ansatz which rest on the entanglement concept. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200743512

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Abstract We develop a variational formalism in order to study the gap structure in the spectrum of frustrated quantum spin systems. We introduce a trial wave function of a two‐leg ladder with one spin 1/2 on each site. The domains in which the wave function behaves realistically are determined. In these domains the spectra show a finite energy gap between the ground state and excited states. Under some approximations which are discussed the result can be extended to 2d and higher dimensional systems with an even number of rows. The gap vanishes for specific values of the coupling strengths which correspond to the location of phase transitions. In a second step we introduce quantitative estimates of the relevance of the variational ansatz which rest on the entanglement concept. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of these states. The variational ground state shows a finite energy gap with respect to the energies of states which span the Hilbert space and are orthogonal to it. This is the case for any size of the system. Under some justifiable approximations the argument can be extended to even-legged ladder systems in 2d and higher dimensional spaces. The Hamiltonian can contain spin-spin coupling interactions of any range. For specific values of the coupling strengths level degeneracies can occur.
The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.
Low-dimensional quantum spin systems is interacting many body systems for which several rigorous results are known. A large number of compounds exist which can effectively be described as low-dimensional spin systems. Frustration occurs when the interaction energies associated with all the spin pairs cannot be simultaneously minimized. The parallel spin pair may be located on any one of the bonds of the triangle. The entropy/spin has a non-zero value in the ground state and there is no ordering of the spins. The sum over permutations is in accordance with the bosonic nature of the waves, the spin waves, propagating along the chain. The energy-momentum relations suggest that the low-lying spectrum is actually a combination of two elementary excitations known as spinons. In the case of integer spin chains, the spinons axe bound and the excitation spectrum consists of spin-wave-like modes exhibiting the Haldane gap.
Abstract The low‐energy spectrum of one‐dimensional lattice electron system with long‐range inter‐electron repulsion is studied at arbitrary electron concentration, ρ. It is established that the value of the gap in this spectrum is an oscillating function of inverse electron concentration. This value tends to zero at ρ = 1/q (q = 1, 2 …), reaching the maximum at ρ = 2/(2q + 1). It is shown that the low‐energy spectrum of the system under consideration may be described in terms of one‐dimensional structures which are analogues of domains in one‐dimensional spin systems. The question about these “domains” decay is considered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with slight diminishing of the distance dependent coupling. Varying the spatial range of the rung coupling, we derive the effective length scale of triplet excitations in these ladder classes of systems.