Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0510343

A variational approach to the low energy properties of even-legged d-dimensional quantum spin systems

J. Richert

Published Oct 13, 2005• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/0510343

Related papers

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

J. Richert, Otfried Gühne

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)

physica status solidi (b)•May 9, 2008•2 citations

The energy spectrum and low-temperature magnetic properties of the decorated two-leg mixed spin ladder

Vladyslav O. Cheranovskii, E. V. Ezerskaya, A. O. Kabatova

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 Temperature Physics•Apr 1, 2023•3 citations

Frustrated spin -1/2 two-leg and three-leg antiferromagnetic Heisenberg ladders

Ningsheng Zhu

The goal of this project is to study the ground-state properties of frustrated spin-1/2 two- and three-leg Heisenberg ladders, and to investigate possible effects of diagonal couplings on spin gaps. The ground-state and the first-excited-state energies of these two systems are calculated systematically by using the density matrix renormalization group method. The ground state phase diagrams for these two systems are obtained. For the frustrated two-leg ladder, we found that the spin gap is insensitive to the change of the FM diagonal coupling constant. This is in agreement with experimental suggestions. For the frustrated three-leg ladder, we conclusively proved that introducing AF diagonal couplings can not change the gapless property of the ground state.

•May 29, 2019•0 citations

Energy-level ordering and ground-state quantum numbers for a frustrated two-leg spin- 1∕2 ladder

Tigran Hakobyan

The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels on bipartite lattices is generalized to finite-size two-leg spin-$1∕2$ ladder model frustrated by diagonal interactions. For reflection-symmetric model with site-dependent interactions, we prove exactly that the lowest energies in sectors with fixed total spin and reflection quantum numbers are monotone increasing functions of total spin. The nondegeneracy of most levels is also proven. We also establish the uniqueness and obtain the spin value of the lowest level multiplet in the whole sector formed by reflection-symmetric (antisymmetric) states. For a wide range of coupling constants, we prove that the ground state is a unique spin singlet. For other values of couplings, it may be also a unique spin triplet or may consist of both multiplets. Similar results have been obtained for the ladder with arbitrary boundary impurity spin. Some partial results have also been obtained in the case of periodical boundary conditions.

arXiv:cond-mat/0702148•Physical Review B•Jun 19, 2007•8 citations

Low-energy properties of spin-1/2 two-leg antiferromagnetic Heisenberg ladders with ferromagnetic diagonal coupling

Ningsheng Zhu, Xiaoqun Wang, Changfeng Chen

Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.

Physical review. B, Condensed matter•Dec 11, 2000•14 citations

Mean-field theory for the spin-ladder system

Xi Dai, Zhao-Bin Su

In the present paper, we propose a mean-field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean-field level that ladders with even-numbered legs open an energy gap in their low-energy excitation with a magnitude close to the corresponding experimental values, whereas the low-energy excitation of the odd-numbered-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of a two-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.

arXiv:cond-mat/9709199•Physical review. B, Condensed matter•Jan 1, 1998•40 citations
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.
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)
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.
The goal of this project is to study the ground-state properties of frustrated spin-1/2 two- and three-leg Heisenberg ladders, and to investigate possible effects of diagonal couplings on spin gaps. The ground-state and the first-excited-state energies of these two systems are calculated systematically by using the density matrix renormalization group method. The ground state phase diagrams for these two systems are obtained. For the frustrated two-leg ladder, we found that the spin gap is insensitive to the change of the FM diagonal coupling constant. This is in agreement with experimental suggestions. For the frustrated three-leg ladder, we conclusively proved that introducing AF diagonal couplings can not change the gapless property of the ground state.
The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels on bipartite lattices is generalized to finite-size two-leg spin-1∕21∕21∕2 ladder model frustrated by diagonal interactions. For reflection-symmetric model with site-dependent interactions, we prove exactly that the lowest energies in sectors with fixed total spin and reflection quantum numbers are monotone increasing functions of total spin. The nondegeneracy of most levels is also proven. We also establish the uniqueness and obtain the spin value of the lowest level multiplet in the whole sector formed by reflection-symmetric (antisymmetric) states. For a wide range of coupling constants, we prove that the ground state is a unique spin singlet. For other values of couplings, it may be also a unique spin triplet or may consist of both multiplets. Similar results have been obtained for the ladder with arbitrary boundary impurity spin. Some partial results have also been obtained in the case of periodical boundary conditions.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.
In the present paper, we propose a mean-field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean-field level that ladders with even-numbered legs open an energy gap in their low-energy excitation with a magnitude close to the corresponding experimental values, whereas the low-energy excitation of the odd-numbered-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of a two-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.