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/9904286 · Physical review. B, Condensed matter

Dimer–resonating valence bond state of the four-leg Heisenberg ladder: Interference among resonances

M. Roncaglia, Germán Sierra, Miguel Angel Martin-Delgado

Published Nov 1, 1999• 8 citations
arXivHTMLPDF

Abstract

We study the ground state of the four-leg spin ladder using a dimer--resonating valence bond (RVB) ansatz and the Lanczos method. Besides the well-known resonance mechanism between valence bond configurations we find interference effects among nearby resonances. These effects were missed by standard factorizing approaches to the RVB states.

DOI
10.1103/physrevb.60.12134

Related papers

Fully variational resonance-valence-bond results on two-, three- and four-legged spin-1/2 Heisenberg ladders

Norbert Flocke

A fully variational resonance-valence-bond (RVB) study is performed for two-, three- and four-legged isotropic spin-1/2 Heisenberg ladders under periodic boundary conditions along the rungs and periodic/twisted boundary conditions along the chains. By using the full lattice groups of these systems very accurate results have been obtained for the ground-state bulk limit properties in the case of the dimer RVB basis. The results reported here represent the best one can do within the dimer RVB ansatz and should be useful when comparing with results obtained from an a priori fixed structure of the wavefunction. Further results are presented for some finite-sized systems, extending beyond the dimer RVB approach by including RVB functions containing spin pairings between non-nearest-neighbour sites. These results indicate that the three-legged ladder with periodic boundary conditions along the rungs falls into the same universality class of ladders possessing short-range RVB wavefunctions as the two- and four-legged ladders.

Journal of Physics Condensed Matter•Aug 26, 1999•1 citation

Short-range resonating-valence-bond state of even-spin ladders: A recurrent variational approach

Germán Sierra, Miguel Angel Martin-Delgado

Using a recursive method we construct dimer and nondimer variational ansatzs of the ground state for the two-legged ladder, and compute the number of dimer coverings, the energy density, and the spin-correlation functions. The number of dimer coverings are given by the Fibonacci numbers for the dimer-resonating-valence-bond state and their generalization for the nondimer states. Our method relies on the recurrent relations satisfied by the overlaps of the states with different lengths, which can be solved using generating functions. The recurrent-relation method is applicable to other short-range systems. Based on our results we make a conjecture about the bond amplitudes of the two-legged ladder.

arXiv:cond-mat/9704212•Physical review. B, Condensed matter•Oct 1, 1997•26 citations

Spin Hamiltonians with Resonating-Valence-Bond Ground States

Jennifer Cano, Paul Fendley

Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical obstacle overcome is the fact that different dimer configurations in the spin model are not orthogonal. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that is likely to be quantum critical.

arXiv:0910.5708•Physical Review Letters•Aug 5, 2010•37 citations

Dualities in spin ladders

Germán Sierra, Miguel A Martin-Delgado

We introduce a set of discrete modular transformations and in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the two-legged ladder we show that the resonating valence bond (RVB) phase is invariant under the transformation, while the Haldane phase is invariant under . These two phases are related by . Moreover, there is a `mixed' phase, that is invariant under , and which under becomes the RVB phase, while under becomes the Haldane phase. For odd ladders there exists only the transformation which, for strong coupling, maps the effective antiferromagnetic spin chain onto the spin chain. Our work is based on a combination of approximate methods such as bosonization, perturbation theory and the nonlinear sigma model, adapted to the different regimes of coupling constants.

arXiv:cond-mat/9706104•Journal of Physics A Mathematical and General•Feb 13, 1998•1 citation

Resonating Valence Bond Theory of Coupled Heisenberg Chains

Steven R. White, R. M. Noack, Douglas J. Scalapino

Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB description of systems with an even number of chains ${n}_{c}$, with a spin gap, short-range correlations, and confinement of topological spin defects. Odd-${n}_{c}$ systems have long-range RVB ground states, no gap, and power-law correlations.

arXiv:cond-mat/9403042•Physical Review Letters•Aug 8, 1994•405 citations

Entanglement in gapless resonating-valence-bond states

Jean-Marie Stéphan, Hyejin Ju, Paul Fendley +1 more

We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU ( N )-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU (2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the Rényi entropy for splitting a torus into two cylinders. We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not identically. We extend the exact computation to an effective theory believed to interpolate among these states. By numerical calculations for the SU (2) RVB state and its SU ( N )-invariant generalizations, we provide further support for this belief. We also show how the entanglement entropy behaves qualitatively differently for different values of the Rényi index n , with large values of n proving a more sensitive probe here, by virtue of exhibiting a striking even/odd effect.

arXiv:1207.3820•New Journal of Physics•Jan 11, 2013•38 citations
We study the ground state of the four-leg spin ladder using a dimer--resonating valence bond (RVB) ansatz and the Lanczos method. Besides the well-known resonance mechanism between valence bond configurations we find interference effects among nearby resonances. These effects were missed by standard factorizing approaches to the RVB states.
A fully variational resonance-valence-bond (RVB) study is performed for two-, three- and four-legged isotropic spin-1/2 Heisenberg ladders under periodic boundary conditions along the rungs and periodic/twisted boundary conditions along the chains. By using the full lattice groups of these systems very accurate results have been obtained for the ground-state bulk limit properties in the case of the dimer RVB basis. The results reported here represent the best one can do within the dimer RVB ansatz and should be useful when comparing with results obtained from an a priori fixed structure of the wavefunction. Further results are presented for some finite-sized systems, extending beyond the dimer RVB approach by including RVB functions containing spin pairings between non-nearest-neighbour sites. These results indicate that the three-legged ladder with periodic boundary conditions along the rungs falls into the same universality class of ladders possessing short-range RVB wavefunctions as the two- and four-legged ladders.
Using a recursive method we construct dimer and nondimer variational ansatzs of the ground state for the two-legged ladder, and compute the number of dimer coverings, the energy density, and the spin-correlation functions. The number of dimer coverings are given by the Fibonacci numbers for the dimer-resonating-valence-bond state and their generalization for the nondimer states. Our method relies on the recurrent relations satisfied by the overlaps of the states with different lengths, which can be solved using generating functions. The recurrent-relation method is applicable to other short-range systems. Based on our results we make a conjecture about the bond amplitudes of the two-legged ladder.
We introduce a set of discrete modular transformations and in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the two-legged ladder we show that the resonating valence bond (RVB) phase is invariant under the transformation, while the Haldane phase is invariant under . These two phases are related by . Moreover, there is a `mixed' phase, that is invariant under , and which under becomes the RVB phase, while under becomes the Haldane phase. For odd ladders there exists only the transformation which, for strong coupling, maps the effective antiferromagnetic spin chain onto the spin chain. Our work is based on a combination of approximate methods such as bosonization, perturbation theory and the nonlinear sigma model, adapted to the different regimes of coupling constants.
Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB description of systems with an even number of chains nc{n}_{c}nc​, with a spin gap, short-range correlations, and confinement of topological spin defects. Odd-nc{n}_{c}nc​ systems have long-range RVB ground states, no gap, and power-law correlations.
We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU ( N )-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU (2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the Rényi entropy for splitting a torus into two cylinders. We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not identically. We extend the exact computation to an effective theory believed to interpolate among these states. By numerical calculations for the SU (2) RVB state and its SU ( N )-invariant generalizations, we provide further support for this belief. We also show how the entanglement entropy behaves qualitatively differently for different values of the Rényi index n , with large values of n proving a more sensitive probe here, by virtue of exhibiting a striking even/odd effect.