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/9611037 · Physical review. B, Condensed matter

Low-energy properties of regularly depleted spin ladders

Takahiro Fukui, Manfred Sigrist, Norio Kawakami

Published Aug 1, 1997• 5 citations
arXivHTMLPDF

Abstract

We investigate a model for the regularly depleted two-leg spin-ladder systems. By using the Lieb-Schultz-Mattis theorem, it is rigorously shown that this model realizes massless excitations or, alternatively, a degenerate ground state, although the original spin-ladder system has a spin gap and a unique ground state. The ground state of the depleted model is either a spin singlet or partially ferromagnetic reflecting topological properties of the depleted sites. In order to show that the low-energy excitations are indeed massless, we proceed in our analysis in two different ways by resorting to effective field theories. We first investigate an effective weak-coupling model in terms of renormalization-group methods. Although the tendency to massless-spin excitations is seen in the strong-coupling regime, it turns out that the model is still massive for any finite coupling, implying that a conventional weak-coupling approach is not efficient to describe massless modes in our model. To overcome this difficulty, we further study low-energy properties of the depleted spin model by mapping on the nonlinear sigma model, and confirm that the massless-spin excitation indeed occurs.

DOI
10.1103/physrevb.56.2530

Related papers

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 ferrimagnetic two-leg ladders: A Lanczos study

A. Langari, Miguel Angel Martin-Delgado

We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes ${(S}_{1}{,S}_{2})=(1,1/2)$ located at alternating positions along the ladder. The effect of dimerization $\ensuremath{\gamma}$ is also considered according to two different patterns. A spin-wave theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low-energy excitations of the model. We compute the ground-state energies, ferromagnetic and antiferromagnetic excitation gaps, magnetizations, and correlation functions as a function of ${J}^{\ensuremath{'}}$ and $\ensuremath{\gamma}$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the spin-Peierls instability and find that it is conditional for any value of ${J}^{\ensuremath{'}}\ensuremath{\in}(0,2)$ and both dimerization patterns.

arXiv:cond-mat/0012209•Physical review. B, Condensed matter•Jan 12, 2001•13 citations

Alternating spin chains with singlet ground states

Takahiro Fukui, Norio Kawakami

We investigate low-energy properties of the alternating-spin-chain model composed of spins ${s}_{1}$ and ${s}_{2}$ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) nonlinear \ensuremath{\sigma} model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting \ensuremath{\sigma} model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.

arXiv:cond-mat/9707148•Physical review. B, Condensed matter•Oct 1, 1997•34 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

Low-energy effective action of lightly doped two-leg t−J ladders

Yu-Wen Lee, Yu-Li Lee

We propose a low-energy effective theory of lightly doped two-leg $t\ensuremath{-}J$ ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg $t\ensuremath{-}J$ ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.

arXiv:cond-mat/9803363•Physical review. B, Condensed matter•Jan 1, 1999•1 citation

Diverging Heisenberg spin ladders: ground state and low energy excitations

Debabrata Parihari, Swapan Kumar Pati

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.

Journal of Physics Condensed Matter•Mar 28, 2007•2 citations
We investigate a model for the regularly depleted two-leg spin-ladder systems. By using the Lieb-Schultz-Mattis theorem, it is rigorously shown that this model realizes massless excitations or, alternatively, a degenerate ground state, although the original spin-ladder system has a spin gap and a unique ground state. The ground state of the depleted model is either a spin singlet or partially ferromagnetic reflecting topological properties of the depleted sites. In order to show that the low-energy excitations are indeed massless, we proceed in our analysis in two different ways by resorting to effective field theories. We first investigate an effective weak-coupling model in terms of renormalization-group methods. Although the tendency to massless-spin excitations is seen in the strong-coupling regime, it turns out that the model is still massive for any finite coupling, implying that a conventional weak-coupling approach is not efficient to describe massless modes in our model. To overcome this difficulty, we further study low-energy properties of the depleted spin model by mapping on the nonlinear sigma model, and confirm that the massless-spin excitation indeed occurs.
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.
We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes (S1,S2)=(1,1/2){(S}_{1}{,S}_{2})=(1,1/2)(S1​,S2​)=(1,1/2) located at alternating positions along the ladder. The effect of dimerization $\ensuremath{\gamma}$ is also considered according to two different patterns. A spin-wave theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low-energy excitations of the model. We compute the ground-state energies, ferromagnetic and antiferromagnetic excitation gaps, magnetizations, and correlation functions as a function of ${J}^{\ensuremath{'}}$ and $\ensuremath{\gamma}$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the spin-Peierls instability and find that it is conditional for any value of ${J}^{\ensuremath{'}}\ensuremath{\in}(0,2)$ and both dimerization patterns.
We investigate low-energy properties of the alternating-spin-chain model composed of spins s1{s}_{1}s1​ and s2{s}_{2}s2​ with a singlet ground state. After examining the spin-wave spectrum in detail, we map low-energy spin excitations to the O(3) nonlinear \ensuremath{\sigma} model in order to take into account quantum fluctuations. Analyzing the topological term in the resulting \ensuremath{\sigma} model, we discuss how the massless or massive excitations are developed, especially according to the topological nature of the alternating spin system.
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.
We propose a low-energy effective theory of lightly doped two-leg $t\ensuremath{-}J$ ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg $t\ensuremath{-}J$ ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.
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.