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

Physical Review B

Existence of dimerized phases in frustrated spin ladder models

Guanghua Liu, Hailong Wang, Guang-Shan Tian

Published Jun 11, 2008• 69 citations
Publisher

Abstract

In the present paper, by using the density-matrix renormalization-group technique, we investigate the existence of dimerized phases in a frustrated spin-1/2 ladder model. By calculating the two-rung localizable entanglement and, in particular, its first-order derivative in the ground state, we show that an intermediate columnar dimerized phase exists indeed in a narrow parameter region between the rung-singlet and the Haldane phases. Furthermore, by introducing an additional interchain next-nearest-neighbor exchange interaction, the stability of this phase can be greatly enhanced and a staggering dimerized phase also appears in the phase diagram. Our results confirm the previous conclusions derived by the bosonization methods.

DOI
10.1103/physrevb.77.214418

Related papers

Frustration and intermediate dimerized phase in spin ladder system

Shi Dong, Rui Wen, Guanghua Liu +1 more

This paper studies a spin ladder model which possesses frustrating interactions. By using both the bosonization and the density matrix renormalization group techniques, it shows that the intermediate columnar dimerized phase, which exists in a narrow parameter region of the so-called J 1 – J 2 model, vanishes if the interchain frustration is weak and anisotropic. Therefore, it concludes that the frustrating interaction indeed plays an important role in producing such a phase. As a complementary to our previous investigation, it reaches a more complete picture of the quantum phase transition in the frustrated spin ladder systems.

Chinese Physics B•Jul 1, 2010•2 citations

Phase diagram of the frustrated spin ladder

Toshiya Hikihara, Oleg A. Starykh

We revisit the phase diagram of the frustrated spin-1/2 ladder with two competing interchain antiferromagnetic exchanges, rung coupling ${J}_{\ensuremath{\perp}}$ and diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$. We suggest, based on the accurate renormalization-group analysis of the low-energy Hamiltonian of the ladder, that marginal interchain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line ${J}_{\ensuremath{\perp}}=2{J}_{\ifmmode\times\else\texttimes\fi{}}$. Following this insight we then suggest that changing these competing interchain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density-matrix renormalization-group and exact-diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is determined.

arXiv:0912.4589•Physical Review B•Feb 25, 2010•47 citations

Search for quantum dimer phases and transitions in a frustrated spin ladder

Hsiang-Hsuan Hung, Chang-De Gong, Yung‐Chung Chen +1 more

A two-leg spin-1/2 ladder with diagonal interactions is investigated numerically. We focus our attention on the possibility of columnar dimer phase, which was recently predicted based on a reformulated bosonization theory. By using density matrix renormalization group technique and exact diagonalization method, we calculate columnar dimer order parameter, spin correlation on a rung, string order parameters, and scaled excitation gaps. Carefully using various finite-size scaling techniques, our results show no support for the existence of columnar dimer phase in the spin ladder under consideration.

arXiv:cond-mat/0605719•Physical Review B•Jun 23, 2006•48 citations

Quantum dimer phases in a frustrated spin ladder

T. Vekua, A. Honecker

The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.

•Jan 24, 2006•0 citations

Quantum phase diagram of the frustrated spin ladder with next-nearest-neighbor interactions

Yanchao Li, Hai‐Qing Lin

Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.

New Journal of Physics•Jun 15, 2012•16 citations

Ground-state phase diagram of the frustrated spin- 12 two-leg honeycomb ladder

Qiang Luo, Shijie Hu, Jize Zhao +3 more

We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration ${J}_{2}$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge $c=2$.

arXiv:1804.00008•Physical review. B./Physical review. B•Jun 27, 2018•14 citations
In the present paper, by using the density-matrix renormalization-group technique, we investigate the existence of dimerized phases in a frustrated spin-1/2 ladder model. By calculating the two-rung localizable entanglement and, in particular, its first-order derivative in the ground state, we show that an intermediate columnar dimerized phase exists indeed in a narrow parameter region between the rung-singlet and the Haldane phases. Furthermore, by introducing an additional interchain next-nearest-neighbor exchange interaction, the stability of this phase can be greatly enhanced and a staggering dimerized phase also appears in the phase diagram. Our results confirm the previous conclusions derived by the bosonization methods.
This paper studies a spin ladder model which possesses frustrating interactions. By using both the bosonization and the density matrix renormalization group techniques, it shows that the intermediate columnar dimerized phase, which exists in a narrow parameter region of the so-called J 1 – J 2 model, vanishes if the interchain frustration is weak and anisotropic. Therefore, it concludes that the frustrating interaction indeed plays an important role in producing such a phase. As a complementary to our previous investigation, it reaches a more complete picture of the quantum phase transition in the frustrated spin ladder systems.
We revisit the phase diagram of the frustrated spin-1/2 ladder with two competing interchain antiferromagnetic exchanges, rung coupling ${J}_{\ensuremath{\perp}}$ and diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$. We suggest, based on the accurate renormalization-group analysis of the low-energy Hamiltonian of the ladder, that marginal interchain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line ${J}_{\ensuremath{\perp}}=2{J}_{\ifmmode\times\else\texttimes\fi{}}$. Following this insight we then suggest that changing these competing interchain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density-matrix renormalization-group and exact-diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is determined.
A two-leg spin-1/2 ladder with diagonal interactions is investigated numerically. We focus our attention on the possibility of columnar dimer phase, which was recently predicted based on a reformulated bosonization theory. By using density matrix renormalization group technique and exact diagonalization method, we calculate columnar dimer order parameter, spin correlation on a rung, string order parameters, and scaled excitation gaps. Carefully using various finite-size scaling techniques, our results show no support for the existence of columnar dimer phase in the spin ladder under consideration.
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.
We investigate a spin-1/21/21/2 two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration J2{J}_{2}J2​ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge c=1/2c=1/2c=1/2. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge c=2c=2c=2.