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/0603153 · Journal of Physics Condensed Matter

Magnetization plateau in the spin ladder with alternating rung exchange

G. I. Japaridze, E Pogosyan

Published Sep 22, 2006• 29 citations
arXivHTMLPDF

Abstract

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an $XXZ$ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is $\sim δ$. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as $δ^ν$, where $ν=4/5$ in the case of ladder with isotropic antiferromagnetic legs and $ν=2$ in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields ($H^{\pm}_{c1}$ and $H^{\pm}_{c2}$) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.

DOI
10.1088/0953-8984/18/40/014

Related papers

Magnetization Plateau in the Spin S=1/2 Two-Leg Ladder with Trimerized Modulation of the Rung Exchange

Niko Avalishvili, G. I. Japaridze, David Nozadze +1 more

The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the critical

•Jan 1, 2012•0 citations

Magnetic Plateaus and Jumps in a Spin‐1/2 Ladder with Alternate Ising–Heisenberg Rungs: A Field‐Dependent Study

Sk Saniur Rahaman, Manoranjan Kumar, Shaon Sahoo

A frustrated two‐legged spin‐1/2 ladder featuring alternating Ising and isotropic Heisenberg exchange interactions on the rungs is investigated, while Ising exchanges are present along the legs and diagonals. This model exhibits the following four ground‐state phases: (i) stripe rung ferromagnet (SRFM), (ii) anisotropic antiferromagnet, (iii) dimer, and (iv) stripe leg ferromagnet. In this work, different magnetization plateaus are analyzed by studying the spin density, quantum fidelity, and quantum concurrence in the presence of longitudinal and transverse magnetic fields. The exact diagonalization and transfer matrix methods are used to solve the model Hamiltonian. In the presence of a longitudinal field, the discrete magnetization plateaus appear at 0, 1/2, and 1 of the saturation value across all phases [(i)–(iv)]. Interestingly, in the presence of an externally applied transverse field, the SRFM phase [(i)] exhibits a continuous change in magnetization. The other three phases [(ii)–(iv)] show both discrete jump and continuous change in magnetization in different limits of the transverse field.

arXiv:2304.12266•physica status solidi (b)•Mar 24, 2025•1 citation

Ground-state phases of a rung-alternated spin−12 Heisenberg ladder

Fatemeh Amiri, Gaoyong Sun, H.-J. Mikeska +1 more

The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.

arXiv:1509.04062•Physical Review B•Nov 20, 2015•16 citations

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Taras Verkholyak, Jozef Strečka

The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.

arXiv:1204.1008•Journal of Physics A Mathematical and Theoretical•Jul 13, 2012•19 citations

Phase transitions and critical behaviors of XXZ ladders

Chengxiang Ding

Abstract We study the phase transitions and critical behaviors of the two-leg dimerized XXZ ladders by extensive Monte Carlo simulations and finite-size scaling analysis. For the Heisenberg model on the staggered ladder, we verify that the phase transition between the two topological phases belongs to the four-state Potts universality class; for the XY case ( ), the phase diagram is similar to the Heisenberg case, but the critical behavior belongs to a new universality class; for the Ising case ( ), we find three topological phases, in which one of them has both the topological orders and the local magnetic order; the two phase transitions associated with these phases also belong to the Ising universality class. On the columnar ladder, we have not found any phase transition for all the three cases. Furthermore, we find that the magnetic field can also induce phase transitions for both the staggered and columnar models, and the topological phases are in certain magnetic plateaux. For the staggered model, we study the phase transition associated with the plateau of zero magnetization; we find that the critical behavior of the string order parameter belongs to the 2D classical Ising model, and the scaling behavior of the uniform magnetization is different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class. For the columnar model, we study the phase transition associated with the plateau whose magnetization is half of the saturation value, which has fractional quantized Berry phase; in this case, the conventional string order parameters are not applicable as order parameters, we determine the critical point of this phase transition by the scaling behavior of the uniform magnetization which is also different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class.

Journal of Statistical Mechanics Theory and Experiment•Jan 1, 2020•3 citations

Mixed-spin Heisenberg ladders in a magnetic field

D. S. Almeida, Anderson S. Bibiano-Filho, W. M. da Silva +1 more

In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.

arXiv:2606.28521•Physical review. E•Jan 27, 2025•2 citations
We have studied the ground state phase diagram of a spin ladder with alternating rung exchange J⊥n=J⊥[1+(−1)nδ]J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]J⊥n​=J⊥​[1+(−1)nδ] in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an XXZXXZXXZ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is ∼δ\sim δ∼δ. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as δνδ^νδν, where ν=4/5ν=4/5ν=4/5 in the case of ladder with isotropic antiferromagnetic legs and ν=2ν=2ν=2 in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields (Hc1±H^{\pm}_{c1}Hc1±​ and Hc2±H^{\pm}_{c2}Hc2±​) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.
The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the critical
A frustrated two‐legged spin‐1/2 ladder featuring alternating Ising and isotropic Heisenberg exchange interactions on the rungs is investigated, while Ising exchanges are present along the legs and diagonals. This model exhibits the following four ground‐state phases: (i) stripe rung ferromagnet (SRFM), (ii) anisotropic antiferromagnet, (iii) dimer, and (iv) stripe leg ferromagnet. In this work, different magnetization plateaus are analyzed by studying the spin density, quantum fidelity, and quantum concurrence in the presence of longitudinal and transverse magnetic fields. The exact diagonalization and transfer matrix methods are used to solve the model Hamiltonian. In the presence of a longitudinal field, the discrete magnetization plateaus appear at 0, 1/2, and 1 of the saturation value across all phases [(i)–(iv)]. Interestingly, in the presence of an externally applied transverse field, the SRFM phase [(i)] exhibits a continuous change in magnetization. The other three phases [(ii)–(iv)] show both discrete jump and continuous change in magnetization in different limits of the transverse field.
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.
The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.
Abstract We study the phase transitions and critical behaviors of the two-leg dimerized XXZ ladders by extensive Monte Carlo simulations and finite-size scaling analysis. For the Heisenberg model on the staggered ladder, we verify that the phase transition between the two topological phases belongs to the four-state Potts universality class; for the XY case ( ), the phase diagram is similar to the Heisenberg case, but the critical behavior belongs to a new universality class; for the Ising case ( ), we find three topological phases, in which one of them has both the topological orders and the local magnetic order; the two phase transitions associated with these phases also belong to the Ising universality class. On the columnar ladder, we have not found any phase transition for all the three cases. Furthermore, we find that the magnetic field can also induce phase transitions for both the staggered and columnar models, and the topological phases are in certain magnetic plateaux. For the staggered model, we study the phase transition associated with the plateau of zero magnetization; we find that the critical behavior of the string order parameter belongs to the 2D classical Ising model, and the scaling behavior of the uniform magnetization is different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class. For the columnar model, we study the phase transition associated with the plateau whose magnetization is half of the saturation value, which has fractional quantized Berry phase; in this case, the conventional string order parameters are not applicable as order parameters, we determine the critical point of this phase transition by the scaling behavior of the uniform magnetization which is also different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class.
In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.