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

Kosterlitz-Thouless transition in a mixed-spin ladder under a magnetic field

Anderson S. Bibiano-Filho

Published Dec 20, 2022• 0 citations
OpenAlex

Abstract

At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.

Related papers

Breakdown of a Magnetization Plateau in Ferrimagnetic Mixed Spin-(1/2,S) Heisenberg Chains due to a Quantum Phase Transition towards the Luttinger Spin Liquid

Jozef Strečka

Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.

arXiv:1607.03617•Acta Physica Polonica A•Apr 1, 2017•13 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

Quantum bicritical point and phase separation in a frustrated Heisenberg ladder

D. S. Almeida, R. R. Montenegro-Filho

We use the density matrix renormalization group (DMRG) and a hard-core boson map to investigate the quantum phase transitions present in the phase diagram of the frustrated Heisenberg ladder in a magnetic field. The quantum bicritical point is observed at the end of a first-order transition line, which is at the meeting of the two second-order transition lines that bound the fully polarized plateau. The characterization of the bicritical point was made using a hard-core boson mapping of the low-energy excitations from the fully polarized phase and through DMRG by studying the probability density of finding the rung spins in a singlet or a triplet state with zero spin component along the magnetic field. In particular, we give conditions for the exchange couplings for the presence of the first-order transition line and the bicritical point in the phase diagram. Moreover, we unveil the phase-separated states for magnetization values inside the magnetization jump and, in particular, the dependence on the system size of the energy curve as a function of magnetization. Finite-size scaling analysis of the transverse spin correlation functions has been used to estimate the critical points of the Kosterlitz-Thouless transitions from the fractional magnetization plateau $m=1/2$ to the respective gapless Luttinger liquid phases for some sets of parameters.

arXiv:2312.17399•Physical review. B./Physical review. B•Dec 27, 2023•7 citations

Magnetization plateau in the spin ladder with alternating rung exchange

G. I. Japaridze, E Pogosyan

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.

arXiv:cond-mat/0603153•Journal of Physics Condensed Matter•Sep 22, 2006•29 citations

Breakdown of intermediate one-half magnetization plateau of spin-1/2 Ising-Heisenberg and Heisenberg branched chains at triple and Kosterlitz-Thouless critical points

Katarína Karľová, Jozef Strečka, M. L. Lyra

The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.

arXiv:1908.05639•Physical review. E•Oct 21, 2019•17 citations

Field-driven quantum phase transitions in a spin-1/2 Heisenberg antiferromagnet on an extended Lieb lattice

Dávid Sivý, Jozef Strečka

The magnetic behavior of the spin-1/2 Heisenberg antiferromagnet on the extended Lieb lattice is examined in the presence of an external magnetic field. Using density matrix renormalization group calculations, we determine the zero-temperature magnetization curves and construct the ground-state phase diagram in the magnetic field vs. the interaction ratio plane. Depending on the interaction ratio, the zero-temperature magnetization curves exhibit field-driven quantum phase transitions between the gapped phases manifested as the intermediate plateaus at $1/5$ and $3/5$ of the saturation magnetization and a gapless spin-canted phase, in which the magnetization varies continuously with the applied magnetic field. Quantum Monte Carlo simulations reveal clear finite-temperatures signatures of the field-induced quantum phase transitions and the intermediate magnetization plateaus, while they provide no evidence for either continuous or discontinuous thermal phase transitions.

arXiv:2609.19051•Jul 21, 2026•0 citations
At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.
Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2.It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state.The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is characterized by a continuous change of the magnetization with the magnetic field until another quantum critical point is reached at the saturation field.
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.
We use the density matrix renormalization group (DMRG) and a hard-core boson map to investigate the quantum phase transitions present in the phase diagram of the frustrated Heisenberg ladder in a magnetic field. The quantum bicritical point is observed at the end of a first-order transition line, which is at the meeting of the two second-order transition lines that bound the fully polarized plateau. The characterization of the bicritical point was made using a hard-core boson mapping of the low-energy excitations from the fully polarized phase and through DMRG by studying the probability density of finding the rung spins in a singlet or a triplet state with zero spin component along the magnetic field. In particular, we give conditions for the exchange couplings for the presence of the first-order transition line and the bicritical point in the phase diagram. Moreover, we unveil the phase-separated states for magnetization values inside the magnetization jump and, in particular, the dependence on the system size of the energy curve as a function of magnetization. Finite-size scaling analysis of the transverse spin correlation functions has been used to estimate the critical points of the Kosterlitz-Thouless transitions from the fractional magnetization plateau m=1/2m=1/2m=1/2 to the respective gapless Luttinger liquid phases for some sets of parameters.
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 spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
The magnetic behavior of the spin-1/2 Heisenberg antiferromagnet on the extended Lieb lattice is examined in the presence of an external magnetic field. Using density matrix renormalization group calculations, we determine the zero-temperature magnetization curves and construct the ground-state phase diagram in the magnetic field vs. the interaction ratio plane. Depending on the interaction ratio, the zero-temperature magnetization curves exhibit field-driven quantum phase transitions between the gapped phases manifested as the intermediate plateaus at 1/51/51/5 and 3/53/53/5 of the saturation magnetization and a gapless spin-canted phase, in which the magnetization varies continuously with the applied magnetic field. Quantum Monte Carlo simulations reveal clear finite-temperatures signatures of the field-induced quantum phase transitions and the intermediate magnetization plateaus, while they provide no evidence for either continuous or discontinuous thermal phase transitions.