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:1808.09240 · Physical review. B./Physical review. B

Magnetic-field–temperature phase diagram of alternating ferrimagnetic chains: Spin-wave theory from a fully polarized vacuum

W. M. da Silva, R. R. Montenegro-Filho

Published Dec 13, 2017• 13 citations
arXivHTMLPDF

Abstract

Quantum critical (QC) phenomena can be accessed by studying quantum magnets under an applied magnetic field ($B$). The QC points are located at the end points of magnetization plateaus and separate gapped and gapless phases. In one dimension, the low-energy excitations of the gapless phase form a Luttinger liquid (LL), and crossover lines bound insulating (plateau) and LL regimes, as well as the QC regime. Alternating ferrimagnetic chains have a spontaneous magnetization at $T=0$ and gapped excitations at zero field. Besides the plateau at the fully polarized (FP) magnetization, due to the gap there is another magnetization plateau at the ferrimagnetic (FRI) magnetization. We develop spin-wave theories to study the thermal properties of these chains under an applied magnetic field: one from the FRI classical state and another from the FP state, comparing their results with quantum Monte Carlo data. We deepen the theory from the FP state, obtaining the crossover lines in the $T$ vs $B$ low-$T$ phase diagram. In particular, from local extreme points in the susceptibility and magnetization curves, we identify the crossover between an LL regime formed by excitations from the FRI state to another built from excitations of the FP state. These two LL regimes are bounded by an asymmetric domelike crossover line, as observed in the phase diagram of other quantum magnets under an applied magnetic field.

DOI
10.1103/physrevb.96.214419

Related papers

Quantum phase transitions in alternating spin-($\frac{1}{2}$, $\frac{5}{2}$) Heisenberg chains

Antônio S F Tenório, R R Montenegro-Filho, M D Coutinho-Filho

The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.

arXiv:1207.5084•Journal of Physics Condensed Matter•Dec 1, 2011•19 citations

Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature*

Tai-Min Cheng, Meilin Li, Zhi-Rui Cheng +4 more

We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H CB, H CE and H CS were obtained, in which the H CB and H CE correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H CS correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ℏ ω σ,k (σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [ℏ ω 3,k (H CB)]min = 0, [ℏ ω 2,k (H CE)]max = 0 and [ℏ ω 2,k (H CS)]min = 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.

Chinese Physics B•Dec 30, 2020•0 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

Ground-state phase diagram and thermodynamics of coupled trimer chains

R. R. Montenegro-Filho, E. J. P. Silva-Júnior, Mauricio D. Coutinho-Filho

The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field $h$. The Hamiltonian contains exchange terms involving the intratrimer coupling ${J}_{1}$ (taken as the unit of energy) and the intertrimer coupling ${J}_{2}$, plus the Zeeman interaction for a magnetic field $h$ along the $z$ direction. Results for the magnetization per trimer $m$ are calculated in regimes of positive and negative values of the ratio $J={J}_{2}/{J}_{1}$, from which the rich field-induced ground state phase diagram $h$ versus $J$ is derived, with the presence of a Luttinger liquid, the 1/3 plateau ($m=1/2$), and the one of fully polarized magnetization ($m=3/2$). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for ${S}^{z}=1$ is shown at the previous regimes of $J$ values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by $1/|J|$ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound ${\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}$ and estimate the model exchange couplings: ${J}_{1}=74.8\phantom{\rule{4pt}{0ex}}\text{K}$ and $J=0.4$. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on ${\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}$ for two excitation modes. The 1/3 plateau closes only at $1/|J|=0$ with $J<0$.

arXiv:2204.11186•Physical review. B./Physical review. B•Apr 20, 2022•12 citations

Thermodynamics around magnetic phase transitions in alternating double-chain spin systems

丁林杰, 钟园, 樊帅伟 +1 more

The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green’s function theory.(i) For the completely antiferromagnetic(AFM) alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic(FM) phases,as a result of the intra-cluster spin-singlet competition. Furthermore, the Gr ¨uneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases.(ii) For the antiferromagnetically coupled FM alternating chains,the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally.Nevertheless, the M–h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.

中国物理B：英文版•Jan 1, 2014•0 citations

Thermodynamics around magnetic phase transitions in alternating double-chain spin systems

Linjie Ding, Yuan Zhong, Shuaiwei Fan +1 more

The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green's function theory. (i) For the completely antiferromagnetic (AFM) alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic (FM) phases, as a result of the intra-cluster spin-singlet competition. Furthermore, the Grüneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases. (ii) For the antiferromagnetically coupled FM alternating chains, the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally. Nevertheless, the M — h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.

Chinese Physics B•Nov 28, 2014•0 citations
Quantum critical (QC) phenomena can be accessed by studying quantum magnets under an applied magnetic field (BBB). The QC points are located at the end points of magnetization plateaus and separate gapped and gapless phases. In one dimension, the low-energy excitations of the gapless phase form a Luttinger liquid (LL), and crossover lines bound insulating (plateau) and LL regimes, as well as the QC regime. Alternating ferrimagnetic chains have a spontaneous magnetization at T=0T=0T=0 and gapped excitations at zero field. Besides the plateau at the fully polarized (FP) magnetization, due to the gap there is another magnetization plateau at the ferrimagnetic (FRI) magnetization. We develop spin-wave theories to study the thermal properties of these chains under an applied magnetic field: one from the FRI classical state and another from the FP state, comparing their results with quantum Monte Carlo data. We deepen the theory from the FP state, obtaining the crossover lines in the TTT vs BBB low-TTT phase diagram. In particular, from local extreme points in the susceptibility and magnetization curves, we identify the crossover between an LL regime formed by excitations from the FRI state to another built from excitations of the FP state. These two LL regimes are bounded by an asymmetric domelike crossover line, as observed in the phase diagram of other quantum magnets under an applied magnetic field.
Quantum phase transitions in alternating spin-(12\frac{1}{2}21​, 52\frac{5}{2}25​) Heisenberg chains
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.
We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H CB, H CE and H CS were obtained, in which the H CB and H CE correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H CS correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ℏ ω σ,k (σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [ℏ ω 3,k (H CB)]min = 0, [ℏ ω 2,k (H CE)]max = 0 and [ℏ ω 2,k (H CS)]min = 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.
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 density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field hhh. The Hamiltonian contains exchange terms involving the intratrimer coupling J1{J}_{1}J1​ (taken as the unit of energy) and the intertrimer coupling J2{J}_{2}J2​, plus the Zeeman interaction for a magnetic field hhh along the zzz direction. Results for the magnetization per trimer mmm are calculated in regimes of positive and negative values of the ratio J=J2/J1J={J}_{2}/{J}_{1}J=J2​/J1​, from which the rich field-induced ground state phase diagram hhh versus JJJ is derived, with the presence of a Luttinger liquid, the 1/3 plateau (m=1/2m=1/2m=1/2), and the one of fully polarized magnetization (m=3/2m=3/2m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for Sz=1{S}^{z}=1Sz=1 is shown at the previous regimes of JJJ values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/∣J∣1/|J|1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ and estimate the model exchange couplings: J1=74.8K{J}_{1}=74.8\phantom{\rule{4pt}{0ex}}\text{K}J1​=74.8K and J=0.4J=0.4J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ for two excitation modes. The 1/3 plateau closes only at 1/∣J∣=01/|J|=01/∣J∣=0 with J<0J<0J<0.
The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green’s function theory.(i) For the completely antiferromagnetic(AFM) alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic(FM) phases,as a result of the intra-cluster spin-singlet competition. Furthermore, the Gr ¨uneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases.(ii) For the antiferromagnetically coupled FM alternating chains,the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally.Nevertheless, the M–h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.
The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green's function theory. (i) For the completely antiferromagnetic (AFM) alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic (FM) phases, as a result of the intra-cluster spin-singlet competition. Furthermore, the Grüneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases. (ii) For the antiferromagnetically coupled FM alternating chains, the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally. Nevertheless, the M — h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.