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

Journal of the Physical Society of Japan

Phase Transition ofS=1/2 Bond-Alternating Chain in a Magnetic Field

Tôru Sakai

Published Jan 15, 1995• 49 citations
Publisher

Abstract

The S =1/2 bond alternating Heisenberg spin chain in a magnetic field is studied by the numerical diagonalization and the finite size scaling based on the conformal field theory. It is found that the magnetic state (0< m <1) is gapless (the central charge c =1) and described by the Luttinger liquid, which corresponds to a spinless Fermion system with repulsive interaction for antiferromagnetic-antiferromagnetic alternating chains, but attractive one for ferromagnetic-antiferromagnetic chains. The critical exponents δ and η are determined at the critical fields. The results suggest that the phase transitions belong to the same universality class as the S =1 antiferromagnetic chain for both alternating cases.

DOI
10.1143/jpsj.64.251

Related papers

A signature for the Luttinger liquid phase in alternating Heisenberg spin-1/2 chains

Jahanfar Abouie, S. Mahdavifar

We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quantum critical points. Using the numerical full diagonalization results, the existence of the double peak structure is confirmed.

arXiv:0811.0880•Nov 6, 2008•0 citations

Fractional Magnetization Plateau in the Alternating Spin Heisenberg Chain

Tetsuji Kuramoto

We study the S =1/2 and S =1 alternating spin Heisenberg chain with the next-nearest neighbor (NNN) interaction J 2 between neighboring S =1/2 spins, by using the numerical diagonalization method of a finite size system. It is found that a fractional plateau appears at magnetization m =1/2 in the magnetization curve for J 2 > J 2 c =0.106±0.001. The phase transition at J 2 c is characterized by the exponent σ=1, which controls the critical behavior of the spin gap Δ as Δ∼ exp(- a /( J 2 - J 2 c ) 1+σ ). For J 2 < J 2 c , the model at m =1/2 is described by the conformal field theory with central charge c =1 and exponent η for the spin correlation function of the transverse component to a magnetic field is calculated.

Journal of the Physical Society of Japan•Jun 15, 1999•12 citations

Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Wei Chen, Kazuo Hida, B. C. Sanctuary

One dimensional S = 1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D≥0. The ground states of this model contain the Haldane state, large-D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.

arXiv:cond-mat/9908125•Progress of Theoretical Physics Supplement•Jan 1, 2000•0 citations

Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Wei Chen, Kazuo Hida, B. C. Sanctuary

One dimensional S =1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D ≥0. The ground states of this model contain the Haldane state, large- D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.

Journal of the Physical Society of Japan•Jan 1, 2000•28 citations

Phase diagrams, distinct conformal anomalies, and thermodynamics of spin-1 bond-alternating Heisenberg antiferromagnetic chain in magnetic fields

Xin Yan, Wei Li, Yang Zhao +2 more

The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group, and the density matrix renormalization group methods. It is found that in the magnetic field--bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau, and spin-polarized phases are identified in a longitudinal field, while in a transverse field there are five phases including singlet dimer, Haldane, ${Z}_{2}$ symmetry breaking, quasi-1/2 magnetization plateau, and quasi-spin-polarized phases. A reentrant behavior of the staggered magnetization in a transverse field is observed. The quantum critical behaviors in longitudinal and transverse magnetic fields are disclosed to fall into different universality classes with corresponding conformal field central charge $c=1$ and $1/2$, respectively. The experimental data of the compound NTENP under both longitudinal and transverse magnetic fields are nicely fitted, and the Luttinger liquid behavior of low-temperature specific heat experimentally observed is also confirmed.

arXiv:1204.3474•Physical Review B•Apr 13, 2012•23 citations

Magnetic properties of the spinS= 1/2 Heisenberg chain with hexamer modulation of exchange

M Shahri Naseri, G I Japaridze, S. Mahdavifar +1 more

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.

arXiv:1110.4467•Journal of Physics Condensed Matter•Feb 21, 2012•7 citations
The S =1/2 bond alternating Heisenberg spin chain in a magnetic field is studied by the numerical diagonalization and the finite size scaling based on the conformal field theory. It is found that the magnetic state (0< m <1) is gapless (the central charge c =1) and described by the Luttinger liquid, which corresponds to a spinless Fermion system with repulsive interaction for antiferromagnetic-antiferromagnetic alternating chains, but attractive one for ferromagnetic-antiferromagnetic chains. The critical exponents δ and η are determined at the critical fields. The results suggest that the phase transitions belong to the same universality class as the S =1 antiferromagnetic chain for both alternating cases.
We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quantum critical points. Using the numerical full diagonalization results, the existence of the double peak structure is confirmed.
We study the S =1/2 and S =1 alternating spin Heisenberg chain with the next-nearest neighbor (NNN) interaction J 2 between neighboring S =1/2 spins, by using the numerical diagonalization method of a finite size system. It is found that a fractional plateau appears at magnetization m =1/2 in the magnetization curve for J 2 > J 2 c =0.106±0.001. The phase transition at J 2 c is characterized by the exponent σ=1, which controls the critical behavior of the spin gap Δ as Δ∼ exp(- a /( J 2 - J 2 c ) 1+σ ). For J 2 < J 2 c , the model at m =1/2 is described by the conformal field theory with central charge c =1 and exponent η for the spin correlation function of the transverse component to a magnetic field is calculated.
One dimensional S = 1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D≥0. The ground states of this model contain the Haldane state, large-D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.
One dimensional S =1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D ≥0. The ground states of this model contain the Haldane state, large- D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group, and the density matrix renormalization group methods. It is found that in the magnetic field--bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau, and spin-polarized phases are identified in a longitudinal field, while in a transverse field there are five phases including singlet dimer, Haldane, Z2{Z}_{2}Z2​ symmetry breaking, quasi-1/2 magnetization plateau, and quasi-spin-polarized phases. A reentrant behavior of the staggered magnetization in a transverse field is observed. The quantum critical behaviors in longitudinal and transverse magnetic fields are disclosed to fall into different universality classes with corresponding conformal field central charge c=1c=1c=1 and 1/21/21/2, respectively. The experimental data of the compound NTENP under both longitudinal and transverse magnetic fields are nicely fitted, and the Luttinger liquid behavior of low-temperature specific heat experimentally observed is also confirmed.
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.