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/0002356 · Low Temperature Physics

Commensurate–incommensurate phase transitions for multichain quantum spin models: exact results

Andrei A. Zvyagin

Published Feb 1, 2000• 12 citations
arXivHTMLPDF

Abstract

The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate–incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated.

DOI
10.1063/1.593878

Related papers

Quantum phase transitions in low-dimensional quantum spin systems with incommensurate magnetic structures

Andrei A. Zvyagin

Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.

Physical Review B•Aug 10, 2005•19 citations

Quantum phase transitions and thermodynamics of quantum antiferromagnets with next-nearest-neighbor couplings

Andrei A. Zvyagin, Andreas Klümper

We study quantum spin models with nearest- and next-nearest-neighbor exchange interactions by means of exact solutions. Depending on the representation, the models can also be viewed as spin ladders with interchain couplings and with ring biquadratic spin-spin interactions. The ground-state phase diagram is constructed as a function of the next-nearest-neighbor couplings and an external magnetic field. Several quantum phase transitions in the ground state, including the possibility of a first-order quantum phase transition, governed by the external magnetic field, are predicted. The low-energy conformal behavior of the low-lying excitations is studied in the commensurate and incommensurate phases. Finally, the properties of the models at finite temperature are studied exactly. A finite set of nonlinear integral equations determining the thermodynamic potential at arbitrary temperature and external magnetic field is derived and solved in several important cases. The results for the magnetic susceptibility and the Sommerfeld coefficient of the specific heat are presented.

Physical review. B, Condensed matter•Oct 20, 2003•36 citations

Exactly solvable quantum spin model with alternating and multiple spin exchange interactions

Andrei A. Zvyagin, Gleb A. Skorobagatko

We propose an exactly solvable quantum spin model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the multiple spin exchange. The model permits us to obtain exactly thermodynamic characteristics of the considered quantum spin chain. In the ground state, depending on the strength of the three-spin coupling, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering with the spontaneous magnetization and with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by an external magnetic field and the multiple spin exchange coupling strength. Our exactly solvable quantum spin model demonstrates that multispin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by multispin couplings, the alternation of nearest neighbor exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations.

Physical Review B•Jan 31, 2006•29 citations

Critical properties of gapped spin-chains and ladders in a magnetic field

R. Chitra, Thierry Giamarchi

An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field ${\mathrm{H}}_{\mathrm{c}1}$ and an upper critical field ${\mathrm{H}}_{\mathrm{c}2}$, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field ${\mathrm{H}}_{\mathrm{c}1}$ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.

arXiv:cond-mat/9611114•Physical review. B, Condensed matter•Mar 1, 1997•218 citations

Thermal entanglement of spin chains with quantum critical behavior

Andrei A. Zvyagin

Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.

Physical Review B•Oct 12, 2009•11 citations

Field-Induced Ising Criticality and Incommensurability in Anisotropic Spin-1 Chains

Y. J. Wang

Quantum phase transitions induced by an external magnetic field in the Haldane-gapped spin-1 chains are studied in a fermionic field-theoretic description of the model. In the case with broken axial symmetry, two transitions occurs consecutively as increasing the field: $h_c=(m_1 m_2)^{1/2}$ (with $m_1$ and $m_2$ the transverse masses) is the critical Ising point and $\tilde{h}_c^* (> h_c)$ is the commensurate-incommensurate transition point. Although the latter is thermodynamically indiscernible, its property is revealed in the spin correlation functions (both uniform and staggered) which are calculated upon expressing the correlations of coupled Ising pair fields in terms of block-Toeplitz determinants.

arXiv:cond-mat/0306365•Jun 13, 2003•2 citations
The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate–incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
We study quantum spin models with nearest- and next-nearest-neighbor exchange interactions by means of exact solutions. Depending on the representation, the models can also be viewed as spin ladders with interchain couplings and with ring biquadratic spin-spin interactions. The ground-state phase diagram is constructed as a function of the next-nearest-neighbor couplings and an external magnetic field. Several quantum phase transitions in the ground state, including the possibility of a first-order quantum phase transition, governed by the external magnetic field, are predicted. The low-energy conformal behavior of the low-lying excitations is studied in the commensurate and incommensurate phases. Finally, the properties of the models at finite temperature are studied exactly. A finite set of nonlinear integral equations determining the thermodynamic potential at arbitrary temperature and external magnetic field is derived and solved in several important cases. The results for the magnetic susceptibility and the Sommerfeld coefficient of the specific heat are presented.
We propose an exactly solvable quantum spin model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the multiple spin exchange. The model permits us to obtain exactly thermodynamic characteristics of the considered quantum spin chain. In the ground state, depending on the strength of the three-spin coupling, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering with the spontaneous magnetization and with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by an external magnetic field and the multiple spin exchange coupling strength. Our exactly solvable quantum spin model demonstrates that multispin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by multispin couplings, the alternation of nearest neighbor exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations.
An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and an upper critical field Hc2{\mathrm{H}}_{\mathrm{c}2}Hc2​, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field Hc1{\mathrm{H}}_{\mathrm{c}1}Hc1​ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.
Results for the characteristics of the macroscopic thermal entanglement for integrable spin-1/2 antiferromagnetic chain models with multispin interactions in the thermodynamic limit are presented. Such interactions cause quantum-phase transitions to incommensurate phases with partial spontaneous magnetization. We have derived exact equations, which determine the thermal and magnetic field behavior of the concurrence of spin chains. The analysis of these equations shows that there exists a critical temperature, below which the thermal entanglement of considered spin chains is nonzero. We have shown that at those quantum-phase transitions, caused by multispin interactions, the thermal entanglement is reduced. Also, we have shown that the thermal entanglement is reduced due to nonzero magnetization of spin chains in the ground state, caused by multispin interactions.
Quantum phase transitions induced by an external magnetic field in the Haldane-gapped spin-1 chains are studied in a fermionic field-theoretic description of the model. In the case with broken axial symmetry, two transitions occurs consecutively as increasing the field: hc=(m1m2)1/2h_c=(m_1 m_2)^{1/2}hc​=(m1​m2​)1/2 (with m1m_1m1​ and m2m_2m2​ the transverse masses) is the critical Ising point and h~c∗(>hc)\tilde{h}_c^* (> h_c)h~c∗​(>hc​) is the commensurate-incommensurate transition point. Although the latter is thermodynamically indiscernible, its property is revealed in the spin correlation functions (both uniform and staggered) which are calculated upon expressing the correlations of coupled Ising pair fields in terms of block-Toeplitz determinants.