We study the dynamical structure factor of gapped one-dimensional spin systems in the critical phase in high magnetic field. It is shown that the presence of a “condensate ” in the ground state in the high-field phase leads to interesting signatures in the response functions. Recently, there has been an increasing interest in the physics of gapped onedimensional spin systems subject to an external magnetic field which is strong enough to close the gap and bring the system into a new critical phase with finite magnetization and gapless excitations. 1)- 13) The low-energy physics of the critical phase is usuallyWe study the dynamical structure factor of gapped one-dimensional spin systems in the critical phase in high magnetic field. It is shown that the presence of a “condensate ” in the ground state in the high-field phase leads to interesting signatures in the response functions. Recently, there has been an increasing interest in the physics of gapped onedimensional spin systems subject to an external magnetic field which is strong enough to close the gap and bring the system into a new critical phase with finite magnetization and gapless excitations. 1)- 13) The low-energy physics of the critical phase is usually

Jan 1, 20088 citations

Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields

A. Friedrich, Alexei K. Kolezhuk, Ian P. McCulloch +1 more

We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an $S=1$ Heisenberg chain, placed in a strong external magnetic field $H$ exceeding the Haldane gap $\ensuremath{\Delta}$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\ensuremath{\omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity ${S}^{\ensuremath{\Vert}}(q=\ensuremath{\pi},\ensuremath{\omega})\ensuremath{\propto}{(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}^{\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}}$. We study the behavior of the high-energy edge exponent ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and the edge ${\ensuremath{\omega}}_{0}$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\ensuremath{\Delta}$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an $S=1$ Heisenberg chain, placed in a strong external magnetic field $H$ exceeding the Haldane gap $\ensuremath{\Delta}$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\ensuremath{\omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity ${S}^{\ensuremath{\Vert}}(q=\ensuremath{\pi},\ensuremath{\omega})\ensuremath{\propto}{(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}^{\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}}$. We study the behavior of the high-energy edge exponent ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and the edge ${\ensuremath{\omega}}_{0}$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\ensuremath{\Delta}$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.

arXiv:cond-mat/0611772Physical Review BMar 13, 200715 citations

Excitation spectra of structurally dimerized and spin-Peierls chains in a magnetic field

Weiqiang Yu, Stephan Haas

The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields $h<{h}_{c1},$ an incommensurate regime ${(h}_{c1}<h<{h}_{c2})$ in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field ${h}_{c2}.$ For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields $h<{h}_{c1},$ an incommensurate regime ${(h}_{c1}<h<{h}_{c2})$ in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field ${h}_{c2}.$ For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.

arXiv:cond-mat/9909093Physical review. B, Condensed matterJul 1, 200016 citations

Interacting spin systems exhibiting spin plateaus and gaps

Bill Sutherland

We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.

Physical review. B, Condensed matterNov 1, 20007 citations

Excited spin states and phase separation in spinor Bose-Einstein condensates

Michał Matuszewski, Tristram J. Alexander, Yuri S. Kivshar

We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a $^{23}\text{N}\text{a}$ condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a $^{23}\text{N}\text{a}$ condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.

arXiv:0904.0086Physical Review AAug 5, 200942 citations

Theory of spin-2 Bose-Einstein condensates: Spin correlations, magnetic response, and excitation spectra

Masahito Ueda, Masato Koashi

The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.

arXiv:cond-mat/0203052Physical Review AMay 29, 2002163 citations

We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an

S=1

Heisenberg chain, placed in a strong external magnetic field

H

exceeding the Haldane gap $\ensuremath{\Delta}$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\ensuremath{\omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity ${S}^{\ensuremath{\Vert}}(q=\ensuremath{\pi},\ensuremath{\omega})\ensuremath{\propto}{(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}^{\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}}$. We study the behavior of the high-energy edge exponent ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and the edge ${\ensuremath{\omega}}_{0}$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\ensuremath{\Delta}$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.

h<{h}_{c1},

an incommensurate regime

{(h}_{c1}<h<{h}_{c2})

in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin-polarized phase above an upper critical field

{h}_{c2}.

For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.

^{23}\text{N}\text{a}

condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.