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/0611772 · Physical Review B

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

A. Friedrich, Alexei K. Kolezhuk, Ian P. McCulloch, Ulrich Schollwöck

Published Mar 13, 2007• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.75.094414

Related papers

Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

Adilet Imambekov, L. I. Glazman

We consider the zero temperature behavior of dynamic response functions of 1D systems near edges of support in the momentum-energy plane (k,omega). The description of the singularities of dynamic response functions near an edge epsilon(k) is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function epsilon(k). This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of epsilon(k) and Luttinger liquid parameters for any k. For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.

arXiv:0812.1046•Physical Review Letters•Mar 26, 2009•124 citations

Edge singularities in the one-dimensional Bariev model

P. Schlottmann

Bariev's model for correlated hopping in one dimension is integrable and soluble within the framework of two nested Bethe Ansätze. For repulsive interaction and finite magnetization the low energy excitation spectrum is a two-component Luttinger liquid with conformal charges c=1. In zero magnetic field the spectrum of spin excitations is gapped. For higher energy excitations the single-hole (single-particle) spectral functions display edge singularities that deviate from those expected from a Luttinger liquid. The system can be described as a mobile impurity coupled to the Luttinger liquid yielding an effective x-ray edge type model. Using the Bethe Ansatz solution for repulsive interaction we obtain expressions for the critical exponents for the single-particle and single-hole Green's functions in zero magnetic field.

Nuclear Physics B•Oct 21, 2019•2 citations

Magnetic Phases and Long-Range Ordering of the Haldane System in High Magnetic Fields

Isao Harada, Yoshihiro Nishiyama

Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.

Progress of Theoretical Physics Supplement•Jan 1, 2002•2 citations

Fermi-Edge Singularity of the Tomonaga-Luttinger Liquids with Spin-Polarized Fermi Points in a Magnetic Field

Tetsuo Ogawa, Hiroshi Otani

The Tomonaga-Luttinger liquids with spin-polarized Fermi points in an external magnetic field are studied theoretically. The critical exponent of the Fermi-edge singularity is analytically obtained. Power-law divergence of edge spectra is possible even for repulsive electron-hole interactions.

Journal of the Physical Society of Japan•Oct 15, 1995•12 citations

Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions

Hiroshi Otani, Tetsuo Ogawa

Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, ${\ensuremath{\lambda}}_{\mathit{e}}$ and ${\ensuremath{\lambda}}_{\mathit{h}}$, of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\infty} and ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\infty}), the correlation function yields a power-law decay only for a long-time regime, which is determined by the force ranges as t>max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]/${\mathit{v}}_{\mathit{F}}$. Corresponding optical spectrum near the Fermi edge (within an energy range of \ensuremath{\Elzxh}${\mathit{v}}_{\mathit{F}}$/max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\rightarrow}\ensuremath{\infty} and/or ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\rightarrow}\ensuremath{\infty}), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power-law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity. Relations between the spectral shape and a measurement time (frequency resolution) are also clarified. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Aug 15, 1996•18 citations

Response functions of gapped spin systems in high magnetic field

Alexei K. Kolezhuk, Hans-Jürgen Mikeska

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 usually

•Jan 1, 2008•8 citations
We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an S=1S=1S=1 Heisenberg chain, placed in a strong external magnetic field HHH exceeding the Haldane gap \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range \ensuremathω\ensuremath≳\ensuremathΔ\ensuremath{\omega}\ensuremath{\gtrsim}\ensuremath{\Delta}\ensuremathω\ensuremath≳\ensuremathΔ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity S\ensuremath∥(q=\ensuremathπ,\ensuremathω)\ensuremath∝(\ensuremathω\ensuremath−\ensuremathω0)\ensuremath−\ensuremathα\ensuremath′{S}^{\ensuremath{\Vert}}(q=\ensuremath{\pi},\ensuremath{\omega})\ensuremath{\propto}{(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}^{\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}}S\ensuremath∥(q=\ensuremathπ,\ensuremathω)\ensuremath∝(\ensuremathω\ensuremath−\ensuremathω0​)\ensuremath−\ensuremathα\ensuremath′. We study the behavior of the high-energy edge exponent \ensuremathα\ensuremath′{\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremathα\ensuremath′ and the edge \ensuremathω0{\ensuremath{\omega}}_{0}\ensuremathω0​ 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>\ensuremathΔH>\ensuremath{\Delta}H>\ensuremathΔ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.
We consider the zero temperature behavior of dynamic response functions of 1D systems near edges of support in the momentum-energy plane (k,omega). The description of the singularities of dynamic response functions near an edge epsilon(k) is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function epsilon(k). This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of epsilon(k) and Luttinger liquid parameters for any k. For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.
Bariev's model for correlated hopping in one dimension is integrable and soluble within the framework of two nested Bethe Ansätze. For repulsive interaction and finite magnetization the low energy excitation spectrum is a two-component Luttinger liquid with conformal charges c=1. In zero magnetic field the spectrum of spin excitations is gapped. For higher energy excitations the single-hole (single-particle) spectral functions display edge singularities that deviate from those expected from a Luttinger liquid. The system can be described as a mobile impurity coupled to the Luttinger liquid yielding an effective x-ray edge type model. Using the Bethe Ansatz solution for repulsive interaction we obtain expressions for the critical exponents for the single-particle and single-hole Green's functions in zero magnetic field.
Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.
Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, ${\ensuremath{\lambda}}_{\mathit{e}}$ and ${\ensuremath{\lambda}}_{\mathit{h}}$, of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\infty} and ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\infty}), the correlation function yields a power-law decay only for a long-time regime, which is determined by the force ranges as t>max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]/vF{\mathit{v}}_{\mathit{F}}vF​. Corresponding optical spectrum near the Fermi edge (within an energy range of \ensuremath{\Elzxh}vF{\mathit{v}}_{\mathit{F}}vF​/max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\rightarrow}\ensuremath{\infty} and/or ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\rightarrow}\ensuremath{\infty}), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power-law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity. Relations between the spectral shape and a measurement time (frequency resolution) are also clarified. \textcopyright{} 1996 The American Physical Society.
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 usually