arXiv:0808.0681 · Physical Review Letters

Spectral Functions of Strongly Interacting Isospin- 12 Bosons in One Dimension

К. А. Матвеев, Akira Furusaki

Published Oct 23, 2008• 48 citations

Abstract

We study a system of one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions. We argue that the low-energy spectrum of the system consists of acoustic density waves and the spin excitations described by an effective ferromagnetic spin chain with a small exchange constant J. We use this description to compute the dynamic spin structure factor and the spectral functions of the system.

DOI: 10.1103/physrevlett.101.170403

Related papers

Spin Waves in a One-Dimensional Spinor Bose Gas

Jean-Noël Fuchs, Dimitri M. Gangardt, Tassilo Keilmann +1 more

arXiv:cond-mat/0507513Physical Review LettersOct 4, 2005105 citations

Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas

Mikhail B. Zvonarev, Vadim Cheianov, Thierry Giamarchi

arXiv:0708.3638Physical Review LettersDec 13, 2007138 citations

Bosonization of strongly interacting one-dimensional electrons

К. А. Матвеев, Akira Furusaki, L. I. Glazman

arXiv:0708.0212Physical Review BOct 31, 200732 citations

Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

J. Y. Lee, Xin Guan, Murray T. Batchelor +1 more

arXiv:0909.2097Physical Review ADec 21, 200910 citations

Emergence of magnetic excitations in one-dimensional quantum mixtures under confinement

P. Capuzzi, Patrizia Vignolo, Anna Minguzzi +1 more

arXiv:2602.03735Physical Review ResearchJul 15, 20260 citations

Spectral function of the U→∞ one-dimensional Hubbard model at finite temperature and the crossover to the spin-incoherent regime

Mohammad Soltanieh-ha, Adrian E. Feiguin

arXiv:1406.4471Physical Review BOct 31, 20147 citations

arXiv:0808.0681 · Physical Review Letters

Spectral Functions of Strongly Interacting Isospin- 12 Bosons in One Dimension

К. А. Матвеев, Akira Furusaki

Published Oct 23, 2008• 48 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.101.170403

Related papers

Spin Waves in a One-Dimensional Spinor Bose Gas

Jean-Noël Fuchs, Dimitri M. Gangardt, Tassilo Keilmann +1 more

We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or "spin charge") separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or "spin charge") separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

arXiv:cond-mat/0507513Physical Review LettersOct 4, 2005105 citations

Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas

Mikhail B. Zvonarev, Vadim Cheianov, Thierry Giamarchi

We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems.We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems.

arXiv:0708.3638Physical Review LettersDec 13, 2007138 citations

Bosonization of strongly interacting one-dimensional electrons

К. А. Матвеев, Akira Furusaki, L. I. Glazman

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling $J$ of electron spins to a value much smaller than the Fermi energy ${E}_{F}$ . The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below $J$ . In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between $J$ and ${E}_{F}$ . The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector $k$ near the Fermi point ${k}_{F}$ , the spectral function has a strong peak centered at $k=0$ . Our theory also provides analytical description of the spectral function singularities near $3{k}_{F}$ (the ``shadow band'' features).Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling $J$ of electron spins to a value much smaller than the Fermi energy ${E}_{F}$. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below $J$. In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between $J$ and ${E}_{F}$. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector $k$ near the Fermi point ${k}_{F}$, the spectral function has a strong peak centered at $k=0$. Our theory also provides analytical description of the spectral function singularities near $3{k}_{F}$ (the ``shadow band'' features).

arXiv:0708.0212Physical Review BOct 31, 200732 citations

Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

J. Y. Lee, Xin Guan, Murray T. Batchelor +1 more

We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin-exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field $H$ is less than the lower critical field ${H}_{c1}$ ; (ii) a ferromagnetic phase of atoms in the hyperfine state $|F=1,\text{ }{m}_{F}=1⟩$ when the external magnetic field exceeds the upper critical field ${H}_{c2}$ ; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region ${H}_{c1}<H<{H}_{c2}$ . At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired ${m}_{F}=1$ bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.We investigate magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin-exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field $H$ is less than the lower critical field ${H}_{c1}$; (ii) a ferromagnetic phase of atoms in the hyperfine state $|F=1,\text{ }{m}_{F}=1⟩$ when the external magnetic field exceeds the upper critical field ${H}_{c2}$; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region ${H}_{c1}<H<{H}_{c2}$. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired ${m}_{F}=1$ bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.

arXiv:0909.2097Physical Review ADec 21, 200910 citations

Emergence of magnetic excitations in one-dimensional quantum mixtures under confinement

P. Capuzzi, Patrizia Vignolo, Anna Minguzzi +1 more

We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi-Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic confinement, we show that, on top of the ladder structure of the density excitations imposed by the external confinement, spin excitations emerge as sideband peaks, with dispersion related to the one of ferromagnetic or antiferromagnetic spin chains and a width fundamentally larger for fermionic mixtures than for bosonic ones, as determined by the different symmetry of spin-excited states. The observation of spin excitation branches can provide a univocal probe of interaction-induced magnetism in ultracold atoms.We obtain an exact solution for the spectral function for one-dimensional Bose-Bose and Fermi-Fermi mixtures with strong repulsive interactions, valid in arbitrary confining potentials and at all frequency scales. For the case of harmonic confinement, we show that, on top of the ladder structure of the density excitations imposed by the external confinement, spin excitations emerge as sideband peaks, with dispersion related to the one of ferromagnetic or antiferromagnetic spin chains and a width fundamentally larger for fermionic mixtures than for bosonic ones, as determined by the different symmetry of spin-excited states. The observation of spin excitation branches can provide a univocal probe of interaction-induced magnetism in ultracold atoms.

arXiv:2602.03735Physical Review ResearchJul 15, 20260 citations

Spectral function of the U→∞ one-dimensional Hubbard model at finite temperature and the crossover to the spin-incoherent regime

Mohammad Soltanieh-ha, Adrian E. Feiguin

The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by ${k}_{F}$ of the minimum of the dispersion.The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by ${k}_{F}$ of the minimum of the dispersion.

arXiv:1406.4471Physical Review BOct 31, 20147 citations

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling

J

of electron spins to a value much smaller than the Fermi energy

{E}_{F}

. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below

J

. In this paper, we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between

J

and

{E}_{F}

. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range $J⪡\ensuremath{\epsilon}⪡{E}_{F}$. We show that in addition to the expected features at the wave vector

k

near the Fermi point

{k}_{F}

, the spectral function has a strong peak centered at

k=0

. Our theory also provides analytical description of the spectral function singularities near

3{k}_{F}

(the ``shadow band'' features).

H

is less than the lower critical field

{H}_{c1}

; (ii) a ferromagnetic phase of atoms in the hyperfine state

|F=1,\text{ }{m}_{F}=1⟩

when the external magnetic field exceeds the upper critical field

{H}_{c2}

; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region

{H}_{c1}<H<{H}_{c2}

. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired

{m}_{F}=1

bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.

{k}_{F}

of the minimum of the dispersion.