Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems.Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one-and two-particle excitations, which are a measure of inter-particle correlations.We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems.Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform.We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below Tc in cuprates or smeared excitation spectra characteristic for strongly interacting systems.Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems.Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one-and two-particle excitations, which are a measure of inter-particle correlations.We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems.Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform.We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below Tc in cuprates or smeared excitation spectra characteristic for strongly interacting systems.

Acta Physica Polonica AAug 1, 20160 citations

Dynamic Stimulation of Phase Coherence in Lattice Bosons

Andrew J. Robertson, Victor M. Galitski, Gil Refael

Bulletin of the American Physical SocietyMar 22, 20110 citations

RVB signatures in the spin dynamics of the square-lattice Heisenberg antiferromagnet

E. A. Ghioldi, M. G. Gonzalez, L. O. Manuel +1 more

We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.

arXiv:1601.01200Europhysics Letters (EPL)Mar 1, 20166 citations

Quantum Phases of Cold Bosons in an Optical Lattice

Michael Aizenman, Elliot H. Lieb, Robert Seiringer +2 more

New Trends in Mathematical PhysicsJan 1, 20090 citations

Bosonization approach to charge and spin dynamics of one-dimensional spin- 12 fermions with band curvature in a clean quantum wire

S. Teber

We consider one-dimensional spin- $\frac{1}{2}$ fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where $v$ is the Fermi velocity and $1∕m$ is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector $q$ with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where ${m}^{*}$ decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.We consider one-dimensional spin-$\frac{1}{2}$ fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where $v$ is the Fermi velocity and $1∕m$ is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector $q$ with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where ${m}^{*}$ decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.

arXiv:cond-mat/0609754Physical Review BJul 9, 200733 citations

We consider one-dimensional spin-

\frac{1}{2}

fermions in a clean quantum wire, with forward scattering interactions and a nonlinear single-particle spectrum ${\ensuremath{\xi}}_{k}=v\ensuremath{\mid}k\ensuremath{\mid}+{k}^{2}∕2m$, where

v

is the Fermi velocity and

1∕m

is the band curvature. We calculate the dynamical structure factor (DSF) of the model at small wave vector

q

with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization emulates the two-parametric excitation spectrum $\ensuremath{\omega}=u\ensuremath{\mid}q\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}{q}^{2}∕2{m}^{*}$, where

{m}^{*}

decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., $\ensuremath{\omega}⪢u\ensuremath{\mid}q\ensuremath{\mid}$, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at $\ensuremath{\omega}={u}_{\ensuremath{\rho}}\ensuremath{\mid}q\ensuremath{\mid}$ but also a spin peak at $\ensuremath{\omega}={u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies $\ensuremath{\omega}>{u}_{\ensuremath{\sigma}}\ensuremath{\mid}q\ensuremath{\mid}$, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.