Hugenholtz-Pines theorem with broken $U(1) \times SO(N)$ or $U(1) \times SU(N)$ symmetryHugenholtz-Pines theorem with broken $U(1) \times SO(N)$ or $U(1) \times SU(N)$ symmetry

Shohei Watabe

The Hugenholtz-Pines (HP) theorem is derived for Bose-Einstein condensates (BECs) with internal degrees of freedom. The low-energy Ward-Takahashi identity is provided in the system with the linear and quadratic symmetry breaking terms. This identity serves to organize the HP theorem for multicomponent BECs, such as the binary BEC as well as the spin- $f$ spinor BEC in the presence of a magnetic field with broken U $(1)$ $\times$ SO $(3)$ symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity.The Hugenholtz-Pines (HP) theorem is derived for Bose-Einstein condensates (BECs) with internal degrees of freedom. The low-energy Ward-Takahashi identity is provided in the system with the linear and quadratic symmetry breaking terms. This identity serves to organize the HP theorem for multicomponent BECs, such as the binary BEC as well as the spin-$f$ spinor BEC in the presence of a magnetic field with broken U$(1)$$\times$SO$(3)$ symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity.

Sep 19, 20170 citations

Goldstone theorem, Hugenholtz–Pines theorem, and Ward–Takahashi relation in finite volume Bose–Einstein condensed gases

Hiroaki Enomoto, Masahiko Okumura, Y. Yamanaka

arXiv:cond-mat/0512294Annals of PhysicsFeb 8, 20068 citations

Conserving Gapless Mean-Field Theory of a Multi-Component Bose–Einstein Condensate

Yoshiyuki Kondo, Takafumi Kita

We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.

arXiv:cond-mat/0608472Journal of the Physical Society of JapanFeb 13, 20071 citation

Bose–Einstein condensation of triplons with a weakly broken U(1) symmetry

Asliddin Khudoyberdiev, Abdulla Rakhimov, A. Schilling

The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl 3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl 3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., of T c in H = 6 T and for .The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl 3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl 3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., of T c in H = 6 T and for .

arXiv:1701.08009New Journal of PhysicsSep 4, 201716 citations

Quantum Field Theory of Correlated Bose–Einstein Condensates: II. Ward–Takahashi Identities and Correlation Functions

Takafumi Kita

We derive Ward-Takahashi identities for correlated Bose-Einstein condensates based on the expressions of the first-order variations $(δΨ,δG)$ due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc. Jpn. $\bf 90$ , 024001 (2021)] for the condensate wave function $Ψ$ and Green's function $G$ . They enable us to obtain several exact results on the density and current correlation functions $K_{νν'}^{}$ , and also express $K_{νν'}^{}$ in terms of low-energy Green's functions and vertices. The latter expressions open up the possibility of constructing theory of superfluid Bose liquids in the same way as that for fermions at low temperatures. The vertices are found to have different limits depending on which of frequency $ω$ and wavenumber $q$ is set equal to zero first.We derive Ward-Takahashi identities for correlated Bose-Einstein condensates based on the expressions of the first-order variations $(δΨ,δG)$ due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc. Jpn. $\bf 90$, 024001 (2021)] for the condensate wave function $Ψ$ and Green's function $G$. They enable us to obtain several exact results on the density and current correlation functions $K_{νν'}^{}$, and also express $K_{νν'}^{}$ in terms of low-energy Green's functions and vertices. The latter expressions open up the possibility of constructing theory of superfluid Bose liquids in the same way as that for fermions at low temperatures. The vertices are found to have different limits depending on which of frequency $ω$ and wavenumber $q$ is set equal to zero first.

arXiv:2101.02396Journal of the Physical Society of JapanJan 7, 20213 citations

Identities and Many-Body Approaches in Bose-Einstein Condensates

Shohei Watabe

This paper discusses exact relations in the Bose-Einstein condensates, starting from basic properties of an ideal Bose gas.In particular, focused on are the Hugenholtz-Pines relation, Nepomnyashchii-Nepomnyashchii identity, and identities for the density response function.After introducing these exact relations, a few approaches of many-body approximations are discussed, which satisfy the exact relations in the Bose-Einstein condensates.This paper will serve as a bridge between theories on exact relations and those on approximations in the Bose-Einstein condensates.This paper discusses exact relations in the Bose-Einstein condensates, starting from basic properties of an ideal Bose gas.In particular, focused on are the Hugenholtz-Pines relation, Nepomnyashchii-Nepomnyashchii identity, and identities for the density response function.After introducing these exact relations, a few approaches of many-body approximations are discussed, which satisfy the exact relations in the Bose-Einstein condensates.This paper will serve as a bridge between theories on exact relations and those on approximations in the Bose-Einstein condensates.

arXiv:1903.03284Acta Physica Polonica AJun 1, 20196 citations

f

spinor BEC in the presence of a magnetic field with broken

\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)

symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity.

Hugenholtz-Pines theorem with broken

U(1) \times SO(N)

U(1) \times SU(N)

symmetry

f

spinor BEC in the presence of a magnetic field with broken U

(1)

\times

(3)

symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity.

T_{c}

for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.

We derive Ward-Takahashi identities for correlated Bose-Einstein condensates based on the expressions of the first-order variations

(δΨ,δG)

due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc. Jpn.

\bf 90

, 024001 (2021)] for the condensate wave function

Ψ

and Green's function

G

. They enable us to obtain several exact results on the density and current correlation functions

K_{νν'}^{}

, and also express

K_{νν'}^{}

in terms of low-energy Green's functions and vertices. The latter expressions open up the possibility of constructing theory of superfluid Bose liquids in the same way as that for fermions at low temperatures. The vertices are found to have different limits depending on which of frequency

ω

and wavenumber

q

is set equal to zero first.