We study the energy-momentum relations of the Nambu-Goldstone modes in quantum antiferromagnetic Heisenberg models on a hypercubic lattice. This work is a sequel to the previous series about the models. We prove that the Nambu-Goldstone modes show a linear dispersion relation for the small momenta, i.e., the low energies of the Nambu-Goldstone excitations are proportional to the momentum of the spin wave above the infinite-volume ground states with symmetry breaking. Our method relies on the upper bounds for the susceptibilities which are derived from the reflection positivity of the quantum Heisenberg antiferromagnets. The method is also applicable to other systems when the corresponding upper bounds for the susceptibilities are justified.We study the energy-momentum relations of the Nambu-Goldstone modes in quantum antiferromagnetic Heisenberg models on a hypercubic lattice. This work is a sequel to the previous series about the models. We prove that the Nambu-Goldstone modes show a linear dispersion relation for the small momenta, i.e., the low energies of the Nambu-Goldstone excitations are proportional to the momentum of the spin wave above the infinite-volume ground states with symmetry breaking. Our method relies on the upper bounds for the susceptibilities which are derived from the reflection positivity of the quantum Heisenberg antiferromagnets. The method is also applicable to other systems when the corresponding upper bounds for the susceptibilities are justified.

arXiv:2105.04970May 11, 20212 citations

Energy spectrum of the Hubbard model with U=∞

Miroslav Kotrla

Physics Letters AMar 1, 199016 citations

Formula for the Number of Nambu-Goldstone Modes

Haruki Watanabe

When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulas for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. In the process we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb-Schultz-Mattis theorem.When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulas for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. In the process we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb-Schultz-Mattis theorem.

arXiv:1904.00569Apr 1, 20193 citations

Self-energy corrections to the electronic spectrum of the Hubbard model

Adolfo Avella, S. Krivenko, Francesco Paolo Mancini +1 more

Journal of Magnetism and Magnetic MaterialsMar 6, 200413 citations

Rainbow Nambu-Goldstone Modes under a Shear Flow

Yuki Minami, Hiroyoshi Nakano, Yoshimasa Hidaka

We study an $\mathrm{O}(N)$ scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking $\mathrm{O}(N)\ensuremath{\rightarrow}\mathrm{O}(N\ensuremath{-}1)$. We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation $\ensuremath{\omega}\ensuremath{\sim}{k}_{1}^{2/3}$, where ${k}_{1}$ is the wave number along the flow. Such behaviors do not have counterparts in an equilibrium state.We study an $\mathrm{O}(N)$ scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking $\mathrm{O}(N)\ensuremath{\rightarrow}\mathrm{O}(N\ensuremath{-}1)$. We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation $\ensuremath{\omega}\ensuremath{\sim}{k}_{1}^{2/3}$, where ${k}_{1}$ is the wave number along the flow. Such behaviors do not have counterparts in an equilibrium state.

arXiv:2009.10357Physical Review LettersApr 7, 20216 citations

Quasiparticel Spectra of the Hubbard Model

James F. Annett, William H. Beere

APSMar 1, 19980 citations

We study an

\mathrm{O}(N)

scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking $\mathrm{O}(N)\ensuremath{\rightarrow}\mathrm{O}(N\ensuremath{-}1)$. We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation $\ensuremath{\omega}\ensuremath{\sim}{k}_{1}^{2/3}$, where

{k}_{1}

is the wave number along the flow. Such behaviors do not have counterparts in an equilibrium state.