We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$= ${\mathit{v}}_{\mathit{F}}$ (\ensuremath{\Vert} ${\mathit{p}}_{\mathit{x}}$ \ensuremath{\Vert}+\ensuremath{\Vert} ${\mathit{p}}_{\mathit{y}}$ \ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range ${\mathit{q}}_{0}$ , which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$=${\mathit{v}}_{\mathit{F}}$(\ensuremath{\Vert}${\mathit{p}}_{\mathit{x}}$\ensuremath{\Vert}+\ensuremath{\Vert}${\mathit{p}}_{\mathit{y}}$\ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range ${\mathit{q}}_{0}$, which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.

arXiv:cond-mat/9312083Physical review. B, Condensed matterSep 15, 199417 citations

Breakdown of the Universality in Few-Boson Systems

Rimantas Lazauskas, Arnoldas Deltuva

Few-Body SystemsMar 13, 20110 citations

Bosonic quantum breakdown Hubbard model

Yu-Min Hu, Biao Lian

We propose a bosonic quantum breakdown Hubbard model, which generalizes the Bose-Hubbard model by adding an asymmetric breakdown interaction turning one boson into two between adjacent sites. When the normal hopping is zero, this model has a global exponential U(1) symmetry, and we show that the ground state undergoes a first-order phase transition from a Mott insulator (MI) to a spontaneously symmetry breaking (SSB) breakdown condensate as the breakdown interaction increases. Surprisingly, the SSB breakdown condensate does not have a gapless Goldstone mode, which invalidates the Mermin-Wagner theorem and leads to stable SSB in one dimension. Moreover, we show that the quench dynamics of a boson added to MI exhibits a dynamical transition from dielectric to breakdown phases, which happens at a larger breakdown interaction than the ground state phase transition. Between these two transitions, the MI (dielectric) state is a false vacuum stable against dynamical breakdown. Our results reveal that quantum models with unconventional symmetries such as the exponential symmetry can exhibit unexpected properties.We propose a bosonic quantum breakdown Hubbard model, which generalizes the Bose-Hubbard model by adding an asymmetric breakdown interaction turning one boson into two between adjacent sites. When the normal hopping is zero, this model has a global exponential U(1) symmetry, and we show that the ground state undergoes a first-order phase transition from a Mott insulator (MI) to a spontaneously symmetry breaking (SSB) breakdown condensate as the breakdown interaction increases. Surprisingly, the SSB breakdown condensate does not have a gapless Goldstone mode, which invalidates the Mermin-Wagner theorem and leads to stable SSB in one dimension. Moreover, we show that the quench dynamics of a boson added to MI exhibits a dynamical transition from dielectric to breakdown phases, which happens at a larger breakdown interaction than the ground state phase transition. Between these two transitions, the MI (dielectric) state is a false vacuum stable against dynamical breakdown. Our results reveal that quantum models with unconventional symmetries such as the exponential symmetry can exhibit unexpected properties.

arXiv:2401.04309Physical review. B./Physical review. BAug 29, 20253 citations

Energy and Structure of Few-Boson Systems

J. Horne, Jorge A. Salas, Kálmán Varga

Few-Body SystemsOct 20, 20149 citations

Theory of many-boson systems

Richard David Etters

Jan 1, 19650 citations

We consider spinless electrons in two dimensions with the bare spectrum ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{p}}$=

{\mathit{v}}_{\mathit{F}}

(\ensuremath{\Vert}

{\mathit{p}}_{\mathit{x}}

\ensuremath{\Vert}+\ensuremath{\Vert}

{\mathit{p}}_{\mathit{y}}

\ensuremath{\Vert}). In momentum space, the interactions among electrons have a finite range

{\mathit{q}}_{0}

, which is small compared to the Fermi momentum. A golden-rule calculation of the electron lifetime indictes a breakdown of Landau's Fermi-liquid theory in the model. At the one-loop level of perturbation theory, we show that the density wave and the superconducting instabilities cancel each other and there is no symmetry breaking. We solve the model via bosonization; the excitation spectrum is found to consist of gapless bosonic modes as in a one-dimensional Luttinger liquid.