We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at $1∕2$ -filling. A general dual-vortex field theory is developed for arbitrary rational filling factors $f$ , based on the appropriate projective symmetry group. At the simple nonfrustrated density $f=1∕3$ , we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to $f=1∕2$ , the behavior is quite different. Here, we find that the low-energy action describing the Mott transition has an emergent non-Abelian $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, which is not present at the microscopic level. This large non-Abelian symmetry is directly related to the frustration-induced quasidegeneracy between many charge-ordered states not related by microscopic symmetries. Through this ``pseudospin'' $SU(2)$ symmetry, the charged excitations in the insulator close to the Mott transition develop a Skyrmion-like character. This leads to an understanding of the supersolid phase of the triangular lattice $XXZ$ model as a ``partially melted'' Mott insulator, for more information see Melko et al. [Phys. Rev. Lett. 95, 127207 (2005)], Heidarian and Damle [Phys. Rev. Lett. 95, 127206 (2005)], and Wessel and Troyer [Phys. Rev. Lett. 95, 127205 (2005)]. The latter picture naturally explains a number of puzzling numerical observations of the properties of this supersolid. Moreover, we predict that the nearby quantum phase transition from this supersolid to the Mott insulator is in the noncompact ${\mathrm{CP}}^{1}$ critical universality class as presented in Motrunich and Vishwanath [Phys. Rev. B. 70, 075104 (2004)]. A description of a broad range of other Mott and supersolid states, and a diverse set of quantum critical points between them, is also provided.We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at $1∕2$-filling. A general dual-vortex field theory is developed for arbitrary rational filling factors $f$, based on the appropriate projective symmetry group. At the simple nonfrustrated density $f=1∕3$, we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to $f=1∕2$, the behavior is quite different. Here, we find that the low-energy action describing the Mott transition has an emergent non-Abelian $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, which is not present at the microscopic level. This large non-Abelian symmetry is directly related to the frustration-induced quasidegeneracy between many charge-ordered states not related by microscopic symmetries. Through this ``pseudospin'' $SU(2)$ symmetry, the charged excitations in the insulator close to the Mott transition develop a Skyrmion-like character. This leads to an understanding of the supersolid phase of the triangular lattice $XXZ$ model as a ``partially melted'' Mott insulator, for more information see Melko et al. [Phys. Rev. Lett. 95, 127207 (2005)], Heidarian and Damle [Phys. Rev. Lett. 95, 127206 (2005)], and Wessel and Troyer [Phys. Rev. Lett. 95, 127205 (2005)]. The latter picture naturally explains a number of puzzling numerical observations of the properties of this supersolid. Moreover, we predict that the nearby quantum phase transition from this supersolid to the Mott insulator is in the noncompact ${\mathrm{CP}}^{1}$ critical universality class as presented in Motrunich and Vishwanath [Phys. Rev. B. 70, 075104 (2004)]. A description of a broad range of other Mott and supersolid states, and a diverse set of quantum critical points between them, is also provided.

arXiv:cond-mat/0506457Physical Review BOct 3, 200538 citations

Quantum Transition to Supersolid Phase

Shinichi Saito, Susumu Kurihara, Y. Y. Suzuki

Journal of SuperconductivityFeb 1, 19990 citations

The Supersolid Phase of Interacting 2D Bosons

Anne van Otterlo, Karl-Heinz Wagenblast

Springer eBooksJan 1, 19950 citations

Pseudospin SU(2)-symmetry breaking, charge-density waves and superconductivity in the Hubbard model

Shun-Qing Shen, Xin Xie

In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.

arXiv:cond-mat/9504019Journal of Physics Condensed MatterJun 24, 199610 citations

Phase Diagram of the Spin- 1/2 Kitaev-Gamma Chain and Emergent SU(2) Symmetry

Wang Yang, Alberto Nocera, Tarun Tummuru +2 more

We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γ term," using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)_{1} Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)_{1} predictions. A modified non-Abelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O_{h}→D_{4} spontaneous symmetry breaking.We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γ term," using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)_{1} Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)_{1} predictions. A modified non-Abelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O_{h}→D_{4} spontaneous symmetry breaking.

arXiv:1910.14304Physical Review LettersApr 10, 202045 citations

Emergent supersymmetry at a critical point of a lattice model

Sung-Sik Lee

Bulletin of the American Physical SocietyMar 5, 20070 citations

1∕2

-filling. A general dual-vortex field theory is developed for arbitrary rational filling factors

f

, based on the appropriate projective symmetry group. At the simple nonfrustrated density

f=1∕3

, we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to

f=1∕2

, the behavior is quite different. Here, we find that the low-energy action describing the Mott transition has an emergent non-Abelian $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, which is not present at the microscopic level. This large non-Abelian symmetry is directly related to the frustration-induced quasidegeneracy between many charge-ordered states not related by microscopic symmetries. Through this ``pseudospin''

SU(2)

symmetry, the charged excitations in the insulator close to the Mott transition develop a Skyrmion-like character. This leads to an understanding of the supersolid phase of the triangular lattice

XXZ

model as a ``partially melted'' Mott insulator, for more information see Melko et al. [Phys. Rev. Lett. 95, 127207 (2005)], Heidarian and Damle [Phys. Rev. Lett. 95, 127206 (2005)], and Wessel and Troyer [Phys. Rev. Lett. 95, 127205 (2005)]. The latter picture naturally explains a number of puzzling numerical observations of the properties of this supersolid. Moreover, we predict that the nearby quantum phase transition from this supersolid to the Mott insulator is in the noncompact

{\mathrm{CP}}^{1}

critical universality class as presented in Motrunich and Vishwanath [Phys. Rev. B. 70, 075104 (2004)]. A description of a broad range of other Mott and supersolid states, and a diverse set of quantum critical points between them, is also provided.