Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1105.1682 · Physical Review B

Generic first-order versus continuous quantum nucleation of supersolidity

Lars Bonnes, Stefan Weßel

Published Aug 5, 2011• 30 citations
arXivHTMLPDF

Abstract

We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultracold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior is consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D ${\mathbb{Z}}_{6}$ clock model description of the enlarged symmetry of the solid order parameter field. In the generic case, however, the symmetry reduces to that of a 3D ${\mathbb{Z}}_{3}$ clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.

DOI
10.1103/physrevb.84.054510

Related papers

Supersolid phase transitions for hard-core bosons on a triangular lattice

Xue‐Feng Zhang, Raoul Dillenschneider, Yue Yu +1 more

Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.

arXiv:1106.0006•Physical Review B•Nov 21, 2011•49 citations

Pair supersolid with atom-pair hopping on the state-dependent triangular lattice

Wanzhou Zhang, Ruoxi Yin, Yan-Cheng Wang

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with $2/3$, 1, and $4/3$ filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional $XY$ university, with dynamical exponent $z=1$ and correlation exponent $\ensuremath{\nu}=0.671\phantom{\rule{0.16em}{0ex}}55$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.

arXiv:1208.6506•Physical Review B•Nov 19, 2013•17 citations

Critical behavior of the supersolid transition in Bose-Hubbard models

Erwin Frey, Leon Balents

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF-CSS transition is in the three-dimensional XY universality class. The SF-XSS transition exhibits nontrivial critical behavior, and appears, within a d=3-\ensuremath{\epsilon} expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in d=2 a strong-coupling fixed point with striking ``non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.

arXiv:cond-mat/9609138•Physical review. B, Condensed matter•Jan 1, 1997•51 citations

Supersolid Hard-Core Bosons on the Triangular Lattice

Stefan Weßel, Matthias Troyer

We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.

arXiv:cond-mat/0505298•Physical Review Letters•Sep 16, 2005•375 citations

Supersolid Bosons on the Triangular Lattice

Stefan Weßel

The zero temperature phase diagram of hardcore bosons on the triangular lattice with nearest neighbor repulsion is determined using quantum Monte Carlo simulations. The system exhibits an extended supersolid phase emerging from an order‐by‐disorder effect as a novel way of a quantum system to avoid classical frustration. We analyze the nature of the supersolid phase and its stability in competition with phase‐separation, which we find to occurs in other regions of parameter space.

AIP conference proceedings•Jan 1, 2006•0 citations

Diverse solid and supersolid phases of bosons in a triangular lattice

Qi-Hui Chen, Peng Li

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.

Chinese Physics B•May 1, 2014•5 citations
We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultracold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior is consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D Z6{\mathbb{Z}}_{6}Z6​ clock model description of the enlarged symmetry of the solid order parameter field. In the generic case, however, the symmetry reduces to that of a 3D Z3{\mathbb{Z}}_{3}Z3​ clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.
Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.
We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale quantum Monte Carlo simulations, the ground-state phase diagram is studied. We find a first-order transition between the atomic superfluid phase and the pair superfluid phase when the ratio of the atomic hopping and the atom-pair hopping is adapted. The first-order transition remains unchanged under various conditions. We then focus on the interplay among the atom-pair hopping, the on-site repulsion, and the nearest-neighbor repulsion. With on-site repulsion present, we observe first-order transitions between the Mott insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/32/32/3, 1, and 4/34/34/3 filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasihardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. Without on-site repulsion, the transitions between the pair supersolid and the atom superfluid or pair superfluid are first order, except for the particle-hole symmetric point. With weak on-site repulsion and atom hopping turning on, the transition between the pair supersolid and pair superfluid phase becomes continuous. The transition between solid and pair supersolid is three-dimensional XYXYXY university, with dynamical exponent z=1z=1z=1 and correlation exponent $\ensuremath{\nu}=0.671\phantom{\rule{0.16em}{0ex}}55$. The thermal melting of pair supersolid belongs to the two-dimensional Ising university. We check both energetic and mechanical balance of pair supersolid phase. Lowering the three-body constraint, no pair supersolid is found due to the absence of degeneracy of pair solids in classical limits. We describe the experimental realization of pair tunneling on state dependent lattice.
We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF-CSS transition is in the three-dimensional XY universality class. The SF-XSS transition exhibits nontrivial critical behavior, and appears, within a d=3-\ensuremath{\epsilon} expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in d=2 a strong-coupling fixed point with striking ``non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.
We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3<rho<2/3 we find an extended supersolid phase even at half filling rho=1/2. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.
We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.