We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square-lattice quantum dimer model as its configuration space comprises fully packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local ${Z}_{3}$ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that ${Z}_{3}$ electric charges are deconfined. Additionally, we introduce a ${Z}_{3}$ magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with ${Z}_{3}$ topological order.We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square-lattice quantum dimer model as its configuration space comprises fully packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local ${Z}_{3}$ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that ${Z}_{3}$ electric charges are deconfined. Additionally, we introduce a ${Z}_{3}$ magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with ${Z}_{3}$ topological order.

arXiv:1704.02063Physical review. B./Physical review. BNov 27, 20173 citations

Numerical studies of the undoped and doped quantum dimer model

P. W. Leung, Kagan Yu

APSMar 1, 20010 citations

Models of spin-orbit-coupled oligomers

Goran Gligorić, Ana Radosavljevic, Jovana S. Petrovic +3 more

We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.

arXiv:1710.06802Chaos An Interdisciplinary Journal of Nonlinear ScienceNov 1, 20174 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Few-body bound states of two-dimensional bosons

G. Guijarro, G. E. Astrakharchik, Jordi Boronat +2 more

We study clusters of the type ${A}_{N}{B}_{M}$ with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of $A$ and $B$ bosons, with attractive $AB$ and equally repulsive $AA$ and $BB$ interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths ${a}_{AB}$ and ${a}_{AA}={a}_{BB}$ , for sufficiently large attraction-to-repulsion ratios ${a}_{AB}/{a}_{BB}$ . When ${a}_{AB}/{a}_{BB}$ decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced $AABB$ and $AAABBB$ clusters break into $AB$ dimers. Calculating the $AAABBB$ hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced $ABB$ trimer, $ABBB$ tetramer, and $AABBB$ pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.We study clusters of the type ${A}_{N}{B}_{M}$ with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of $A$ and $B$ bosons, with attractive $AB$ and equally repulsive $AA$ and $BB$ interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths ${a}_{AB}$ and ${a}_{AA}={a}_{BB}$, for sufficiently large attraction-to-repulsion ratios ${a}_{AB}/{a}_{BB}$. When ${a}_{AB}/{a}_{BB}$ decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced $AABB$ and $AAABBB$ clusters break into $AB$ dimers. Calculating the $AAABBB$ hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced $ABB$ trimer, $ABBB$ tetramer, and $AABBB$ pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.

arXiv:1911.01701Physical Review AApr 7, 202021 citations

{Z}_{3}

gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that

{Z}_{3}

electric charges are deconfined. Additionally, we introduce a

{Z}_{3}

magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with

{Z}_{3}

topological order.

We study clusters of the type

{A}_{N}{B}_{M}

with $N\ensuremath{\le}M\ensuremath{\le}3$ in a two-dimensional mixture of

A

and

B

bosons, with attractive

AB

and equally repulsive

AA

and

BB

interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths

{a}_{AB}

and

{a}_{AA}={a}_{BB}

, for sufficiently large attraction-to-repulsion ratios

{a}_{AB}/{a}_{BB}

. When

{a}_{AB}/{a}_{BB}

decreases below $\ensuremath{\approx}10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced

AABB

and

AAABBB

clusters break into

AB

dimers. Calculating the

AAABBB

hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced

ABB

trimer,

ABBB

tetramer, and

AABBB

pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at ${a}_{AB}\ensuremath{\approx}2{a}_{BB}$, where the atom-dimer interaction switches to repulsion.