We study hard-core bosons on a class of frustrated lattices with the lowest Bloch band having a degenerate minimum along a closed contour, the moat, in the reciprocal space. We show that at small density the ground state of the system is given by a noncondensed state, which may be viewed as a state of fermions subject to Chern-Simons gauge field. At fixed density of bosons, such a state exhibits domains of incompressible liquids. Their fixed densities are given by fractions of the reciprocal-space area enclosed by the moat.We study hard-core bosons on a class of frustrated lattices with the lowest Bloch band having a degenerate minimum along a closed contour, the moat, in the reciprocal space. We show that at small density the ground state of the system is given by a noncondensed state, which may be viewed as a state of fermions subject to Chern-Simons gauge field. At fixed density of bosons, such a state exhibits domains of incompressible liquids. Their fixed densities are given by fractions of the reciprocal-space area enclosed by the moat.

Mar 28, 20130 citations

Fermionization of bosons in a flat band

Saurabh Maiti, Tigran Sedrakyan

Strongly interacting bosons that live in a lattice with degeneracy in its lowest-energy band experience frustration that can prevent the formation of a Bose-Einstein condensate. Such systems form an ideal playground to investigate spin-liquid behavior. We use the variational principle and the Chern-Simons technique of fermionization of hard-core bosons on the kagome lattice to find that below lattice filling fraction $\ensuremath{\nu}=\frac{1}{3}$ the system favors a topologically ordered chiral spin-liquid state that is gapped in bulk, spontaneously breaks time-reversal symmetry, and supports massless chiral bosonic edge mode. We construct the many-body variational wave function of the state and show that the corresponding energy coincides with the energy of the flat band. This result proves that the ground state of the system cannot stabilize a Bose condensate below $\ensuremath{\nu}=\frac{1}{3}$. The fermionization and variational scheme we outline apply to any non-Bravais lattice. We distinguish between the roles played by the Chern-Simons gauge field in lattices with a flat band and those exhibiting a moatlike dispersion (which is degenerate along a closed contour in the reciprocal space). We also suggest experimental probes to differentiate the proposed ground state from a condensate.Strongly interacting bosons that live in a lattice with degeneracy in its lowest-energy band experience frustration that can prevent the formation of a Bose-Einstein condensate. Such systems form an ideal playground to investigate spin-liquid behavior. We use the variational principle and the Chern-Simons technique of fermionization of hard-core bosons on the kagome lattice to find that below lattice filling fraction $\ensuremath{\nu}=\frac{1}{3}$ the system favors a topologically ordered chiral spin-liquid state that is gapped in bulk, spontaneously breaks time-reversal symmetry, and supports massless chiral bosonic edge mode. We construct the many-body variational wave function of the state and show that the corresponding energy coincides with the energy of the flat band. This result proves that the ground state of the system cannot stabilize a Bose condensate below $\ensuremath{\nu}=\frac{1}{3}$. The fermionization and variational scheme we outline apply to any non-Bravais lattice. We distinguish between the roles played by the Chern-Simons gauge field in lattices with a flat band and those exhibiting a moatlike dispersion (which is degenerate along a closed contour in the reciprocal space). We also suggest experimental probes to differentiate the proposed ground state from a condensate.

arXiv:1810.00910Physical review. B./Physical review. BMay 20, 201925 citations

Spontaneous formation of a non-uniform chiral spin liquid in a "moat" lattice

Tigran Sedrakyan, L. I. Glazman, Alex Kamenev

A number of lattices exhibit moat-like band structures, i.e. a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to $s=1/2$ XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.A number of lattices exhibit moat-like band structures, i.e. a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to $s=1/2$ XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.

Sep 25, 20140 citations

Spontaneous Formation of a Nonuniform Chiral Spin Liquid in a Moat-Band Lattice

Tigran Sedrakyan, L. I. Glazman, Alex Kamenev

A number of lattices exhibit moatlike band structures, i.e., a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to the s=1/2 XY model at a zero magnetic field, while the absence of condensation translates into the absence of magnetic order in the XY plane. Here, we show that the ground state breaks time reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.A number of lattices exhibit moatlike band structures, i.e., a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to the s=1/2 XY model at a zero magnetic field, while the absence of condensation translates into the absence of magnetic order in the XY plane. Here, we show that the ground state breaks time reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.

arXiv:1409.7359Physical Review LettersJan 21, 201558 citations

Frustrated Bose condensates in optical lattices

Tanja Đurić, Derek K. K. Lee

We study the Bose-condensed ground states of bosons in a two-dimensional optical lattice in the presence of frustration due to an effective vector potential, for example, due to lattice rotation. We use a mapping to a large- $S$ frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a $1/S$ expansion around the classical ground state. The large- $S$ regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large- $S$ results show that, even when the system is very dilute, the holes remain a (partially) condensed system. Moreover, the superfluid density is comparable to the condensate density. In other words, the large- $S$ regime does not display an instability to noncondensed phases. However, for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that the fractional condensate depletion increases as the system approaches the Mott phase, giving rise to the possibility of a noncondensed state before the Mott phase is reached for systems with smaller $S$ .We study the Bose-condensed ground states of bosons in a two-dimensional optical lattice in the presence of frustration due to an effective vector potential, for example, due to lattice rotation. We use a mapping to a large-$S$ frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a $1/S$ expansion around the classical ground state. The large-$S$ regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large-$S$ results show that, even when the system is very dilute, the holes remain a (partially) condensed system. Moreover, the superfluid density is comparable to the condensate density. In other words, the large-$S$ regime does not display an instability to noncondensed phases. However, for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that the fractional condensate depletion increases as the system approaches the Mott phase, giving rise to the possibility of a noncondensed state before the Mott phase is reached for systems with smaller $S$.

arXiv:0906.1600Physical Review BJan 22, 201012 citations

Nematic quantum liquid crystals of bosons in frustrated lattices

Guanyu Zhu, Jens Koch, Ivar Martin

The problem of interacting bosons in frustrated lattices is an intricate one due to the absence of a unique minimum in the single-particle dispersion where macroscopic number of bosons can condense. Here, we consider a family of tight-binding models with macroscopically degenerate lowest energy bands, separated from other bands by a gap. We predict the formation of exotic states that spontaneously break rotational symmetry at relatively low filling. These states belong to three nematic phases: Wigner crystal, supersolid, and superfluid. The Wigner crystal phase is established exactly at low filling. Supersolid and superfluid phases, at larger filling, are obtained by making use of a projection onto the flat band, construction of an appropriate Wannier basis, and subsequent mean-field treatment. The nematic superfluid that we predict is uniform in real space but has an anisotropic momentum distribution, providing a novel scenario for Bose condensation with an additional nematic order. Our findings open up a promising direction of studying microscopic quantum liquid crystalline phases of bosons.The problem of interacting bosons in frustrated lattices is an intricate one due to the absence of a unique minimum in the single-particle dispersion where macroscopic number of bosons can condense. Here, we consider a family of tight-binding models with macroscopically degenerate lowest energy bands, separated from other bands by a gap. We predict the formation of exotic states that spontaneously break rotational symmetry at relatively low filling. These states belong to three nematic phases: Wigner crystal, supersolid, and superfluid. The Wigner crystal phase is established exactly at low filling. Supersolid and superfluid phases, at larger filling, are obtained by making use of a projection onto the flat band, construction of an appropriate Wannier basis, and subsequent mean-field treatment. The nematic superfluid that we predict is uniform in real space but has an anisotropic momentum distribution, providing a novel scenario for Bose condensation with an additional nematic order. Our findings open up a promising direction of studying microscopic quantum liquid crystalline phases of bosons.

arXiv:1411.0043Physical review. B./Physical review. BApr 15, 201610 citations

s=1/2

XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.

S

frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a

1/S

expansion around the classical ground state. The large-

S

regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large-

S

results show that, even when the system is very dilute, the holes remain a (partially) condensed system. Moreover, the superfluid density is comparable to the condensate density. In other words, the large-

S

regime does not display an instability to noncondensed phases. However, for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that the fractional condensate depletion increases as the system approaches the Mott phase, giving rise to the possibility of a noncondensed state before the Mott phase is reached for systems with smaller

S