Grand-canonical phase diagram and chiral-current suppression at $π$ flux in a bosonic two-leg ladderGrand-canonical phase diagram and chiral-current suppression at $π$ flux in a bosonic two-leg ladder

Meng Zhang, Qingyun Xu, Zhi Lin

We investigate the ground-state phase diagram of repulsively interacting bosons on a two-leg ladder threaded by a uniform artificial magnetic flux, using the cluster Gutzwiller mean-field method. In the strong-rung-coupling regime, self-consistent calculations are performed on a $2\times4$ cluster. By analyzing the superfluid order parameter, leg-resolved currents, chiral current, the current ratio on adjacent legs, and the density imbalance between the two legs, we distinguish Mott-insulating from superfluid regimes and characterize the observed states as Meissner-like, vortex-like (superfluid or Mott insulating), or biased-ladder. In regions overlapping with previous DMRG studies, our results qualitatively agree with the established phase structure, demonstrating that the cluster Gutzwiller approach balances computational efficiency and physical accuracy. We then construct the first grand-canonical $t$ -- $μ$ phase diagrams for this system, revealing how the magnetic flux modifies the shape, tilt, and extent of the Mott lobes. We further explore previously inaccessible regimes, including higher fillings $ρ\gtrsim1$ and the intermediate interaction window $U/t\in[7.69,9.09]$ . Special attention is paid to $φ=π$ , where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of $φ=π$ and $-π$ modulo $2π$ , a combined symmetry forbids net chiral currents, leading to a nonchiral Mott-insulating state, in contrast to the chiral-superfluid tendency expected away from $φ=π$ . Our results offer a computationally efficient route for mapping the global phase structure of bosonic flux ladders and provide guidance for future ultracold-atom experiments in artificial gauge fields.We investigate the ground-state phase diagram of repulsively interacting bosons on a two-leg ladder threaded by a uniform artificial magnetic flux, using the cluster Gutzwiller mean-field method. In the strong-rung-coupling regime, self-consistent calculations are performed on a $2\times4$ cluster. By analyzing the superfluid order parameter, leg-resolved currents, chiral current, the current ratio on adjacent legs, and the density imbalance between the two legs, we distinguish Mott-insulating from superfluid regimes and characterize the observed states as Meissner-like, vortex-like (superfluid or Mott insulating), or biased-ladder. In regions overlapping with previous DMRG studies, our results qualitatively agree with the established phase structure, demonstrating that the cluster Gutzwiller approach balances computational efficiency and physical accuracy. We then construct the first grand-canonical $t$--$μ$ phase diagrams for this system, revealing how the magnetic flux modifies the shape, tilt, and extent of the Mott lobes. We further explore previously inaccessible regimes, including higher fillings $ρ\gtrsim1$ and the intermediate interaction window $U/t\in[7.69,9.09]$. Special attention is paid to $φ=π$, where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of $φ=π$ and $-π$ modulo $2π$, a combined symmetry forbids net chiral currents, leading to a nonchiral Mott-insulating state, in contrast to the chiral-superfluid tendency expected away from $φ=π$. Our results offer a computationally efficient route for mapping the global phase structure of bosonic flux ladders and provide guidance for future ultracold-atom experiments in artificial gauge fields.

arXiv:2606.12159Jun 10, 20260 citations

Phase transition in quantum spin ladder systems

敬吾肘井

Jan 1, 20050 citations

Opening of the Haldane gap in anisotropic two- and four-leg spin ladders

Eugene H. Kim, Jenő Sólyom

We study the opening of the Haldane gap in two-leg and four-leg anisotropic spin ladders using bosonization and renormalization group methods, and we determine the phase diagram as a function of the interchain coupling and relative anisotropy ${J}^{z}{/J}^{\mathrm{xy}}.$ It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of ${J}^{z}{/J}^{\mathrm{xy}},$ and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as ${J}^{z}{/J}^{\mathrm{xy}},$ and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.We study the opening of the Haldane gap in two-leg and four-leg anisotropic spin ladders using bosonization and renormalization group methods, and we determine the phase diagram as a function of the interchain coupling and relative anisotropy ${J}^{z}{/J}^{\mathrm{xy}}.$ It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of ${J}^{z}{/J}^{\mathrm{xy}},$ and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as ${J}^{z}{/J}^{\mathrm{xy}},$ and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.

arXiv:cond-mat/9903241Physical review. B, Condensed matterDec 1, 199917 citations

Grand-canonical phase diagram and chiral-current suppression at

π

flux in a bosonic two-leg ladder

2\times4

cluster. By analyzing the superfluid order parameter, leg-resolved currents, chiral current, the current ratio on adjacent legs, and the density imbalance between the two legs, we distinguish Mott-insulating from superfluid regimes and characterize the observed states as Meissner-like, vortex-like (superfluid or Mott insulating), or biased-ladder. In regions overlapping with previous DMRG studies, our results qualitatively agree with the established phase structure, demonstrating that the cluster Gutzwiller approach balances computational efficiency and physical accuracy. We then construct the first grand-canonical

t

μ

phase diagrams for this system, revealing how the magnetic flux modifies the shape, tilt, and extent of the Mott lobes. We further explore previously inaccessible regimes, including higher fillings

ρ\gtrsim1

and the intermediate interaction window

U/t\in[7.69,9.09]

. Special attention is paid to

φ=π

, where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of

φ=π

and

-π

modulo

2π

, a combined symmetry forbids net chiral currents, leading to a nonchiral Mott-insulating state, in contrast to the chiral-superfluid tendency expected away from

φ=π

. Our results offer a computationally efficient route for mapping the global phase structure of bosonic flux ladders and provide guidance for future ultracold-atom experiments in artificial gauge fields.

{J}^{z}{/J}^{\mathrm{xy}}.

It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of

{J}^{z}{/J}^{\mathrm{xy}},

and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as

{J}^{z}{/J}^{\mathrm{xy}},

and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.