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arXiv:2209.06149 · Physical Review A

Spin-flip-induced superfluidity in a ring of spinful hard-core bosons

Kaushal Kumar Kesharpu, E. A. Kochetov

Published Sep 29, 2022• 2 citations
arXivHTMLPDF

Abstract

The $t\ensuremath{-}J$ Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains $N=2$ and 3 spinful hard-core bosons; for all other $N$ it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for $N=3$. It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.

DOI
10.1103/physreva.106.033323

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The t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J Hamiltonian of the spinful hard-core bosonic ring in the Nagaoka limit is solved. The energy spectrum becomes quantized due to presence of spin, where each energy level corresponds to a cyclic permutation state of the spin chains. The ground state is true ferromagnetic when the ring contains N=2N=2N=2 and 3 spinful hard-core bosons; for all other NNN it is a mixture of the ferromagnetic and nonferromagnetic states. This behavior is different from the fermionic ring, where ground state is true ferromagnetic only for N=3N=3N=3. It is shown that the intrinsic spin-generated gauge fields are analogous to the synthetic gauge fields generated by rotation of either the condensate or the confining potential. It is argued that the low-lying excited levels of the spin-flipped states intrinsically support the superfluidity. Possible ways to experimentally verify these results are also discussed.
We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\ensuremath{\nu}=1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\ensuremath{\nu}=1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.
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.
The ground states of Bose-Einstein condensates (BECs) of spin-2 bosons are classified into three distinct phases (ferromagnetic, ``antiferromagnetic,'' and cyclic) depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the thermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied magnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ``pairs'' undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ``trios'' condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.
Following Nagaoka, the ground state of the large-U nearly half-filled Hubbard model is ``ferromagnetic.'' However, because of the anisotropic exchange energy JA{\mathit{J}}_{\mathit{A}}JA​, the physical Nagaoka ground state is nondegenerate and comprises a totally disordered spin state, i.e., a linear combination of all possible spin arrangements. For this ground state the susceptibility is Pauli-like but of a magnitude associated with a narrow band of width \ensuremath{\sim}JA{\mathit{J}}_{\mathit{A}}JA​ while the holons, i.e., the charge excitations, correspond to spinless fermions with a band of width 2zt. Associated with the spinon sector are very poorly defined spin waves, i.e., bosons, with a quadratic dispersion relation. These spin waves do not become soft at any finite temperature, rather, they soften as they approach the metal-insulator transition, i.e., as the number of holes n0{\mathit{n}}_{0}n0​ becomes small. Examined is the problem of constructing a mean-field slave-boson approach for the present problem.
Spin-1 bosons on a one-dimensional chain, at incommensurate filling with an antiferromagnetic spin interaction between neighboring bosons, may form a spin-1 boson condensed state that contains both a gapless charge and spin excitations. We argue that the spin-1 boson condensed state is unstable, and will become one of two superfluids by opening a spin gap. One superfluid must have a spin-1 ground state on a ring if it contains an odd number of bosons and has no degenerate states at the chain end. The other superfluid has a spin-0 ground state on a ring for any number of bosons and has a spin-1/2 degeneracy at the chain end. The two superfluids have the same symmetry and only differ by a spin-SO(3) symmetry protected topological order. Although Landau theory forbids a continuous phase transition between two phases with the same symmetry, the phase transition between the two superfluids can be generically continuous, which is described by conformal field theory (CFT) su(2)_{2}⊕u(1)_{4}⊕su(2)[over ¯]_{2}⊕u(1)[over ¯]_{4}. Such a CFT has a spin fractionalization: spin-1 excitation can decay into a spin-1/2 right mover and a spin-1/2 left mover. We determine the critical theory by solving the partition function based on emergent symmetries and modular invariance condition of CFTs.
This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.