We investigate the Zeeman-field-driven quantum phase transitions between singlet spin liquids and algebraically ordered O(2) nematic spin liquids of spin-one bosons in one-dimensional optical lattices. We find that the critical behavior is characterized by condensation of hardcore bosons instead of ideal magnons in high dimensional lattices. Critical exponents are strongly renormalized by hardcore interactions and critical states are equivalent to the free Fermion model up to the Friedal oscillations. We also find that the algebraically ordered nematic spin liquids close to critical points are fully characterized by the Luttinger liquid dynamics with Luttinger liquid parameters magnetically tunable. The Bethe Ansatz solution has been applied to determine the critical magnetization and nematic correlations.
We study magnetically stabilized nematic order for spin-one bosons in optical lattices. We show that the Zeeman field-driven quantum phase transitions between non-nematic Mott states and quantum spin nematic Mott states in the weak hopping limit are in the universality class of the ferromagnetic
XXZ (S=1∕2) spin model. We further discuss these transitions as condensation of interacting magnons. The development of O(2) nematic order when external fields are applied corresponds to condensation of magnons, which breaks a U(1) symmetry. Microscopically, this results from a coherent superposition of two non-nematic states at each individual site. Nematic order and spin-wave excitations around critical points are studied and critical behaviors are obtained in a dilute gas approximation. We also find that spin-singlet states are unstable with respect to quadratic Zeeman effects and Ising nematic order appears in the presence of any finite quadratic Zeeman coupling. All discussions are carried out for states in three-dimensional bipartite lattices.
We theoretically study an ultracold gas of spin-1 polar bosons in a one-dimensional continuum, which are subject to linear and quadratic Zeeman fields and a Raman induced spin orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively, we analytically solve the model in its low-energy sector; i.e., we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field ε, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At ε=0, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases, and the transition to the spin-disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at ε≠0, the quantum critical theory separating nematic and strong coupling spin-disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e., the critical theory at finite ε maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Because of an emergent Lorentz symmetry, both have the same logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultracold atomic gases of ^{23}Na.
We investigate strongly correlated spin-1 ultracold gases with antiferromagnetic interactions in a three-dimensional optical lattice in the presence of an external magnetic field, based on bosonic dynamical mean-field theory. Due to the interplay of spin-dependent and quadratic Zeeman interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phases, depending on longitudinal magnetization. The dependence of first-order superfluid-insulator transition on external magnetic fields is explored. Interestingly, at low magnetic field, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the
mF=−1 component demonstrates an abnormal increase with longitudinal magnetization, in contrast to weakly interacting cases.
Magnon bound states emerging in one-dimensional (1D) spin chains still lack a rigorous understanding. In this Rapid Communication we show that the length-1 spin strings significantly dominate the critical properties of spinons, magnons, and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution, we analytically calculate the scaling functions of the thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double maxima in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), the quantum critical, and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio
RW=4Ks remains almost temperature independent, where
Ks is the Luttinger parameter. Furthermore, by applying our results, we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet
Cu(C4H4N2)(NO3)2, recently studied by Kono et al. [Phys. Rev. Lett. 114, 037202 (2015)]. We further find that the magnetization maximum used in experiments is not a good quantity to map out the finite-temperature TLL phase boundary.
We discuss spin-
21 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor
J1 and antiferromagnetic next-nearest-neighbor
J exchange interactions in a strong magnetic field
H. It is well known that, due to attraction between magnons, quantum phase transitions (QPTs) take place at
H=Hs from the fully polarized phase to the nematic phase if
J>∣J1∣/4. Such a transition at
J>0.368∣J1∣ is characterized by a softening of the two-magnon bound-state spectrum. Using a bond-operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at $H\ensuremath{\ge}{H}_{s}$ with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at
H=Hs makes the QPT consideration substantially standard. In the 1D case at
H<Hs, we find an expression for the magnetization which well describes existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before, either in the limiting case of $J\ensuremath{\gg}|{J}_{1}|$ or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the
H-
T plane between the fully polarized and the nematic phases is given by ${H}_{s}(0)\ensuremath{-}{H}_{s}(T)\ensuremath{\propto}{T}^{3/2}$. Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization, and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to
1/ln(1+∣J1∣/J). Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel.