We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that, in the case of strong leg coupling, the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the strong plaquette coupling limit (weakly interacting plaquettes). Subsequently, in the limit of weakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chain in a longitudinal magnetic field under QRG transformation. Furthermore, the effective Hamiltonian of the spin nanotube inspires both first and second order phase transitions accompanied by the fractional magnetization plateaus. Our results show that the anisotropy changes the magnetization curve and the phase transition points, significantly. Finally, we report the numerical exact diagonalization results to compare the ground state phase diagram with our analytical visions.
We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian, a Hartree variational approach, and density matrix renormalization group for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet, and quintuplet states play an important role in the formation of fractional magnetization plateaus. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an
XXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the
XXZ model. All techniques provide consistent results which allow us to predict the existence of fractional plateaus in an important region in the space of parameters of the model.
We study the ground-state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely, density matrix renormalization group, exact diagonalization, Schwinger boson mean-field theory, quantum Monte Carlo, and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes, we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely, a plaquette, an incommensurate, and an antiferromagnetic quasispin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long-range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange, the tube exhibits a deconfinement crossover from gapped magnon-like excitations to spinons.
We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.
We explore the ground-state phase diagram of the
S=1/2 two-leg ladder with different leg interactions. The
xy and
z components of the leg interactions between nearest-neighbor spins in the
a (
b) leg are respectively denoted by
Jl,a and
ΔlJl,a (
Jl,b and
ΔlJl,b). On the other hand, the
xy and
z components of the uniform rung interactions are respectively denoted by
ΓrJr and
Jr. In the above,
Δl and
Γr are the
XXZ-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when
Jl,aJl,b<0 irrespective of the sign of
Jr. The phase diagram on the
Δl (
∣Δl∣≤1.0) versus
Jl,b (
−2.0≤Jl,b≤3.0) plane in the case where
Jl,a=0.2,
Jr=−1.0, and
Γr=0.5 is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and
XY1 phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.
Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Néel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced.
The ground state, magnetization curves, low-temperature thermodynamics, and heat-engine performance of the fully frustrated spin-
1/2 Heisenberg four-leg tube with antiferromagnetic inter- and intra-plaquette coupling constants J1 and J2 are examined using exact diagonalization, density matrix renormalization group, and localized-magnon theory. In the unfrustrated to weakly frustrated regime J2/J1 << 2, the system exhibits a continuous field-driven quantum phase transition between the gapped Haldane phase and a gapless Tomonaga-Luttinger quantum spin liquid. In the highly frustrated regime J2/J1 > 2, the system contrarily displays discontinuous field-driven quantum phase transitions between the Wigner magnon crystals, which are manifested in zero-temperature magnetization curves as intermediate plateaus at zero, one-quarter, one-half, and three-quarters of the saturation magnetization. The low-temperature magnetic and thermodynamic properties in this regime are accurately captured by an effective interacting lattice-gas model of two monomer quasi-particle species constructed from localized one- and two-magnon states. Finally, we explore a quantum Stirling heat engine using the fully frustrated four-leg tube as the working medium. The work output and efficiency are strongly suppressed near discontinuous field-induced transitions and reach pronounced local maxima well inside the stability regions of the Wigner magnon crystals.