Using an exact diagonalization treatment of Ising and Heisenberg model Hamiltonians, we study field-induced phase transitions for two-dimensional antiferromagnets. It is found that a first-order phase transition occurs for both the Ising and Heisenberg antiferromagnets. For the Ising antiferromagnet a mixture of antiferromagnetic and ferromagnetic phases exists only at a critical value of Zeeman energy, while for the Heisenberg antiferromagnet the mixed phase appears over a wide range of Zeeman energy. It is shown that the mixed phase for the Heisenberg antiferromagnet occurs owing to the presence of a spin-flop process as an intermediate step.
The magnetization process of the spin-
1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the
1/3 and
2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the
1/3 plateau are obtained by using the approximated state in the unit cell and compared with the numerical results of the exact diagonalization of 42 sites.
The prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature
T0 arbitrarily closely, was discovered in 1D decorated Ising chains and ladders. Here we present a theoretical study of similarly decorated, yet much more challenging, quantum Heisenberg ferrimagnets in a magnetic field, which features ferromagnetic backbone exchange
J, antiferromagnetic site-decoration coupling
JAF, and different magnetic moments for the backbone and decorating spins
μaSa<μbSb. We exactly solved the model in the large
J limit -- as a central-macrospin model -- and found two finite-temperature second-order transitions; just above
Tc2 a ``half-ice, half-fire'' regime appears. Finite-
J weak-field results follow from an effective-field mapping, suggesting the emergence of UNPC at finite
T0 in 2D square lattices thanks to its exponentially strong initial magnetic susceptibility
χ0∝e4πSa2J/T0, though less likely in 1D chains where
χ0∝J/T0. These results may shed light on new technological applications of low-dimensional quantum spin systems and attract experimental and computational tests.
Antiferromagnetic Heisenberg integer-spin chains are characterized by a spin-liquid ground state with no long-range order, due to the relevance of quantum fluctuations. Spin anisotropy, however, freezes quantum fluctuations, and the system is magnetized in the presence of a sufficiently large easy-axis anisotropy. We numerically investigate the case S=1, by means of the density-matrix renormalization group, and find that the freezing of the spin liquid into a Néel spin solid, with increasing easy-axis anisotropy, is a continuous quantum phase transition. Numerical evidence indicates that the transition is not in the two-dimensional Ising universality class.
We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field
h. In this model,
J represents the traditional antiferromagnetic Heisenberg exchange and
Q is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for
q>qmin, where we have calculated
qmin=92 exactly. For
q>qmin, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for
q>qmin. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain
(J1>0,J2<0), but only if
J2 is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at
T>0. While the expected ``zero-scale-factor'' universality is clearly seen for
q=0 and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for
q closer to
qmin we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at
qmin. In the low-energy theory, one can expect the quartic nonlinearity to vanish at
qmin and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature
T∗(q) between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.
The quantum phases of one-dimensional spin
s=1/2 chains are discussed for models with two parameters, frustrating exchange
g=J2>0 between second neighbors and normalized nonfrustrating power-law exchange with exponent $\ensuremath{\alpha}$ and distance dependence ${r}^{\ensuremath{-}\ensuremath{\alpha}}$. The ground state (GS) at
g=0 has a long-range order (LRO) for $\ensuremath{\alpha}<2$ and long-range spin fluctuations for $\ensuremath{\alpha}>2$. The models conserve total spin
S=SA+SB, have singlet GS for any
g, $\ensuremath{\alpha}\ensuremath{\ge}0$ and decouple at
1/g=0 to linear Heisenberg antiferromagnets on sublattices
A and
B of odd- and even-numbered sites. Exact diagonalization of finite chains gives the sublattice spin $\ensuremath{\langle}{S}_{A}^{2}\ensuremath{\rangle}$, the magnetic gap
Em to the lowest triplet state, and the excitation ${E}_{\ensuremath{\sigma}}$ to the lowest singlet with opposite inversion symmetry to the GS. An analytical model that conserves sublattice spin has a first-order quantum transition at
gc=1/4ln2 from a GS with perfect LRO to a decoupled phase with
SA=SB=0 for $g\ensuremath{\ge}4/{\ensuremath{\pi}}^{2}$ and no correlation between spins in different sublattices. The model with $\ensuremath{\alpha}=1$ has a first-order transition to a decoupled phase that closely resembles the analytical model. The bond order wave (BOW) phase and continuous quantum phase transitions of finite models with $\ensuremath{\alpha}\ensuremath{\ge}2$ are discussed in terms of GS degeneracy where ${E}_{\ensuremath{\sigma}}(g)=0$, excited state degeneracy where ${E}_{\ensuremath{\sigma}}(g)={E}_{m}(g)$, and $\ensuremath{\langle}{S}_{A}^{2}\ensuremath{\rangle}$. The decoupled phase at large frustration has nondegenerate GS for any exponent $\ensuremath{\alpha}$ and excited states related to sublattice excitations.