Accidental ground state degeneracies-those not a consequence of global symmetries of the Hamiltonian-are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order by thermal disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, Δ, and show that at low temperatures it scales as the square root of temperature, sqrt[T]. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy.
The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S=1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also found that the similarity of the selected states in the classical and quantum models are not the case in a two-leg ladder lattice, although the lattice consists of triangles locally and the ground state of this lattice in the classical case is the same as that of the triangular lattice.
We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor
(J1) and next-nearest-neighbor
(J2) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all
J2/J1 and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin
S, for
J2/J1<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for
J2=0, and for
1/8<J2/J1<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary
S, including
S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all
S. We show that for
S>1, the transition remains first order, with a finite hysteresis width, but for
S=1/2 and, possibly,
S=1, there appears a new intermediate phase without a quasiclassical long-range order.
Frustrated magnets can have accidental ground state degeneracies which may be lifted by various forms of disorder, for example in the form of thermal or quantum fluctuations. This order by disorder (ObD) paradigm is well established in equilibrium and here is generalized to Floquet many-body systems. Investigating a periodically driven XXZ-compass model on the square lattice, we show that in a prethermal regime, dynamical fluctuations induced by high-frequency drives select a discrete set of states out of a degenerate ground state manifold of the lowest order Floquet Hamiltonian chosen as initial states. Remarkably, prior to the ObD selection, an unusual fluctuating regime emerges leading to a prethermalization timescale scaling linearly with the drive frequency. We argue that prethermal ObD with its unusual approach to the selected states is a generic phenomenon of driven frustrated systems and confirm it in the paradigmatic J 1 − J 2 XX model. Published by the American Physical Society 2024
We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model.
We study the effects of a periodically varying electric field on the Hubbard model at half filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction
U is much larger than the hopping, the effective Hamiltonian
Heff describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping,
Heff is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $({J}_{\ensuremath{\alpha}},{J}_{\ensuremath{\beta}},{J}_{\ensuremath{\gamma}})$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry,
Heff can also have a chiral three-spin interaction in each triangle, with the coefficient
C of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks time-reversal symmetry can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $({J}_{\ensuremath{\alpha}},{J}_{\ensuremath{\beta}},{J}_{\ensuremath{\gamma}},C)$ depend on the amplitude, frequency, and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (collinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.