Ground States Of Spin Systems Research Articles

Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality

Chiral three-spin interactions can suppress long-range magnetic order and stabilize quantum spin liquid states in frustrated lattices. We study a spin-1/2 model on the kagome lattice involving a staggered three-spin interaction J_\chiJχ in addition to Heisenberg exchange couplings J_1J1 on nearest-neighbor bonds and J_dJd across the diagonals of the hexagons. We explore the phase diagram using a combination of a classical approach, parton mean-field theory, and variational Monte Carlo methods. We obtain a variety of noncoplanar magnetic orders, including a phase that interpolates between cuboc-1 and cuboc-2 states. In the regime of dominant J_{\chi}Jχ, we find a classically disordered region and argue that it may harbor a gapless chiral spin liquid with a spinon Fermi surface. Our results show that the competition between the staggered three-spin interaction and Heisenberg exchange interactions gives rise to unusual ground states of spin systems.

Polynomial scaling enhancement in the ground-state preparation of Ising spin models via counterdiabatic driving

The preparation of ground states of spin systems is a fundamental operation in quantum computing and serves as the basis of adiabatic quantum computing. This form of quantum computation is subject to the adiabatic theorem which in turn poses a fundamental speed limit. We show that by employing diabatic transitions via counterdiabatic driving, a less strict requirement on adiabaticity applies. We demonstrate a scaling advantage from local and multispin counterdiabatic driving in the ground-state fidelity compared to their adiabatic counterpart, for different Ising spin models.

Lee–Yang Polynomials and Ground States of Spin Systems

We obtain two kinds of results on the region in the space of the interactions of lattice systems where the Lee–Yang property holds (LY domain). First we show that the LY domain is related to interactions with exactly two ground states. Then we give a description of the full LY domain of an extended “plaquette model” analyzed by Lebowitz and Ruelle (Commun Math Phys 304:711–722, 2011). This allows us to prove a permanence property of the system, which we conjecture to hold in general.

Evaluation of entanglement measures in spin systems with the random phase approximation

We discuss a general formalism based on the mean field plus random phase approximation (RPA) for the evaluation of entanglement measures in the ground state of spin systems. The method provides a tractable scheme for determining the entanglement entropy as well as the negativity of finite subsystems, which becomes analytic in the case of systems with translational invariance, in one or D dimensions. The approach improves as the spin increases, and also as the interaction range or connectivity increases. Illustrative results for different types of entanglement entropies (single site, block and comb) in the ground state of a small spin lattice with ferromagnetic type XY couplings in a transverse field are shown and compared with the exact numerical result. Effects arising from symmetry breaking at the mean field level are also discussed.

Evaluation of ground-state entanglement in spin systems with the random phase approximation

We discuss a general treatment based on the mean field plus random phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method, becoming straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with $XYZ$ couplings of general range in a uniform transverse field, where the RPA around both the normal and parity breaking mean field state, together with parity restoration effects, are discussed in detail. In the case of a uniformly connected $XYZ$ array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin $s$ pair is also discussed.

A Modified Mean Field Theory for Spin Systems with OrbitalDegeneracy

In order to understand the ground state of spin systems with orbitaldegeneracy, we present a modified mean-field theory that includes fourorder parameters. Our mean-field results suggest that for a smallHund interaction, the flavour liquid state is still stable against thesolid state, but long-range orders may be attained in the system withsufficient deviation from the SU(4) limit. Finally, theimplications for the experimental observations on the systemLaMnO3 are discussed.

Long-range order in the ground state of spin systems with orbital degeneracy

We apply the method of infrared bounds to the spin-orbital systems with isotropic and anisotropic interactions to examine the existence of long-range order (LRO) in two or more dimensions. For the isotropic case, we prove the existence of antiferro-spin and antiferro-orbital LRO in three or more dimensions and ferro-spin-orbital LRO in seven or more dimensions. For the anisotropic case, we prove the existence of antiferro-orbital LRO in two or more dimensions. Under some acceptable assumptions we conjecture on the existence of antiferro-spin LRO in three or more dimensions and extend the region where we can show antiferro-orbital LRO in two or more dimensions.

On the Ground State of Spin Systems with Orbital Degeneracy

In order to understand the properties of the spin system with orbital degeneracy, we first study the ground state of the SU(4) spin-orbital model on a square lattice. The mean-field results suggest that for a small Hund's interaction, the flavor liquid state is stable against the solid state, but with sufficient deviation from the SU(4) limit the long-range order may be attained in 2D system. Furthermore, we employ a variational approach to calculate the phase diagram of the ground state and the temperature-dependent susceptibility by taking into account the Hund's interaction and the anisotropy in orbital wavefunctions. Finally, the implications for the experimental observations on the material, , are discussed.

The ground state of rhombohedral crystals in an external magnetic field

This paper deals with the ground state of spin systems in an external magnetic field interacting with dipole–dipole and exchange interactions. The Luttinger and Tisza approach is adopted. By using group theoretic techniques a simplified form of the equation and constraints results. It is shown that the ground state problem can be solved by using only two out of the eight constraints. Application has been made in the case of cerium magnesium nitrate (CMN). It is found that in general the magnetic moment increases with the magnetic field but it is not parallel to it. Above a critical field hc the crystal goes into the metamagnetic state. Comparison is made with the experimental results.