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Register a new userSpectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
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We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a Neel antiferromagnet to a $mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly-deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results show how free spinons emerge across a quantum critical point, providing evidence for the fractionalization of magnons into deconfined spinons.
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We consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a $mathbb{Z}_2$ spin liquid and a ferromagnetic phase. The model is amenable to sign free auxiliary field quantum Monte Carlo simulations. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the $mathbb{Z}_2$ spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per unit cell, this phase is a non-Fermi liquid that violates the conventional Luttinger theorem which relates the Fermi surface volume to the particle density in a Fermi liquid. This non-Fermi liquid is a specific realization of the so called fractionalized Fermi liquid proposed in the context of heavy fermions. We probe the Kondo breakdown in this non-Fermi liquid phase via conventional observables such as the spectral function, and also by studying the mutual information between the electrons and the spins.
We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.
Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we extend the cluster perturbation theory to spin systems and study the whole excitation spectrum of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the square lattice. In the Neel phase for $J_{2}lesssim0.4J_{1}$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(pi,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_{2}gtrsim0.6J_{1}$, we find similar high-energy two-spinon continuums at $(pi/2,pi/2)$ and $(pi/2,pi)$, respectively. The intermediate phase is characterized by a spectrum with completely deconfined broad continuum, which is attributed to a $Z_{2}$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis.
We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and thus determine the microscopic parameters of the low-energy long-wavelength description. In a second part, we present a comprehensive study of dynamical spin correlation functions for magnetic fields ranging from zero up to saturation. We find that at low fields, magnons are well defined in the whole Brillouin zone, but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multi-magnon scattering. Our results directly apply to inelastic neutron scattering experiments.
We investigate the role of a transverse field on the Ising square antiferromagnet with first-($J_1$) and second-($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1$-$J_2$ Ising antiferromagnet.
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