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Register a new userExact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
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Added by
Camilla Buhl Larsen
Publication date
2018
fields
Physics
and research's language is
English
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We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the $s=1/2$ next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange from higher order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters, $t/U$, to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling, $J_r$, which have been varied between 0$J$ and 1.5$J$. We find that ring exchange induces a quantum phase transition from the $(pi, pi)$ ordered Ne`el state to a $(pi/2, pi/2)$ ordered state. This quantum critical point is reduced by quantum fluctuations from its mean field value of $J_r/J = 2$ to a value of $sim 1.1$. At the quantum critical point, the dynamical correlation function shows a pseudo-continuum at $q$-values between the two competing ordering vectors.
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We employ the cluster slave-spin method to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $delta$ and coupling strength $U$ being its parameters. In addition to a crossover reflected in the behavior of the antiferromagnetic gap $Delta_{text{AFM}}$, this property can also be observed in the energetics of the cluster slave-spin Hamiltonian -- the antiferromagnetism at small $U$ is due to the potential energy gain while that in the strong coupling limit is driven by the kinetic energy gain, which is consistent with the results from the cluster dynamical mean-field theory calculation and the quantum Monte Carlo simulation. We find the interaction $U_{c}$ for the crossover in the AFM state, separating the weak- and strong- coupling regimes, almost remains unchanged upon doping, and it is smaller than the critical coupling strength $U_{text{Mott}}$ for the first-order metal-insulator Mott transition in the half-filled paramagnetic state. At half-filling, a relationship between the staggered magnetization $M$ and $Delta_{text{AFM}}$ is established in the small $U$ limit to nullify the Hartree-Fock theory, and a first-order Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at $U_{text{Mott}}=10t$. Finally, an overall phase diagram in the $U$-$delta$ plane is presented, which is composed of four regimes: the antiferromagnetic insulator, the antiferromagnetic metal with the compressibility $kappa>0$ or $kappa<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the antiferromagnetic metal to the paramagnetic metal, (ii) between the antiferromagnetic metal phases with positive and negative $kappa$, and (iii) separating the antiferromagnetic insulating phase from the antiferromagnetic metal phase.
Ring-exchange interactions have been proposed as a possible mechanism for a Bose-liquid phase at zero temperature, a phase that is compressible with no superfluidity. Using the Stochastic Green Function algorithm (SGF), we study the effect of these interactions for bosons on a two-dimensional triangular lattice. We show that the supersolid phase, that is known to exist in the ground state for a wide range of densities, is rapidly destroyed as the ring-exchange interactions are turned on. We establish the ground-state phase diagram of the system, which is characterized by the absence of the expected Bose-liquid phase.
We present an alternative scheme to the widely used method of representing the basis of one-band Hubbard model through the relation $I=I_{uparrow}+2^{M}I_{downarrow}$ given by H. Q. Lin and J. E. Gubernatis [Comput. Phys. 7, 400 (1993)], where $I_{uparrow}$, $I_{downarrow}$ and $I$ are the integer equivalents of binary representations of occupation patterns of spin up, spin down and both spin up and spin down electrons respectively, with $M$ being the number of sites. We compute and store only $I_{uparrow}$ or $I_{downarrow}$ at a time to generate the full Hamiltonian matrix. The non-diagonal part of the Hamiltonian matrix given as ${cal{I}}_{downarrow}otimes{bf{H}_{uparrow}} oplus {bf{H}_{downarrow}}otimes{cal{I}}_{uparrow}$ is generated using a bottom-up approach by computing the small matrices ${bf{H}_{uparrow}}$(spin up hopping Hamiltonian) and ${bf{H}_{downarrow}}$(spin down hopping Hamiltonian) and then forming the tensor product with respective identity matrices ${cal{I}}_{downarrow}$ and ${cal{I}}_{uparrow}$, thereby saving significant computation time and memory. We find that the total CPU time to generate the non-diagonal part of the Hamiltonian matrix using the new one spin configuration basis scheme is reduced by about an order of magnitude as compared to the two spin configuration basis scheme. The present scheme is shown to be inherently parallelizable. Its application to translationally invariant systems, computation of Greens functions and in impurity solver part of DMFT procedure is discussed and its extention to other models is also pointed out.
By means of quantum Monte Carlo simulations, combined with a stochastic analytic continuation, we examine the spin dynamics of the spin-1/2 planar (XY) ferromagnet on the kagome lattice with additional four-site ring exchange terms. Such exchange processes were previously considered to lead into an extended $Z_2$ quantum spin liquid phase beyond a quantum critical point from the XY-ferromagnet. We examine the dynamical spin structure factor in the non-magnetic regime and probe for signatures of spin fractionalization. Furthermore, we contrast our findings and the corresponding energy scales of the excitation gaps in the ring exchange model to those emerging in a related Balents-Fisher-Girvin model with a $Z_2$ quantum spin liquid phase, and monitor the softening of the magnon mode upon approaching the quantum critical point from the XY-ferromagnetic regime.
High order ring-exchange interactions are crucial for the study of quantum fluctuations on highly frustrated systems. We present the first exact quantum Monte Carlo study of a model of hard-core bosons with sixth order ring-exchange interactions on a two-dimensional kagome lattice. By using the Stochastic Green Function algorithm, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at 1/3 and 2/3 fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed.
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