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Magnetic-Field-Induced RVB State in the t-J Model

A. Fabricio Albuquerque, George Balster Martins

Published Apr 7, 2004• 0 citations
OpenAlex

Abstract

Exact Diagonalization (ED) calculations are presented for the t-J model in the presence of a uniform magnetic field. Results for 4 x 4 clusters and 2 x L ladders (L=8,10,12) with 1 and 2 holes indicate that the diamagnetic response to a perpendicular magnetic field induces a Resonating Valence Bond (RVB) state in the spin background. In the 4 x 4 square cluster, this RVB-like state competes with the zero-field AF quasi-long-range-order(QLRO): the RVB-like state is favored by higher doping and smaller values of J/t. In 2-leg ladders, the zero-field spin-liquid state is reinforced by the magnetic field: a considerable increase of rung AF correlations is observed for J/t < 0.6, for 1 and 2 holes. Pair-breaking is clearly observed in the ladders: this seems to be associated in part with changes promoted by the field in the spin correlations around the zero-fied pair.

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Exact diagonalization calculations are presented for the t – J model in the presence of a uniform magnetic field. Results for 2 × L ladders ( L = 8,10,12) and 4 × 4 square clusters with one and two holes indicate that the diamagnetic response to a perpendicular magnetic field tends to induce a spin liquid state in the spin background. The zero-field spin liquid state of a two-leg ladder is reinforced by the magnetic field: a considerable increase of rung antiferromagnetic correlations is observed for J / t up to 0.6, for one and two holes. Pair breaking is also clearly observed in the ladders and seems to be associated in part with changes promoted by the field in the spin correlations around the zero-field pair. In the 4 × 4 cluster, the numerical results seem to indicate that the field-induced spin liquid state competes with the zero-field antiferromagnetic short range order, the spin liquid state being favoured by higher doping and smaller values of J / t . It is interesting to note that the field effect can also be observed in a 2 × 2 plaquette with one and two holes. This opens up the possibility of gaining a qualitative understanding of the effect.

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We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the $S=1∕2$ Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a $d$-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.

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Exact Diagonalization (ED) calculations are presented for the t-J model in the presence of a uniform magnetic field. Results for 4 x 4 clusters and 2 x L ladders (L=8,10,12) with 1 and 2 holes indicate that the diamagnetic response to a perpendicular magnetic field induces a Resonating Valence Bond (RVB) state in the spin background. In the 4 x 4 square cluster, this RVB-like state competes with the zero-field AF quasi-long-range-order(QLRO): the RVB-like state is favored by higher doping and smaller values of J/t. In 2-leg ladders, the zero-field spin-liquid state is reinforced by the magnetic field: a considerable increase of rung AF correlations is observed for J/t < 0.6, for 1 and 2 holes. Pair-breaking is clearly observed in the ladders: this seems to be associated in part with changes promoted by the field in the spin correlations around the zero-fied pair.
Exact diagonalization calculations are presented for the t – J model in the presence of a uniform magnetic field. Results for 2 × L ladders ( L = 8,10,12) and 4 × 4 square clusters with one and two holes indicate that the diamagnetic response to a perpendicular magnetic field tends to induce a spin liquid state in the spin background. The zero-field spin liquid state of a two-leg ladder is reinforced by the magnetic field: a considerable increase of rung antiferromagnetic correlations is observed for J / t up to 0.6, for one and two holes. Pair breaking is also clearly observed in the ladders and seems to be associated in part with changes promoted by the field in the spin correlations around the zero-field pair. In the 4 × 4 cluster, the numerical results seem to indicate that the field-induced spin liquid state competes with the zero-field antiferromagnetic short range order, the spin liquid state being favoured by higher doping and smaller values of J / t . It is interesting to note that the field effect can also be observed in a 2 × 2 plaquette with one and two holes. This opens up the possibility of gaining a qualitative understanding of the effect.
Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin-spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.
We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare with the classical dimer model (CDM). The latter system also corresponds to the ground state of the Rokhsar-Kivelson quantum dimer model at its critical point. We find that, although spin-spin correlations decay exponentially in the RVB, four-spin valence-bond-solid correlations are critical, qualitatively like the well-known dimer-dimer correlations of the CDM, but decaying more slowly (as $1/{r}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}1.20$, compared with $\ensuremath{\alpha}=2$ for the CDM). We also compute the distribution of monomer (defect) pair separations, which decay by a larger exponent in the RVB than in the CDM. We further study both models in their different winding-number sectors and evaluate the relative weights of different sectors. Like the CDM, all the observed RVB behaviors can be understood in the framework of a mapping to a ``height'' model characterized by a gradient-squared stiffness constant KKK. Four independent measurements consistently show a value ${K}_{\mathrm{RVB}}\ensuremath{\approx}1.6{K}_{\mathrm{CDM}}$, with the same kinds of numerical evaluations of KCDM{K}_{\mathrm{CDM}}KCDM​ giving results in agreement with the rigorously known value ${K}_{\mathrm{CDM}}=\ensuremath{\pi}/16$. The background of a nonzero winding-number gradient W/LW/LW/L introduces spatial anisotropies and an increase in the effective KKK, both of which can be understood as a consequence of anharmonic terms in the height-model free energy, which are of relevance to the recently proposed scenario of ``Cantor deconfinement'' in extended quantum dimer models. In addition to the standard case of short bonds only, we also studied ensembles in which fourth-neighbor (bipartite) bonds are allowed at a density controlled by a tunable fugacity, resulting (as expected) in a smooth reduction of KKK.
Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called C1S0C1S0C1S0 phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/tJ/tJ/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.
We propose a class of ground states for doped Mott insulators in the electron second quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the $t\text{\penalty1000-\hskip0pt}J$ model. At half filling, the ground state describes spin correlations of the S=1∕2S=1∕2S=1∕2 Heisenberg model very accurately. Its spin degrees of freedom are characterized by RVB pairing of spins, the size of which decreases continuously as holes are doped into the system. Charge degrees of freedom emerge upon doping and are described by twisted holes in the RVB background. We show that the twisted holes exhibit an off diagonal long range order (ODLRO) in the pseudogap ground state, which has a finite pairing amplitude, but is short of phase coherence. Unpaired spins in such a pseudogap ground state behave as free vortices, preventing superconducting phase coherence. The existence of nodal quasiparticles is also ensured by such a hidden ODLRO in the ground state, which is non-Fermi liquidlike in the absence of superconducting phase coherence. Two distinct types of spin excitations can also be constructed. The superconducting instability of the pseudogap ground state is discussed and a ddd-wave superconducting ground state is obtained. This class of pseudogap and superconducting ground states unifies antiferromagnetism, pseudogap, superconductivity, and Mott physics into a new state of matter.