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Register a new userHilbert space and ground state structure of bilayer quantum Hall systems at $ u=2/lambda$
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We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $ u=2/lambda$ ($lambda$ odd) and we also study the large $SU(4)$ isospin-$lambda$ limit. The model Hamiltonian is an adaptation of the $ u=2$ case [Z.F. Ezawa {it et al.}, Phys. Rev. {B71} (2005) 125318] to the many-body situation (arbitrary $lambda$ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeeman, tunneling, etc, control parameters) is obtained by using previously introduced Grassmannian $mathbb{G}^4_{2}=U(4)/[U(2)times U(2)]$ coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any $lambda$, but the phase transition points depend on $lambda$, and the instance $lambda=1$ is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly $lambda$ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.
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We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $ u=2/lambda$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $lambda$. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space $mathbb{G}^4_{2}=U(4)/[U(2)times U(2)]$ (a higher-dimensional generalization of the Haldanes 2-dimensional sphere $mathbb{S}^2=U(2)/[U(1)times U(1)]$). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e., as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrodinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.
We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $lambda$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlayer entanglement more effective and robust under perturbations than in the spin-frozen situation, mainly for a large number of flux quanta $lambda$. Interlayer entanglement of an equilibrium thermal state and its dependence with temperature and bias voltage is also studied for a pseudo-Zeeman interaction.
The Hall-plateau width and the activation energy were measured in the bilayer quantum Hall state at filling factor u=2, 1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells. Their behavior are remarkably different from one to another. The u=1 state is found stable over all measured range of the density difference, while the u=2/3$ state is stable only around the balanced point. The u=2 state, on the other hand, shows a phase transition between these two types of the states as the electron density is changed.
Magnetotransport properties are investigated in the bilayer quantum Hall state at the total filling factor $ u=2$. We measured the activation energy elaborately as a function of the total electron density and the density difference between the two layers. Our experimental data demonstrate clearly the emergence of the canted antiferromagnetic (CAF) phase between the ferromagnetic phase and the spin-singlet phase. The stability of the CAF phase is discussed by the comparison between experimental results and theoretical calculations using a Hartree-Fock approximation and an exact diagonalization study. The data reveal also an intrinsic structure of the CAF phase divided into two regions according to the dominancy between the intralayer and interlayer correlations.
We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ u=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ u =1$ and discovered at $ u =2$. In particular, three different $ u =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
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