The ground-state phase diagram of 2D electrons in a high Landau level (index $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ ) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to $1/2$ . It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.The ground-state phase diagram of 2D electrons in a high Landau level (index $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to $1/2$. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.

arXiv:cond-mat/0101401Physical Review LettersJun 18, 2001148 citations

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method

Naokazu Shibata

The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at ν= 2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor ν= 1.

arXiv:0906.1036Progress of Theoretical Physics SupplementJan 1, 20089 citations

Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

Naokazu Shibata, D. Yoshioka

The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.

arXiv:cond-mat/0403493Journal of the Physical Society of JapanAug 15, 200411 citations

DMRG Investigation of Stripe Formation in Doped Hubbard Ladders

Georg Hager, Gerhard Wellein, Eric Jeckelmann +1 more

Springer eBooksNov 17, 20051 citation

The ground-state phase diagram of 2D electrons in a high Landau level (index

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to

1/2

. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.