arXiv subjects

Shiuan-Fan Liou

Publications and source records attributed to Shiuan-Fan Liou.

6 recordsLinked to original sources

arXiv2020

Characterizing The Many-Body Localization via Studying State Sensitivity to Boundary Conditions

We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to antiperiodic and calculate shift in the system's energy and shifts in the single-particle density matrix eigenvalues in the corresponding energy window. We employ the typical model for studying MBL, a one-dimensional disordered system of fermions with nearest-neighbor repulsive interaction where disorder is introduced as randomness on on-site energies. By calculating numerically the shifts in the system's energy and eigenvalues of the single-particle density matrix, we observe that in the localized regime, both shifts are vanishing; while in the extended regime, both shifts are on the order of the corresponding level spacing. We also applied these characterizations of the phase transition to the case of having next-nearest-neighbor interactions in addition to the nearest-neighbor interactions, and studied its effect on the transition.

cond-mat.str-el↗

arXiv2019

Chiral Gravitons in Fractional Quantum Hall Liquids

We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.

cond-mat.str-el↗

arXiv2018

Topological phase transition in a two-species fermion system: Effects of a rotating trap potential or a synthetic gauge field

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor $ν_f = 2$. We show that the system undergoes a continuous quantum phase transition from a $ν_f = 2$ fermionic integer quantum Hall state formed by atoms, to a $ν_b = 1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field theoretical predictions, and the case of $p$-wave pairing.

cond-mat.str-el↗

arXiv2018

Quench Dynamics Across Topological Quantum Phase Transitions

We study the dynamics of systems quenched through topological quantum phase transitions and investigate the behavior of the bulk and edge excitations with various quench rates. Specifically, we consider the Haldane model and checkerboard model in slow quench processes with distinct band-touching structures leading to topology changes. The generation of bulk excitations is found to obey the power-law relation Kibble-Zurek and Landau-Zener theories predict. However, an anti-Kibble-Zurek behavior is observed in the edge excitations. The mechanism of excitation generation on edge states is revealed, which explains the anti-Kibble-Zurek behavior.

cond-mat.str-el↗

arXiv2017

Topological Quantum Phase Transition from Fermionic Integer Quantum Hall Phase to Bosonic Fractional Quantum Hall Phase through P-Wave Feshbach Resonance

We use exact diagonalization to study the quantum phases and phase transitions when a single species of fermionic atoms at Landau level filling factor $ν_f = 1$ in a rotating trap interact through a p-wave Feshbach resonance. We show that under weak pairing interaction, the system undergoes a second order quantum phase transition from $ν_{f} = 1$ fermionic integer quantum Hall (FIQH) state at positive detuning, to $ν_{b} = \frac{1}{4}$ bosonic fractional quantum Hall (BFQH) state at negative detuning. However, when the pairing interaction increases, a new phase between them emerges, corresponding to a fraction of fermionic atoms stay in a coherent superposition of bosonic molecule state and an unbound pair. The phase transition from FIQH phase to the new phase is of second order and that from the new phase to BFQH phase is of first order.

cond-mat.str-el↗

arXiv2013

Effect of Ridge-Ridge Interactions in Crumpled Thin Sheets

We study whether and how the energy scalings based on the single-ridge approximation are revised in an actual crumpled sheet; namely, in the presence of ridge-ridge interactions. Molecular Dynamics Simulation is employed for this purpose. In order to improve the data quality, modifications are introduced to the common protocol. As crumpling proceeds, we find that the average storing energy changes from being proportional to one-third of the ridge length to a linear relation, while the ratio of bending and stretching energies decreases from 5 to 2. The discrepancy between previous simulations and experiments on the material-dependence for the power-law exponent is resolved. We further determine the averaged ridge length to scale linearly with the crumpled ball size $R$, the ridge number as $1/R^2$, and the average storing energy per unit ridge length as $1/R^{2.364\sim 2.487}$. These results are consistent with the mean-field predictions. Finally, we extend the existent simulations to the high-pressure region for completeness, and verify the existence of a new scaling relation that is more general than the familiar power law at covering the whole density range.

cond-mat.soft↗