arXiv subjects

Hangmo Yi

Publications and source records attributed to Hangmo Yi.

17 recordsLinked to original sources

arXiv2015

Quantum phase transition of the transverse-field quantum Ising model on scale-free networks

I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent $λ=6$, I obtain results that are consistent with the mean-field theory. For $λ=4.5$ and $4$, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. The deviation from the mean-field theory becomes more pronounced for smaller $λ$.

cond-mat.stat-mech↗

arXiv2014

Quantum critical behavior of the quantum Ising model on fractal lattices

I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point, and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly two, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.

cond-mat.stat-mech↗

arXiv2009

Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which electric current and mechanical oscillation are treated fully quantum mechanically on an equal footing. Quantum mechanically fluctuating Aharonov-Bohm phases obtained by the electrons cause nontrivial contribution to mechanical vibration and electrical conduction of the wire. We demonstrate our theory by calculating the admittance of the wire which are influenced by the multiple interplay between the mechanical and the electrical energy scales, magnetic field strength, and the electron-electron interaction.

cond-mat.mes-hall↗

arXiv2004

Dynamical Conductivity of Disordered Quantum Hall Stripes

We present a detailed theory for finite-frequency conductivities Re$[σ_{αβ}(ω)]$ of quantum Hall stripes, which form at Landau level $N\geq 2$ close to half filling, in the presence of weak Gaussian disorder. We use an effective elastic theory to describe the low-energy dynamics of the stripes with the dynamical matrix being determined through matching the density-density correlation function obtained in the microscopic time-dependent Hartree-Fock approximation. We then apply replicas and the Gaussian variational method to deal with the disorder. Within this method, a set of saddle point equations for the retarded self energies are obtained, which are solved numerically to get Re$[σ_{αβ}(ω)]$. We find a quantum depinning transition as $Δν$, the fractional part of the filling factor, approaches a critical value $Δν_c$ from below. For $Δν<Δν_c$, the pinned state is realized in a replica symmetry breaking (RSB) solution, and the frequency-dependent conductivities in both the directions perpendicular and parallel to the stripes show resonant peaks. These peaks shift to zero frequency as $Δν\to Δν_c$. For $Δν\geΔν_c$, we find a partial RSB (PRSB) solution in which there is RSB perpendicular to the stripes, but replica symmetry along the stripes, leading to free sliding along the stripe direction. The quantum depinning transition is in the Kosterlitz-Thouless universality class. The result is consistent with a previous renormalization group analysis.

cond-mat.mes-hall↗

arXiv2004

Quantum Depinning Transition of Quantum Hall Stripes

We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor $Δν_c$. For $Δν<Δν_c$, the pinned state is realized in a replica symmetry breaking (RSB) solution, and the frequency-dependent conductivities in both perpendicular and parallel to the stripes show resonant peaks. These peaks shift to zero frequency as $Δν\to Δν_c$. For $Δν\geΔν_c$, we find a {\em partial RSB (PRSB)} solution in which there is free sliding only along the stripe direction. The transition is analogous to the Kosterlitz-Thouless phase transition.

cond-mat.mes-hall↗

arXiv2004

Hole maximum density droplets of an antidot in strong magnetic fields

We investigate a quantum antidot in the integer quantum Hall regime (the filling factor is two) by using a Hartree-Fock approach and by transforming the electron antidot into a system which confines holes via an electron-hole transformation. We find that its ground state is the maximum density droplet of holes in certain parameter ranges. The competition between electron-electron interactions and the confinement potential governs the properties of the hole droplet such as its spin configuration. The ground-state transitions between the droplets with different spin configurations occur as magnetic field varies. For a bell-shape antidot containing about 300 holes, the features of the transitions are in good agreement with the predictions of a recently proposed capacitive interaction model for antidots as well as recent experimental observations. We show this agreement by obtaining the parameters of the capacitive interaction model from the Hartree-Fock results. An inverse parabolic antidot is also studied. Its ground-state transitions, however, display different magnetic-field dependence from that of a bell-shape antidot. Our study demonstrates that the shape of antidot potential affects its physical properties significantly.

cond-mat.mes-hall↗

arXiv2003

Coulomb Blockade and Kondo Effect in a Quantum Hall Antidot

We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, h/(2e) Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.

cond-mat.mes-hall↗

arXiv2003

Elementary Excitations in One-Dimensional Electromechanical Systems; Transport with Back-Reaction

Using an exactly solvable model, we study low-energy properties of a one-dimensional spinless electron fluid contained in a quantum-mechanically moving wire located in a static magnetic field. The phonon and electric current are coupled via Lorentz force and the eigenmodes are described by two independent boson fluids. At low energies, the two boson modes are charged while one of them has excitation gap due to back-reaction of the Lorentz force. The theory is illustrated by evaluating optical absorption spectra. Our results are exact and show a non-perturbative regime of electron transport.

cond-mat.mes-hall↗

arXiv2003

Quantum Dissipative Dynamics of the Magnetic Resonance Force Microscope in the Single-Spin Detection Limit

We study a model of a magnetic resonance force microscope (MRFM) based on the cyclic adiabatic inversion technique as a high-resolution tool to detect single electron spins. We investigate the quantum dynamics of spin and cantilever in the presence of coupling to an environment. To obtain the reduced dynamics of the combined system of spin and cantilever, we use the Feynman-Vernon influence functional and get results valid at any temperature as well as at arbitrary system-bath coupling strength. We propose that the MRFM can be used as a quantum measurement device, i.e., not only to detect the modulus of the spin but also its direction.

cond-mat↗

arXiv2002

Effect of Quantum Fluctuations in an Ising System on Small-World Networks

We study quantum Ising spins placed on small-world networks. A simple model is considered in which the coupling between any given pair of spins is a nonzero constant if they are linked in the small-world network and zero otherwise. By applying a transverse magnetic field, we have investigated the effect of quantum fluctuations. Our numerical analysis shows that the quantum fluctuations do not alter the universality class at the ferromagnetic phase transition, which is of the mean-field type. The transition temperature is reduced by the quantum fluctuations and eventually vanishes at the critical transverse field $Δ_c$. With increasing rewiring probability, $Δ_c$ is shown to be enhanced.

cond-mat.stat-mech↗

arXiv2002

Nonmonotonic behavior of resistance in a superconductor-Luttinger liquid junction

Transport through a superconductor-Luttinger liquid junction is considered. When the interaction in the Luttinger liquid is repulsive, the resistance of the junction with a sufficiently clean interface shows nonmonotonic temperature- or voltage-dependence due to the competition between the superconductivity and the repulsive interaction. The result is discussed in connection with recent experiments on single-wall carbon nanotubes in contact with superconducting leads.

cond-mat.mes-hall↗

arXiv2001

Resonant tunneling and the multichannel Kondo problem: the quantum Brownian motion description

We study mesoscopic resonant tunneling as well as multichannel Kondo problems by mapping them to a first-quantized quantum mechanical model of a particle moving in a multi-dimensional periodic potential with Ohmic dissipation. From a renormalization group analysis, we obtain phase diagrams of the quantum Brownian motion model with various lattice symmetries. For a symmorphic lattice, there are two phases at T=0: a localized phase in which the particle is trapped in a potential minimum, and a free phase in which the particle is unaffected by the periodic potential. For a non-symmorphic lattice, however, there may be an additional intermediate phase in which the particle is neither localized nor completely free. The fixed point governing the intermediate phase is shown to be identical to the well-known multichannel Kondo fixed point in the Toulouse limit as well as the resonance fixed point of a quantum dot model and a double-barrier Luttinger liquid model. The mapping allows us to compute the fixed-poing mobility $μ^*$ of the quantum Brownian motion model exactly, using known conformal-field-theory results of the Kondo problem. From the mobility, we find that the peak value of the conductance resonance of a spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the resonance line shape is predicted.

cond-mat.mes-hall↗

arXiv2000

Stability of the Smectic Quantum Hall State: A Quantitative Study

We present an effective elastic theory which {\em quantitatively} describes the stripe phase of the two-dimensional electron gas in high Landau levels ($N\geq2$). The dynamical matrix is obtained with remarkably high precision from the density-density correlation function in the time-dependent Hartree-Fock approximation. A renormalization group analysis shows that at T=0, as the partial filling factor $Δν\equivν-\lfloorν\rfloor$ moves away from 1/2, the anisotropic conducting state may undergo quantum phase transitions: stripes may get pinned along their conducting direction by disorder, or may lock into one another to form a two-dimensional crystal. The model predicts values of $Δν$ for each transition. The transitions should be reflected in the temperature dependence of the dissipative conductivity.

cond-mat.mes-hall↗

arXiv1999

Electromagnetic absorption of a pinned Wigner crystal at finite temperatures

We investigate the microwave absorption of a pinned, two-dimensional Wigner crystal in a strong magnetic field at finite temperatures. Using a model of a uniform commensurate pinning potential, we analyze thermal broadening of the electromagnetic absorption resonance. Surprisingly, we find that the pinning resonance peak should remain sharp even when the temperature is comparable or greater than the peak frequency. This result agrees qualitatively with recent experimental observations of the ac conductivity in two-dimensional hole systems in a magnetically induced insulating state. It is shown, in analogy with Kohn's theorem, that the electron-electron interaction does not affect the response of a harmonically pinned Wigner crystal to a spatially uniform external field at any temperature. We thus focus on anharmonicity in the pinning potential as a source of broadening. Using a 1/N expansion technique, we show that the broadening is introduced through the self-energy corrections to the magnetophonon Green's functions.

cond-mat.mes-hall↗

arXiv1998

Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field

We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors.

cond-mat.mes-hall↗

arXiv1996

Quantum Brownian Motion in a Periodic Potential and the Multi Channel Kondo Problem

We study the motion of a particle in a periodic potential with Ohmic dissipation. In $D=1$ dimension it is well known that there are two phases depending on the dissipation: a localized phase with zero temperature mobility $μ=0$ and a fully coherent phase with $μ$ unaffected by the periodic potential. For $D>1$, we find that this is also the case for a Bravais lattice. However, for non symmorphic lattices, such as the honeycomb lattice and its $D$ dimensional generalization, there is a new intermediate phase with a universal mobility $μ^*$. We study this intermediate fixed point in perturbatively accessible regimes. In addition, we relate this model to the Toulouse limit of the $D+1$ channel Kondo problem. This mapping allows us to compute $μ^*$ exactly using results known from conformal field theory. Experimental implications are discussed for resonant tunneling in strongly coupled Coulomb blockade structures and for multi channel Luttinger liquids.

cond-mat↗

arXiv1996

Coulomb Blockade in a Quantum Dot Coupled Strongly to a Lead

We study theoretically a quantum dot in the quantum Hall regime that is strongly coupled to a single lead via a point contact. We find that even when the transmission through the point contact is perfect, important features of the Coulomb blockade persist. In particular, the tunneling into the dot via a second weakly coupled lead is suppressed, and shows features which can be ascribed to elastic or inelastic cotunneling through the dot. When there is weak backscattering at the point contact, both the tunneling conductance and the differential capacitance are predicted to oscillate as a function of gate voltage. We point out that the dimensionless ratio $ξ$ between the fractional oscillations in $G$ and $C$ is an intrinsic property of the dot, which, in principle, can be measured. We compute $ξ$ within two models of electron-electron interactions. In addition, we discuss the role of additional channels.

cond-mat↗