arXiv subjects

Min-Chul Cha

Publications and source records attributed to Min-Chul Cha.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement Properties of the One-Dimensional Dimerized Fermi-Hubbard Model

We study the entanglement properties of the one-dimensional dimerized Fermi-Hubbard model. Using a matrix-product-state approach, we compute the ground state and identify two insulating phases at 1/2- and 3/4-filling, along with a metallic phase, whose mechanisms can be characterized by their entanglement spectra. Our findings indicate that the two insulating phases are distinct, implying that the phase at 1/2-filling has a charge gap arising from the band gap, which is enhanced by repulsive interactions, while the phase at 3/4-filling exhibits a Mott gap resulting from particle interactions. This difference between the two insulating phases is reflected in the scaling properties of the half-chain entanglement entropy and the distribution of the entanglement spectrum.

cond-mat.str-el↗

arXiv2020

Topologically ordered zigzag nanoribbon: $e/2$ fractional edge charge, spin-charge separation, and ground state degeneracy

We numerically compute the density of states (DOS) of interacting disordered zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional edge charges. The computed Hartree-Fock DOS is linear at the critical disorder strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of $I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of fractional charges in interacting disordered ZGNR. We show that even a weak disorder potential acts as a singular perturbation on zigzag edge electronic states, producing drastic changes in the energy spectrum. Spin-charge separation and fractional charges play a key role in the reconstruction of edge antiferromagnetism. Our results show that an interacting disordered ZGNR is a topologically ordered Mott-Anderson insulator.

cond-mat.str-el↗

arXiv2018

Finite entanglement properties in the matrix product states of the one-dimensional Hubbard model

We study the effects due to limited entanglement in the one-dimensional Hubbard model by representing the ground states in the form of the matrix product states. Finite-entanglement scaling behavior over a wide range is observed at half-filling. The critical exponents characterizing the length scale in terms of the size of matrices used are obtained, confirming the theoretical prediction that the values of the exponents are solely determined by the central charge. The entanglement spectrum shows that a global double degeneracy occurs in the ground states with a charge gap. We also find that the Mott transition, tuned by changing the chemical potential, always occurs through a first-order transition and the metallic phase has a few conducting states, including the states with the mean-field nature close to the critical point, as expected in variational matrix product states with a finite amount of entanglement.

cond-mat.str-el↗

arXiv2015

Continuous and reversible tuning of the disorder-driven superconductor-insulator transition in bilayer graphene

The influence of static disorder on a quantum phase transition (QPT) is a fundamental issue in condensed matter physics. As a prototypical example of a disorder-tuned QPT, the superconductor-insulator transition (SIT) has been investigated intensively over the past three decades, but as yet without a general consensus on its nature. A key element is good control of disorder. Here, we present an experimental study of the SIT based on precise in-situ tuning of disorder in dual-gated bilayer graphene proximity-coupled to two superconducting electrodes through electrical and reversible control of the band gap and the charge carrier density. In the presence of a static disorder potential, Andreev-paired carriers formed close to the Fermi level in bilayer graphene constitute a randomly distributed network of proximity-induced superconducting puddles. The landscape of the network was easily tuned by electrical gating to induce percolative clusters at the onset of superconductivity. This is evidenced by scaling behavior consistent with the classical percolation in transport measurements. At lower temperatures, the solely electrical tuning of the disorder-induced landscape enables us to observe, for the first time, a crossover from classical to quantum percolation in a single device, which elucidates how thermal dephasing engages in separating the two regimes.

cond-mat.supr-con↗

arXiv2007

Order-Parameter Correlation Functions in Quantum Critical Phenomena

We investigate the functional form of the order-parameter (two-point) correlation function in quantum critical phenomena. Contrary to the common lore, when there is no particle-hole symmetry we find that the equal-time correlation function at criticality does not display a diverging correlation length. We illustrate our conclusions by Monte Carlo calculations of the quantum rotor model in $d=2$ space dimensions

cond-mat.stat-mech↗

arXiv2007

Finite-temperature phase transitions in a two-dimensional boson Hubbard model

We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of quantum rotor model, and construct the corresponding phase diagram. Compressibility shows a thermally activated gapped behavior in the insulating regime. Finite-size scaling of the superfluid stiffness clearly shows the nature of the Kosterlitz-Thouless transition. The transition temperature, $T_c$, confirms a scaling relation $T_c \propto ρ_0^x$ with $x=1.0$. Some evidences of anomalous quantum behavior at low temperatures are presented.

cond-mat.str-el↗

arXiv2005

The quasi-particle gap in a disordered boson Hubbard model in two dimensions

We investigate the behavior of the quasi-particle energy gap near quantum phase transitions in a two-dimensional disordered boson Hubbard model at a commensurate filling. Via Monte Carlo simulations of ensembles with fixed numbers of particles, we observe the behavior of the gap as a function of the tuning parameter for various strength of diagonal disorder. For weak disorder, we find that gapped Mott insulating phase is sustained up to the transition point and disappears only in a superfluid, strongly supporting a direct Mott-insulator-to-superfluid transition. Bose glass behavior, insulating with vanishing gap, appears only when the strength of disorder is bigger than a critical value.

cond-mat.str-el↗

arXiv2005

Superfluid-insulator transitions of two-species Bosons in an optical lattice

We consider a realization of the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram for odd filling at commensurate densities. We find that in contrast to the even commensurate filling case, the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.

cond-mat.stat-mech↗

arXiv2005

Correlations at a quantum phase transition in interacting Bose systems

We have investigated the correlation functions of interacting bosons at the generic superfluid-insulator transition, a prototypical quantum phase transition, in two dimensions in the spherical limit. Unexpectedly the spatial correlation functions show non-power-law behavior consisting of two parts: short-range correlation due to the particle-hole pair excitations and long-range off-diagonal order due to the single-particle condensation. The temporal correlation functions, on the other hand, show power-law behavior.

cond-mat.str-el↗

arXiv2004

Separation of two regimes in a disordered boson Hubbard Model

We study the insulator-to-superfluid transition in a two-dimensional disordered boson Hubbard model at zero temperature for intermediate strength of disorder at commensurate density. Via Monte Carlo calculations of the correlation functions in the integer current representation of the model, we obtain the dynamical critical exponent $z=1.5 \pm 0.1$, supporting the multi-critical behavior separating the strong and weak disorder regimes. Investigating the density profile, we suggest that the density fluctuations due to the particle-hole excitations drive the transition in the weak disorder regime.

cond-mat.str-el↗

arXiv2003

Strongly correlated quantum dots in weak confinement potentials and magnetic fields

We explore a strongly correlated quantum dot in the presence of a weak confinement potential and a weak magnetic field. Our exact diagonalization studies show that the groundstate property of such a quantum dot is rather sensitive to the magnetic field and the strength of the confinement potential. We have determined rich phase diagrams of these quantum dots. Some experimental consequences of the obtained phase diagrams are discussed.

cond-mat.mes-hall↗

arXiv2002

Superfluid-insulator transition of the Josephson junction array model with commensurate frustration

We have studied the rationally frustrated Josephson-junction array model in the square lattice through Monte Carlo simulations of $(2+1)$D XY-model. For frustration $f=1/4$, the model at zero temperature shows a continuous superfluid-insulator transition. From the measurement of the correlation function and the superfluid stiffness, we obtain the dynamical critical exponent $z=1.0$ and the correlation length critical exponent $ν=0.4 \pm 0.05$. While the dynamical critical exponent is the same as that for cases $f=0$, 1/2, and 1/3, the correlation length critical exponent is surprisingly quite different. When $f=1/5$, we have the nature of a first-order transition.

cond-mat.str-el↗

arXiv2001

Phase diagram of a Disordered Boson Hubbard Model in Two Dimensions

We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram of this model is constructed in terms of the disorder strength and the chemical potential. Via quantum Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where a random potential is irrelevant, from the strong-disorder regime. In the weak-disorder regime, the Mott-insulator-to-superfluid transition occurs, while, in the strong-disorder regime, the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z=1.35 \pm 0.05$ and the correlation length critical exponent $ν=0.67 \pm 0.03$, that are different from the values for the transitions off the line. We suggest that the proliferation of the particle-hole pairs screens out the weak disorder effects.

cond-mat.dis-nn↗

arXiv2000

Numerical Test of Disk Trial Wave function for Half-Filled Landau Level

The analyticity of the lowest Landau level wave functions and the relation between filling factor and the total angular momentum severely limits the possible forms of trial wave functions of a disk of electrons subject to a strong perpendicular magnetic field. For N, the number of electrons, up to 12 we have tested these disk trial wave functions for the half filled Landau level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies obtained from these two methods is excellent. We have also compared the profile of the occupation number near the edge with that obtained from a field-theoretical method. The results give qualitatively identical edge profiles. Experimental consequences are briefly discussed.

cond-mat.mes-hall↗

arXiv1999

Level Fluctuations and Many-Body Effects in Disorder-Free Quantum Dots

We have investigated whether many-body effects can induce significant level fluctuations in a disorder-free quantum dot. The closed energy shell structures and relaxation of the Hartree-Fock potentials are found to play a significant role. The level degeneracy consistent with the rotational symmetry of the confining potential determines the structure of the energy shells. A closed shell state of a dot can give rise to large fluctuations. When a strong magnetic field is present the shell structure is absent and fluctuations are significantly reduced.

cond-mat.mes-hall↗

arXiv1999

Possibility of direct Mott insulator-to-superfluid transitions in weakly disordered boson systems

We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent nu. In the presence of weak disorder, we obtain nu=0.5 +- 0.1, the same value as that in the pure model, near the tip of a Mott insulator lobe, using the dynamical critical exponent z=2. As the strength of disorder is increased beyond a certain value, however, the value of nu is found to change to 0.9 +- 0.1. This result strongly suggests that there exist direct Mott insulator-to-superfluid transitions around the tip of a Mott insulator lobe in the weak disorder regime.

cond-mat↗

arXiv1998

Peak Effect and the Transition from Elastic to Plastic Depinning

We demonstrate for the first time an observation of the peak effect in simulations of magnetic vortices in a superconductor. The shear modulus $c_{66}$ of the vortex lattice is tuned by adding a fictitious {attractive} short range potential to the usual long-range repulsion between vortices. The peak effect is found to be most pronounced in low densities of pinning centers, and is always associated with a transition from elastic to plastic depinning. The simulations suggest in some situations that over a range of values of $c_{66}$ the production of lattice defects by a driving force enhances the pinning of the lattice.

cond-mat.supr-con↗

arXiv1997

Linear Chain of Coupled Quantum Dots

A linearly coupled chain of spin-polarized quantum dots is investigated under the condition that the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, $μ_{N}=E(N)-E(N-1)$, satisfies, $(μ_{N}+μ_{N_{\ell}+2-N)}/2 \approx V+2t (N, N_{\ell}, V, E(N)$ and $t$ are the number of electrons, the number of dots, and the strength of nearest neighbor electron-electron interactions, the total groundstate energy and the hopping integral between two adjacent dots). This property will be reflected in the spacing between the conductance peaks. The electron density structures are determined using a quantum Monte Carlo method. As the number of electrons is varied several correlated structures are found that are commensurate/incommensurate with the periodic dot system. Hartree-Fock theory fails to predict the correct electronic structures of this system because several nearly degenerate solutions exist.

cond-mat.mes-hall↗