arXiv subjects

Myung-Hoon Chung

Publications and source records attributed to Myung-Hoon Chung.

13 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↗

arXiv2025

Tensor network method for solving the Ising model with a magnetic field

We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network. The tensor has a different symmetry property for ferromagnets and antiferromagnets. The tensor network of the partition function is interpreted as a multiple product of the one-dimensional quantum Hamiltonian. We perform infinite density matrix renormalization group to contract the two-dimensional tensor network. We present the numerical result of magnetization and entanglement entropy for the Ising ferromagnet and antiferromagnet side by side. In order to determine the critical line in the parameter space of temperature and magnetic field, we use the half-chain entanglement entropy of the one-dimensional quantum state. The entanglement entropy precisely indicates the critical line forming the parabolic shape for the antiferromagnetic case, but shows the critical point for the ferromagnetic case.

cond-mat.stat-mech↗

arXiv2020

Phase transitions in the one-dimensional ionic Hubbard model

We study quantum phase transitions by measuring the bond energy, the number density, and the half-chain entanglement entropy in the one-dimensional ionic Hubbard model. By performing the infinite density matrix renormalization group with matrix product operator, we obtain ground states as the canonical form of matrix product states. Depending on the chemical potential and the staggered potential, the number density and the half-chain entanglement entropy shows clear signatures of the Mott transition. Our results confirm the success of the matrix product operator method for investigation of itinerant fermion systems.

cond-mat.str-el↗

arXiv2020

Ground-state properties of the one-dimensional Hubbard model with pairing potential

We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mott phase and the fully gapped nature of the many-body spectrum of the superconducting phase, in the presence of explicit U(1)-charge symmetry breaking.

cond-mat.str-el↗

arXiv2016

Half-Chain Entanglement Entropy in the One-Dimensional Spinless Fermion Model

We calculate the half-chain entanglement entropy of the ground state in the one-dimensional spinless fermion model. Considering a tiny corner of the Hilbert space represented by matrix product states, we efficiently find the ground state by the infinite time-evolving block decimation. The Schmidt coefficients are used to determine the half-chain entanglement entropy. Using the bond dimension scaling of the half-chain entanglement entropy, we find the critical region, which is consistent with the previous results.

cond-mat.str-el↗

arXiv2014

A Solution of the Hubbard Model

We report a ground-state solution for the two-dimensional fermionic Hubbard model, which is obtained via a numerical variational method. The two ingredients in this approach are tensor network states and the time-evolving block decimation. We easily handle the horizontal hopping in the Hamiltonian, and we proceed further to observe the fermion-exchange effect caused by the vertical hopping. By requiring no divergence and no convergence to zero for the ground state, we successively determine the ground-state energy per site as a function of the chemical potential and the lattice length. In addition, we observe saturation in the behavior of the ground-state energy as the lattice length increases.

cond-mat.str-el↗

arXiv2013

Topological entanglement entropy in bilayer quantum Hall systems

We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer separation and tunneling amplitude. We perform the finite size scaling analysis of the topological entanglement entropy in order to see the quantum phase transition clearly.

cond-mat.str-el↗

arXiv2013

Matrix Product States for Quantum Many-Fermion Systems

We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum many-fermion systems with matrix product states, which are updated consistently in a way that accounts for fermion exchange effects. This method can be applied to a wide class of fermion systems. We test this method in spinless fermion system where the exact ground state energy is known. We analyze finite size effects to determine the ground state energy in the thermodynamic limit that is compared to the exact value.

cond-mat.str-el↗

arXiv2003

Physics0.01 : Object-Oriented Programming for Exact Diagonalization

A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. The language C# invented by Microsoft is adopted in this project. Several rules of thumb are suggested in order to obtain easy-readable coherent codes. As a first step, we present the library code for exact diagonalization in physics. When we build codes, we clearly distinguish between model independent and dependent parts, and we use familiar terminologies like {\sf Hamiltonian}, {\sf HilbertSpace}, {\sf GroundState}, {\it etc} as class names. As an explicit example, we calculate ground state energy of a quantum dot, showing the triplet-singlet transition.

cond-mat.mes-hall↗

arXiv2000

Localization-Delocalization Transition in a Quantum Dot

A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a finite dimensional Hilbert space. As a result, exact diagonalization is performed to find the ground state energy of the system. It is the purpose to explain the peculiar pattern of the electron addition energy measured in the dot of two gate voltages.

cond-mat.mes-hall↗

arXiv1999

Low Energy Effective Hamiltonian for the Fractional Quantum Hall Effect

A low energy effective Hamiltonian for the fractional quantum Hall effect is obtained by using irreducible representations of the symmetry group. It is found that the model described by the effective Hamiltonian is similar to the Heisenberg spin chain. Symmetries of the effective Hamiltonian are studied in order to decompose the relevant Hilbert space. This decomposition will be useful for further numerical analysis on the gap of the quantum Hall system.

cond-mat.mes-hall↗

arXiv1998

Fractional Populations in Sex-linked Inheritance

We study the fractional populations in chromosome inherited diseases. The governing equations for the fractional populations are found and solved in the presence of mutation and selection. The physical fixed points obtained are used to discuss the cases of color blindness and hemophilia.

cond-mat↗

arXiv1993

Many Particle Hamiltonian for the Fractional Quantum Hall Effect

A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $ν< 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE from the point of view of the single quasi-particle energy spectrum. It is shown how the specific couplings in the many-particle Hamiltonian depend on the magnetic field and the area density of electrons. The degeneracies of the quasi-particle states are related to the fractional filling factors $ν$. It is suggested that the energy gaps obtained in the quasi-particle energy spectrum are comparable with the experimentally measured quantities. An explicit calculation for the FQH - conductance is given and its character as a topological invariant is discussed.

cond-mat↗