arXiv subjects

Chia-Min Chung

Publications and source records attributed to Chia-Min Chung.

At least 19 recordsLinked to original sources

arXiv2026

The topological Kondo model out of equilibrium

The topological Kondo effect is a genuine manifestation of the nonlocality of Majorana modes. We investigate its out-of-equilibrium signatures in a model with a Cooper-pair box hosting four of these topological modes, each connected to a metallic lead. Through an advanced matrix-product-state approach tailored to study the dynamics of superconductors, we simulate the relaxation of the Majorana magnetization, which allows us to determine the related Kondo temperature, and we analyze the onset of electric transport after a quantum quench of a lead voltage. Our results apply to Majorana Cooper-pair boxes fabricated in double nanowire devices and provide nonperturbative evidence of the crossover from weak-coupling states to the strongly correlated topological Kondo regime. The latter dominates at the superconductor charge degeneracy points and displays the expected universal fractional zero-bias conductance.

cond-mat.str-el↗

arXiv2026

Spin modulations in the Rashba-Hubbard chain -- a tensor network study

Uniform spin-orbit coupling in an open single-band Hubbard chain is an exactly removable $SU(2)$ gauge field at the Hamiltonian level, but not at the level of laboratory-frame spin correlations. We study this separation using density matrix renormalization group calculations for the repulsive one-dimensional Rashba-Hubbard chain. For open boundary conditions, a site-dependent spin rotation maps the model with hopping $t$ and Rashba spin-orbit strength $λ$ onto the ordinary Hubbard chain with renormalized hopping $t_λ=\sqrt{t^2+λ^2}$. Consequently, charge and energy diagnostics are affected only through the bandwidth renormalization, which is quadratic in weak $λ/t$. Spin correlations, however, respond already at linear order because the same transformation rotates the local spin basis by the wave vector $k_{\rm so}=2\arctan(λ/t)$. We use DMRG to verify this observable consequence across the filling diagram of finite open chains. The filling structure follows the gauge-equivalent Hubbard model, whereas the spin structure factor shows the predicted spin-orbit sidebands. A dominant Hubbard-chain magnetic wave vector $k_0$ is transformed into components at $k_0\pm k_{\rm so}$, folded into the open-chain Brillouin zone. At half filling, where $k_0=π$, the two sidebands fold onto a single, in-plane, spin spiral wave with $k=π-k_{\rm so}<π$. Away from half filling, the incommensurate Hubbard spin response splits into two distinct spin-orbit-shifted components, producing a real-space beating pattern. Our results provide a filling-resolved tensor-network benchmark for the exactly removable limit of one-dimensional spin-orbit coupling, and establish a controlled reference point for ladders, multiorbital chains, rings, proximitized wires, and higher-dimensional Hubbard systems where spin-orbit coupling can no longer be gauged away.

cond-mat.str-el↗

arXiv2026

Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics

We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations.

cond-mat.quant-gas↗

arXiv2025

The Cytnx Library for Tensor Networks

We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.

cs.MS↗

arXiv2024

Simulations of the dynamics of quantum impurity problems with matrix product states

The Anderson impurity model is a paradigmatic example in the study of strongly correlated quantum systems and describes an interacting quantum dot coupled to electronic leads. In this work, we characterize the emergence of the Kondo effect by investigating the model dynamics following a quantum quench based on matrix product state simulations. The relaxation of the impurity magnetization allows for the estimate of the predicted universal scaling of the Kondo temperature as a function of the impurity-lead hybridization and quantum dot repulsion. Additionally, our simulations permit us to evaluate the current in the nonequilibrium quasi-steady state appearing after the quench. Through their values, we examine the dependence of the conductance on the voltage bias $V_b$ and on the impurity chemical potential $V_g$, which displays a zero-bias Kondo peak. Our results are relevant for transport measurements in Coulomb blockaded devices, and, in particular, in quantum dots induced in nanowires.

cond-mat.str-el↗

arXiv2023

Coexistence of superconductivity with partially filled stripes in the Hubbard model

Combining the complementary capabilities of two of the most powerful modern computational methods, we find superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model (with next nearest neighbor hopping). In the electron-doped regime, superconductivity is weaker and is accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexists with stripe order, which persists into the overdoped region with weaker hole density modulation. These stripe orders, neither filled as in the pure Hubbard model (no next nearest neighbor hopping) nor half-filled as seen in previous state-of-the-art calculations, vary in fillings between 0.6 and 0.8. The resolution of the tiny energy scales separating competing orders requires exceedingly high accuracy combined with averaging and extrapolating with a wide range of system sizes and boundary conditions. These results validate the applicability of this iconic model for describing cuprate high-$T_c$ superconductivity.

cond-mat.supr-con↗

arXiv2022

Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices

Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is non-trivial and some of their non-perturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the real-time dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a mean-field BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device total charge. This approach allows us to treat non-perturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zero-bias peaks caused by Majorana modes in a blockaded Kitaev chain, and compare our results with common Breit-Wigner predictions.

cond-mat.mes-hall↗

arXiv2021

Response to comment on "Spin-lattice coupling and the emergence of the trimerized phase in the $S=1$ kagome antiferromagnet Na$_2$Ti$_3$Cl$_8$", Phys. Rev. Lett. 124, 167203 (2020)

In the context of the $S=1$ kagome antiferromagnet Na$_2$Ti$_3$Cl$_8$, we respond to the comment by Khomskii et al. [D.I. Khomskii, T. Mizokawa and S.V. Streltsov, Phys. Rev. Lett. 127, 049701 (2021)] on previous work by Paul et al. [A. Paul, C.-M. Chung, T. Birol, and H. J. Changlani, Phys. Rev. Lett. 124, 167203 (2020)].

cond-mat.str-el↗

arXiv2021

$\mathbb{Z}_N$ lattice gauge theory in a ladder geometry

Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in two-leg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $\mathbb{Z}_N$ gauge symmetries. We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a Berezinskii-Kosterlitz-Thouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.

quant-ph↗

arXiv2020

Absence of superconductivity in the pure two-dimensional Hubbard model

We study the superconducting pairing correlations in the ground state of the doped Hubbard model -- in its original form without hopping beyond nearest neighbor or other perturbing parameters -- in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art many-body computational methods, constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods, deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be non-superconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.

cond-mat.str-el↗

arXiv2020

Plaquette versus ordinary $d$-wave pairing in the $t'$-Hubbard model on a width 4 cylinder

The Hubbard model and its extensions are important microscopic models for understanding high- $T_c$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping $t'$ (the $t'$- Hubbard model), pairing is strongly influenced by $t'$ . In particular, a recent study on a width-4 cylinder observed quasi-long-rage superconducting order, associated with a negative $t'$ , which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-4 $t'$-Hubbard model. We show that in this specific system, the pairing symmetry with $t'<0$ is not the ordinary $d$-wave one would expect in the 2D limit. Instead we observe a so-called plaquette d-wave pairing. The plaquette d-wave exists only on a width-4 cylinder, and so is not representative of the 2D limit. We find that a negative $t'$ suppresses the conventional d-wave, leading to plaquette pairing. In contrast, a different $t''$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$-wave pairing.

cond-mat.str-el↗

arXiv2019

Entanglement Renyi negativity across a finite temperature transition: a Monte Carlo study

Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo simulations to study the third Renyi negativity, a generalization of entanglement negativity, as a proxy of mixed-state entanglement in the 2D transverse field Ising model across its finite temperature phase transition. We find that the area-law coefficient of the Renyi negativity is singular across the transition, while its subleading constant is zero within the statistical error. This indicates that the entanglement is short-ranged at the critical point despite a divergent correlation length. Renyi negativity in several exactly solvable models also shows qualitative similarities to that in the 2D transverse field Ising model.

cond-mat.str-el↗

arXiv2019

Minimally entangled typical thermal states with auxiliary matrix-product-state bases

Finite temperature problems in the strong correlated systems are important but challenging tasks. Minimally entangled typical thermal states (METTS) are a powerful method in the framework of tensor network methods to simulate finite temperature systems, including Fermions and frustrated spins which introduce a sign problem in the typical Monte Carlo methods. In this work, we introduce an extension of the METTS algorithm by using a new basis, the auxiliary matrix product state. This new basis achieves the pre-summation process in the partition function, and thus improve the convergence in the Monte Carlo samplings. The method also has the advantage of simulating the grand canonical ensemble in a computationally efficient way by employing good quantum numbers. We benchmark our method on the spin-$1/2$ XXZ model on the triangular lattice, and show that the new method outperforms the original METTS as well as the purification methods at sufficiently low temperature, the usual range of applications of METTS. The new method also naturally connects the METTS method to the purification method.

cond-mat.str-el↗

arXiv2019

Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na$_2$Ti$_3$Cl$_8$

Spin-1 antiferromagnets are abundant in nature, but few theories or results exist to understand their general properties and behavior, particularly in situations when geometric frustration is present. Here we study the $S=1$ Kagome compound Na$_2$Ti$_3$Cl$_8$ using a combination of Density Functional Theory, Exact Diagonalization, and Density Matrix Renormalization Group methods to achieve a first principles supported explanation of exotic magnetic phases in this compound. We find that the effective magnetic Hamiltonian includes essential non-Heisenberg terms that do not stem from spin-orbit coupling, and both trimerized and spin-nematic magnetic phases are relevant. The experimentally observed structural transition to a breathing Kagome phase is driven by spin--lattice coupling, which favors the trimerized magnetic phase against the quadrupolar one. We thus show that lattice effects can be necessary to understand the magnetism in frustrated magnetic compounds, and surmise that Na$_2$Ti$_3$Cl$_8$ is a compound which cannot be understood from only electronic or only lattice Hamiltonians, very much like VO$_2$.

cond-mat.str-el↗

arXiv2018

Resonating quantum three-coloring wavefunctions for the kagome quantum antiferromagnet

Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-$1/2$ $XXZ$ model for $J_z/J=-1/2$ on the kagome lattice [H. J. Changlani et al. Phys. Rev. Lett 120, 117202 (2018)] -- a result that holds for arbitrary magnetization -- we develop an exact mapping between its exact quantum three-coloring wavefunctions and the characteristic localized and topological magnons. This map, involving resonating two-color loops, is developed to represent exact many-body ground state wavefunctions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any $J_z/J \geq -1/2$. This demonstrates the equivalence of the ground-state wavefunction of the Ising, Heisenberg and $XY$ regimes all the way to the $J_z/J=-1/2$ point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions ($J_z \geq 0$), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising ($J_z \gg J$), Heisenberg ($J_z=J$) and $XY$ ($J_z=0$) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate $J_z/J=-1/2$ point. These findings offer a framework for recent results in the literature, and also suggest that the $J_z/J=-1/2$ point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-$1/2$ kagome problem.

cond-mat.str-el↗

arXiv2017

Stripe order in the underdoped region of the two-dimensional Hubbard model

Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few Kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models even in challenging settings.

cond-mat.str-el↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2013

Entanglement negativity via replica trick: a Quantum Monte Carlo approach

Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. These quantities can serve as witnesses of criticality. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. These are more pronounced in the presence of boundaries. For large chains we find perfect agreement with CFT. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. Remarkably, the finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.

cond-mat.str-el↗