arXiv subjects

Jintae Kim

Publications and source records attributed to Jintae Kim.

16 recordsLinked to original sources

arXiv2025

Noninvertible symmetry and topological holography for modulated SPT in one dimension

We examine noninvertible symmetry (NIS) in one-dimensional (1D) symmetry-protected topological (SPT) phases protected by dipolar and exponential-charge symmetries, which are two key examples of modulated SPT (MSPT). To set the stage, we first study NIS in the $\mathbb{Z}_N \times \mathbb{Z}_N$ cluster model, extending previous work on the $\mathbb{Z}_2 \times \mathbb{Z}_2$ case. For each symmetry type (charge, dipole, exponential), we explicitly construct the noninvertible Kramers-Wannier (KW) and Kennedy-Tasaki (KT) transformations, revealing dual models with spontaneous symmetry breaking (SSB). The resulting symmetry group structure of the SSB model is rich enough that it allows the identification of other SSB models with the same symmetry. Using these alternative SSB models and KT duality, we generate novel MSPT phases distinct from those associated with the standard decorated domain wall picture, and confirm their distinctiveness by projective symmetry analyses at their interfaces. Additionally, we establish a topological-holographic correspondence by identifying the 2D bulk theories-two coupled layers of toric codes (charge), anisotropic dipolar toric codes (dipole), and exponentially modulated toric codes (exponential)-whose boundaries host the respective 1D MSPT phases.

cond-mat.str-el↗

arXiv2025

Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits

We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously. Simultaneous gauging can capture a broader class of dualities than sequential gauging, the latter corresponding to the conventional gauging applied in successive steps. In general, performing simultaneous gauging and conventional gauging in sequence constitutes the most general framework for gauging modulated symmetries. We further show that the associated duality transformations can be implemented via adaptive state preparation protocols. As a concrete example, we consider a dipole symmetry in $(2+1)$D and illustrate both the simultaneous gauging procedure and the adaptive preparation protocol. Interestingly, we find that the intermediate state of the simultaneous gauging/adaptive circuit corresponds to a symmetry-protected topological phase protected by the dipole bundle symmetry. Finally, we utilize the duality to analyze the phase diagram of the rank-2 toric code under transverse fields.

cond-mat.str-el↗

arXiv2024

Forbes: Face Obfuscation Rendering via Backpropagation Refinement Scheme

A novel algorithm for face obfuscation, called Forbes, which aims to obfuscate facial appearance recognizable by humans but preserve the identity and attributes decipherable by machines, is proposed in this paper. Forbes first applies multiple obfuscating transformations with random parameters to an image to remove the identity information distinguishable by humans. Then, it optimizes the parameters to make the transformed image decipherable by machines based on the backpropagation refinement scheme. Finally, it renders an obfuscated image by applying the transformations with the optimized parameters. Experimental results on various datasets demonstrate that Forbes achieves both human indecipherability and machine decipherability excellently. The source codes are available at https://github.com/mcljtkim/Forbes.

cs.CV↗

arXiv2024

Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters

We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact with a stream of photons and their neighboring emitters. Depending on the number of emitters $n_e$, we study the effect of delay line errors in two regimes: when $n_e$ is a small constant of order unity and when $n_e$ scales with the code distance. Between these two regimes, the logical error rate steadily decreases as $n_e$ increases, from a scaling of $\exp(-c\eta^{-1/2})$ to $\exp(-c'\eta^{-1})$, where $\eta$ is the error rate per unit length in the delay line, for some constants $c,c'>0$. We also carry out a detailed study of the break-even point and the fault-tolerance overhead. These studies suggest that the multi-emitter architecture, using the state-of-the-art delay lines, can be used to demonstrate error suppression, assuming other sources of errors are sufficiently small.

quant-ph↗

arXiv2023

Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy

Some topological lattice models in two spatial dimensions exhibit intricate lattice size dependence in their ground state degeneracy (GSD). This and other features such as the position-dependent anyonic excitations are manifestations of UV/IR mixing. In the first part of this paper, we perform an exact calculation of the topological entanglement entropy (TEE) for a specific model, the rank-2 toric code. This analysis includes both contractible and non-contractible boundaries, with the minimum entropy states identified specifically for non-contractible boundaries. Our results show that TEE for a contractible boundary remains independent of lattice size, whereas TEE for non-contractible boundaries, similarly to the GSD, shows intricate lattice-size dependence. In the latter part of the paper we focus on the fact that the rank-2 toric code is an example of a translation symmetry-enriched topological phase, and show that viewing distinct lattice size as a consequence of different translation symmetry defects can explain both our TEE results and the GSD of the rank-2 toric code. Our work establishes the translation symmetry defect framework as a robust description of the UV/IR mixing in topological lattice models.

cond-mat.str-el↗

arXiv2023

BiFormer: Learning Bilateral Motion Estimation via Bilateral Transformer for 4K Video Frame Interpolation

A novel 4K video frame interpolator based on bilateral transformer (BiFormer) is proposed in this paper, which performs three steps: global motion estimation, local motion refinement, and frame synthesis. First, in global motion estimation, we predict symmetric bilateral motion fields at a coarse scale. To this end, we propose BiFormer, the first transformer-based bilateral motion estimator. Second, we refine the global motion fields efficiently using blockwise bilateral cost volumes (BBCVs). Third, we warp the input frames using the refined motion fields and blend them to synthesize an intermediate frame. Extensive experiments demonstrate that the proposed BiFormer algorithm achieves excellent interpolation performance on 4K datasets. The source codes are available at https://github.com/JunHeum/BiFormer.

cs.CV↗

arXiv2022

Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions

A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and J. H. Han, Phys. Rev. B {\bf 105}, 045128] the quasiparticles in that model shows unusual braiding statistics that depends on the initial locations of the particles which participate in the braiding. We show that this new kind of statistical phase captures the total dipole moment of quasiparticles encompassed in the braiding, in contrast to the conventional anyonic braiding seeing the total charge. An Aharonov-Bohm interpretation of such {\it dipolar braiding statistics} is made in terms of emergent, rank-1 vector potentials that are built out of the underlying rank-2 gauge fields. Pertinent field theories of the quasiparticle dynamics in the R2TC are developed, and the accompanying conservation laws derived. A {\it dipolar BF theory} of the rank-2 gauge fields is constructed and shown to correctly capture the dipolar braiding statistics, in contrast to the conventional BF theory capturing the monopolar braiding statistics of anyons in the rank-1 toric code.

cond-mat.str-el↗

arXiv2022

Hybrid rank-1 and rank-2 U(1) lattice gauge theory, the F3 model, and its effective field theory

A number of exactly solvable spin models, including the Kitaev toric code in two and three dimensions and the X-cube model in three dimensions, can be related to their respective parent lattice gauge theories (LGT) through the mathematical process of 'Higgsing'. Field theories of the low-energy excitations of these spin models can be developed subsequently, building upon the symmetry of the parent LGTs. Recently, two of the present authors proposed a variant of the three-dimensional toric code which we now call the F3 model, whose elementary excitations consist of freeon and fluxon excitations of the three-dimensional toric code and fracton excitations of the X-cube model. In this work, we identify the parent LGT of the F3 model as the hybrid rank-1 and rank-2 U(1) LGT, and develop the corresponding field theory. The resulting Lagrangian of the F3 model is that of a three-dimensional toric code with an extra term, which ties the dynamics of fractons to that of fluxons. The matter part of the effective action for the F3 model can be derived as well, by carefully keeping track of the gauge invariance of the F3 model. Hydrodynamic equations of motion of the quasiparticles are derived, which properly reflect their constrained dynamics. Finally, we present a tight-binding model for the quasiparticle motion in the F3 model.

cond-mat.str-el↗

arXiv2021

Rank-2 Toric Code in Two Dimensions

We study a two-dimensional spin model obtained by "Higgsing" the rank-2 U(1) lattice gauge theory (LGT) with scalar or vector charges on the L_x * L_y square lattice under the periodic boundary condition (PBC). There are p degrees of freedom per orbital and three orbitals per unit cell in the spin model. The resulting spin model is a stabilizer code consisting of three mutually commuting projectors that are, in turn, obtained by Higgsing the mutually commuting Gauss's law operators and the magnetic field operators in the underlying LGT. The spin model thus obtained is exactly solvable, with the ground state degeneracy (GSD) D given by log_p D=2+(1+delta_{L_x mod p,0})(1+delta_{L_y mod p,0}) when p is a prime number. Two types of dipole excitations, pristine and emergent, are identified. Both the monopoles and the dipoles are free to move, with restrictions on monopoles to hop only by p lattice spacing along with certain directions. The monopole-monopole braiding phase depends on the separation of the x or y coordinates of the initial monopole positions, making it distinct from the ordinary anyon braiding statistics. The monopole-dipole braiding obeys the usual anyonic statistics. Despite the oddity, the monopole-monopole braiding phase can be understood as the Aharonov-Bohm phase of some emergent vector potentials.

cond-mat.str-el↗

arXiv2021

A New Model for Fractons, Fluxons, and Freeons

We propose a lattice spin model on a cubic lattice that shares many of the properties of the 3D toric code and the X-cube fracton model. The model, made of Z_3 degrees of freedom at the links, has the vertex, the cube, and the plaquette terms. Being a stabilizer code the ground states are exactly solved. With only the vertex and the cube terms present, we show that the ground state degeneracy (GSD) is 3^(L3+3L-1) where L is the linear dimension of the cubic lattice. In addition to fractons, there are free vertex excitations we call the freeons. With the addition of the plaquette terms, GSD is vastly reduced to 3^3, with fracton, fluxon, and freeon excitations, among which only the freeons are deconfined. The model is called the AB model if only the vertex (A_v) and the cube (B_c) terms are present, and the ABC model if in addition the plaquette terms (C_p) are included. The AC model consisting of vertex and plaquette terms is the Z_3 3D toric code. The extensive GSD of the AB model derives from the existence of both local and non-local logical operators that connect different ground states. The latter operators are identical to the logical operators of the Z_3 X-cube model. Fracton excitations are immobile and accompanied by the creation of fluxons - plaquettes having nonzero flux. In the ABC model, such fluxon creation costs energy and ends up confining the fractons. Unlike past models of fractons, vertex excitations are free to move in any direction and pick up a non-trivial statistical phase when passing through a fluxon or a fracton cluster.

cond-mat.str-el↗

arXiv2021

Frustration-free Hamiltonian with Topological Order on Graphs

It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) on the open chain {\it and} multiple ground state degeneracy (GSD) that is unrelated to global symmetry breaking on the closed chain. Instead of global symmetry breaking, there exists a {\it local} symmetry operator that commutes with the Hamiltonian and connects the multiple ground states, reminiscent of how the topologically distinct ground states of the toric code are connected by various winding operators. Our model solved on an open chain demonstrates symmetry fractionalization as an indication of SPT order and on a general graph the GSD can be shown to scale with the first Betti number - a topological invariant that counts the number of independent cycles or one dimensional holes of the graph.

cond-mat.str-el↗

arXiv2021

A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph

We analyze a model demonstrating the co-existence of subsystem symmetry breaking (SSB) and symmetry-protected topological (SPT) order, or subsystem LSPT order for short. Its mathematical origin is the existence of both a subsystem and a local operator, both of which commute with the Hamiltonian but anti-commute between themselves. The reason for the exponential growth of the ground state degeneracy is attributed to the existence of subsystem symmetries, which allows one to define both the Landau order parameter and the SPT-like order for each independent loop.

cond-mat.str-el↗

arXiv2020

Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture of the spin liquid, with the energy only 0.024% higher than the exact value given by Bethe ansatz. Building on the ground-state vMPS, the one-spin wave function is constructed in a simple manner with the dispersion that matches well with the exact spectrum. The vMPS scheme is applied to the family of Hamiltonian extrapolating between the Heisenberg model and the Majumdar-Ghosh model.

cond-mat.str-el↗

arXiv2020

Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain

We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.

cond-mat.str-el↗

arXiv2020

Path Integral for Spin-1 Chain in the Fluctuating Matrix Product State Basis

A new method of writing down the path integral for spin-1 Heisenberg antiferromagnetic chain is introduced. In place of the conventional coherent state basis that leads to the non-linear sigma-model, we use a new basis called the fluctuating matrix product states (fMPS) which embodies inter-site entanglement from the outset. It forms an overcomplete set spanning the entire Hilbert space of the spin-1 chain. Saddle-point analysis performed for the bilinear-biquadratic spin model predicts Affeck-Kennedy-Lieb-Tasaki (AKLT) state as the ground state in the vicinity of the AKLT Hamiltonian. Quadratic effective action derived by gradient expansion around the saddle point is free from constraints that plagued the non-linear sigma model and exactly solvable. The obtained excitation modes agree precisely with the single-mode approximation result for the AKLT Hamiltonian. Excitation spectra for other BLBQ Hamiltonians are obtained as well by diagonalizing the quadratic action.

cond-mat.str-el↗

arXiv2019

Low-energy dynamics of the Affleck-Kennedy-Lieb-Tasaki model in the one- and two-triplon basis

The elementary excitation in the antiferromagnetic spin-1 model known as the Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian has been described alternatively as magnons or kink-like solitons (triplons). The latter, which we call the triplon throughout this paper, has been proven equivalent descriptions of the same magnon excitation and not an independent branch of excited states. On the other hand, no careful examination of multi-magnon and multi-triplon equivalence was made in the past. In this paper we prove that two-magnon and two-triplon states are also identical descriptions of the same excited states, and furthermore that their energies break down as the sum of one-triplon energies exactly for the AKLT Hamiltonian. The statement holds despite the fact that the model is non-integrable. Such magnon/triplon dichotomy is conjectured to hold for arbitrary n-magnon and n-triplon states. The one- and two-triplon states form orthogonal sets that can be used to span the low-energy Hilbert space. We construct an effective version of the AKLT Hamiltonian within such subspace, and work out the correction to the one-triplon energy gap that finds excellent agreement with the known exact value.

cond-mat.str-el↗