Searcharxiv⌕ Search

arXiv subjects

Jung Hoon Han

Publications and source records attributed to Jung Hoon Han.

At least 19 recordsLinked to original sources
arXiv2026

Dynamics of $\mathrm{CP}^{N-1}$ skyrmions

We derive several exact results for the dynamics of CP$^{N-1}$ skyrmions with arbitrary $N$. Fractonic continuity equation is shown to hold for arbitrary CP$^{N-1}$ fluid implying the conservation of the topological charge and the dipole moment. Inclusion of the Gilbert damping modifies the continuity equation, resulting in the violation of the dipole moment conservation but not of the topological charge. Thiele's equation for the CP$^{N-1}$ skyrmion follows from the modified continuity equation. The Girvin-MacDonald-Platzman (GMP) algebra in the long-wavelength limit is derived for arbitrary CP$^{N-1}$ fluid. In the case of CP$^2$ skyrmions, we identify stable skyrmions in which the ferromagnetic moments are dominant. One can associate a nonzero CP$^1$ charge equal to half the CP$^2$ skyrmion charge and argue that the topological Hall effect of electrons should exist due to their coupling to the ferromagnetic part of the CP$^2$ texture.

cond-mat.str-el↗
arXiv2026

Landau theory of quenched criticality in linear in-context learning

In-context learning (ICL) allows a pretrained model to infer a new task from examples supplied in its prompt without updating its parameters. In linear models of ICL, the prediction error develops a double-descent singularity when the number of pretraining samples becomes comparable to the number of learnable parameters. We formulate this interpolation singularity as a critical phenomenon of a quenched disordered system. By comparing annealed and quenched descriptions of the same linear ICL model, we identify the connected sample-to-sample fluctuations of the learned parameters as the microscopic origin of the singular error. A Landau potential is constructed by integrating the cavity self-consistency equation for the renormalized ridge parameter $ξ$. The role of (magnetization) order parameter is played by $ξ$, while the bare ridge parameter $λ$ becomes its conjugate magnetic field. The normalized sample complexity $τ$ acts as a temperature and the double-descent singularity occurs at the critical temperature $τ_c =1$. The Landau susceptibility is precisely the quantity that diverges in the fluctuation contribution to the prediction error. The order parameter is closely related to the fraction of zero eigenvalues of the empirical relaxation matrix in the ridgeless limit, which define flat directions in the learning dynamics. The Landau theory is generically cubic in the order parameter with critical exponents $(β_{\rm cr},δ_{\rm cr},γ_{\rm cr})=(1,2,1)$. In the large-context regime, there appears a pseudogap-like regime characterized by suppressed order parameter. Predictions of the Landau theory are independently confirmed from numerical solutions of the original learning problem with good quantitative agreement. Our results pave the way for solid statistical-physics understanding of the interpolation criticality in linear in-context learning.

cond-mat.dis-nn↗
arXiv2026

Spin-orbit-induced quantum chiral phases

The scalar spin chirality (SSC), whose nonzero value $\langle {\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k) \rangle \neq 0$ implies the breaking of time-reversal and certain point-group symmetries in the ground state, is a key quantity characterizing chiral magnetism in both classical and quantum settings. The classical SSC is manifested, for instance, in skyrmion crystal phase, while the quantum SSC is still highly sought after in various frustrated spin-1/2 models. An interesting possibility that has not been explored so far is the case in which SSC is symmetry-wise allowed, yet remains zero classically due to the collinear or coplanar arrangement of spins, but is generated by virtue of quantum fluctuation. We demonstrate the existence of precisely such a phase in a spin-1/2 triangular-lattice model with XXZ interaction, spin-orbit-induced exchange interactions, and an external magnetic field. Using iDMRG, we thoroughly map out the phase diagram of the model and identify several phases with coexisting magnetic order and SSC. The nonzero SSC arises despite the classical magnetic order being collinear or coplanar. We provide detailed magnon analysis to ascribe its origin to quantum fluctuations around classical magnetic order. The estimate of SSC from magnon analysis agrees with iDMRG results quantitatively. We map out the magnon spectrum and its Berry curvature, culminating in the prediction of finite thermal Hall conductivity in these phases with SSC.

cond-mat.str-el↗
arXiv2026

Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States

The $\mathbb{Z}_N$ cluster-state wavefunction, a paradigmatic example of symmetry-protected topological (SPT) order with $\mathbb{Z}_N \times \mathbb{Z}_N$ symmetry, is expressed in various equivalent ways. We identify the projector-based scheme called the $P$-representation as the efficient way to express cluster and dipolar cluster state's wavefunctions. Employing the restricted Boltzmann machine scheme to re-write the interaction matrix in the $P$-representation in terms of neural weight matrices allows us to develop the neural quantum state (NQS) and the matrix product state (MPS) representations of the same state. The NQS and MPS representations differ only in the way the weight matrices are split and grouped together in a matrix product. For both $\mathbb{Z}_N$ cluster and dipolar cluster states, we derive in closed form the weight function $W(s,h)$ that couples physical spins $s$ to hidden variables $h$, generalizing the previous construction for $Z_2$ cluster states to $\mathbb{Z}_N$. For the dipolar cluster state protected by two charge and two dipole symmetries, the procedure we have developed leads to the tensor product state (TPS) representation of the wavefunction where each local tensor carries three virtual indices connecting a given site to two nearest neighbors and one further neighbor. We benchmark the resulting TPS construction against conventional MPS representation using density-matrix renormalization group simulations and argue that the TPS could offer a more efficient representation for some modulated SPT states. As a by-product of the investigation, we generalize the previous $Z_2$ matrix product operator construction of the Kramers-Wannier (KW) operator to $\mathbb{Z}_N$ and interprets it as the dipolar generalization of the discrete Fourier transform on $\mathbb{Z}_N$ variables. The new interpretation naturally explains why the KW map is non-invertible.

cond-mat.dis-nn↗
arXiv2026

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↗
arXiv2025

Gyrotropic magnetic effect in metallic chiral magnets

We study the gyrotropic magnetic effect (GME), the low-frequency limit of optical gyrotropy, in metals and semimetals coupled to chiral spin textures. In these systems, the chiral spin texture which lacks inversion symmetry can imprint itself upon the electronic structure through Hund's coupling, leading to novel low-frequency optical activity. Using perturbation theory and numerical diagonalization of both relativistic and non-relativistic models of conduction electrons coupled to spin textures, we analyze how the GME manifests in both single-$q$ and multi-$q$ textures. Analytical expressions for the rotatory power are derived in terms of universal scaling functions. Estimates based on realistic material parameters reveal an experimentally viable range of values for the rotatory power. The GME arises from the orbital and spin magnetic moments of conduction electrons, with the orbital part closely tied to Berry curvature and playing a significant role in relativistic metals but not so in non-relativistic metals where there is no inherent Berry curvature. The spin contribution to the GME can be significant in non-relativistic metals with a large Fermi energy. Our work establishes the GME as a sensitive probe of magnetic chirality and symmetry breaking in metallic chiral magnets.

cond-mat.mes-hall↗
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

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 $\exp(-cη^{-1/2})$ to $\exp(-c'η^{-1})$, where $η$ 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↗
arXiv2025

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↗
arXiv2024

Fractonic Quantum Quench in Dipole-constrained Bosons

We investigate the quench dynamics in the dipolar Bose-Hubbard model (DBHM) in one dimension. The boson hopping is constrained by dipole conservation and show fractonic dynamics. The ground states at large Hubbard interaction $U$ are Mott insulators at integer filling and a period-2 charge density wave (CDW) at half-integer filling. We focus on Mott-to-Mott and CDW-to-CDW quenches and find that dipole correlation spreading shows the light-cone behavior with the Lieb-Robinson (LR) velocity proportional to the dipole kinetic energy $J$ and the square of the density in the case of Mott quench at integer filling. Effective model for post-quench dynamics is constructed under the dilute-dipole approximation and fits the numerical results well. For CDW quench we observe a much reduced LR velocity of order $J^2/U$ and additional periodic features in the time direction. The emergence of CDW ground state and the reduced LR velocity at half-integer filling can both be understood by careful application of the second-order perturbation theory. The oscillatory behavior arises from quantum scars in the quadrupole sector of the spectrum and is captured by a PXP-like model that we derive by projecting the DBHM to the quadrupolar sector of the Hilbert space.

cond-mat.quant-gas↗
arXiv2024

Topological Dipole Insulator

We expand the concept of two-dimensional topological insulators to encompass a novel category known as topological dipole insulators (TDIs), characterized by conserved dipole moments along the $x$-direction in addition to charge conservation. By generalizing Laughlin's flux insertion argument, we prove a no-go theorem and predict possible edge patterns and anomalies in a TDI with both charge $U^e(1)$ and dipole $U^d(1)$ symmetries. The edge of a TDI is characterized as a quadrupolar channel that displays a dipole $U^d(1)$ anomaly. A quantized amount of dipole gets transferred between the edges under the dipolar flux insertion, manifesting as `quantized quadrupolar Hall effect' in TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed by introducing a mutually commuting pair-hopping terms between wires to gap out all the bulk modes while preserving the dipole moment. The effective action at the quadrupolar edge can be derived from the wire model, with the corresponding bulk dipolar Chern-Simons response theory delineating the topological electromagnetic response in TDIs. Finally, we enrich our exploration of topological dipole insulators to the spinful case and construct a dipolar version of the quantum spin Hall effect, whose boundary evidences a mixed anomaly between spin and dipole symmetry. Effective bulk and the edge action for the dipolar quantum spin Hall insulator are constructed as well.

cond-mat.mes-hall↗
arXiv2024

Dipolar BF theory and dipolar braiding statistics

We analyze the recently proposed dipolar BF theory with couplings to charge and dipole currents. The quasiparticles of the theory are either charge-like or dipole-like, and the mutual braiding statistics between charge-like and dipole-like quasiparticles are dipolar, meaning that it depends on the position of the quasiparticle being encircled. The braiding statistics between two dipole-like quasiparticles is that of ordinary anyons. We further prove that the dipolar BF theory is equivalent to the rank-2 tensor BF theory developed earlier as an effective theory for the rank-2 toric code. Although the two theories are equivalent, the dipolar BF formulation embodies the dipole symmetry explicitly and gives a clean insight into the way the dipole symmetry manifests itself in various conservation laws and the dipolar braiding statistics.

cond-mat.str-el↗
arXiv2024

Scaling and localization in multipole-conserving diffusion

We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are exponentially localized near system boundaries. It also yields an unusual approach to equilibrium, which in $d$ dimensions exhibits scaling with dynamical exponent $z = 4+d$. Similar phenomena occur for dynamics that conserves higher moments of the density, which we systematically classify using a family of nonlinear diffusion equations. In the quantum setting, analogous fermionic systems are shown to form real-space Fermi surfaces, while bosonic versions display a real-space analog of Bose-Einstein condensation.

cond-mat.stat-mech↗
arXiv2023

Topological quantum chains protected by dipolar and other modulated symmetries

We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear (i.e., dipolar), quadratic and exponential modulations. We present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls to spatially modulated symmetry defects, and develop several tools for characterizing and classifying modulated SPT phases. A salient feature of modulated symmetries is that they are generically only present for open chains, and are broken upon the imposition of periodic boundary conditions. Nevertheless, we show that SPT order is present even with periodic boundary conditions, a phenomenon we understand within the context of an object we dub a ``bundle symmetry''. In addition, we show that modulated SPT phases can avoid a certain no-go theorem, leading to an unusual algebraic structure in their matrix product state descriptions.

cond-mat.str-el↗
arXiv2023

Supercurrent-induced Anomalous Thermal Hall Effect as a New Probe to Superconducting Gap Anisotropy

Two-dimensional superconductors have been realized in various atomically thin films such as the twisted bilayer graphene, some of which are anticipated to involve unconventional pairing mechanism. Due to their low dimensionality, experimental probes of the exact nature of superconductivity in these systems have been limited. We propose, by applying a \emph{vertical} supercurrent to a bilayer superconductor where the mirror symmetry is naturally broken by the twisting, there will be anomalous thermal Hall effect induced by the supercurrent that can serve as a sharp probe for the \emph{in-plane} anisotropy of the superconducting gap function. This effect occurs in the \emph{absence} of an external magnetic field and spontaneous breaking of the time-reversal symmetry in the ground state. We derive explicit formulas for the induced thermal Hall conductivity and show them to be significant in the examples of twisted cuprates and twisted FeSe where monolayer superconductivity have already been observed. Though technical challenges still exist, we propose this to be a generic probe of the gap anisotropy in a twisted bilayer superconductor.

cond-mat.supr-con↗
arXiv2023

Aspects of $\mathbb{Z}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those of the standard toric code. Specifically, it features a blending of UV and IR in its ground state, restricted mobility of its quasiparticles, and variations in the braiding statistics of its quasiparticles based on their position. In this paper, we investigate various aspects of $\mathbb{Z}_N$ rank-2 gauge theory in ${(2+1)}$-dimensional spacetime. Firstly, we demonstrate that $U(1)$ rank-2 gauge theory can arise from ${U(1)\times U(1)}$ rank-1 gauge theory after condensing the gauge charges in a specific way. This construction scheme of $U(1)$ rank-2 gauge theory carries over to the $\mathbb{Z}_N$ case simply by Higgsing $U(1)$ to $\mathbb{Z}_N$, after which the resulting rank-2 gauge theory can be tuned to the R2TC. The holonomy operators of R2TC are readily identified using this scheme and are given clear physical interpretation as the pair creation/annihilation of various monopoles and dipoles. Explicit tensor network construction of the ground states of R2TC are given as two copies of the ground states of Kitaev's toric code that are `sewn together' according to the condensation scheme. In addition, through a similar anyon condensation protocol, we present a double semion version of rank-2 toric code whose flux excitations exhibit restricted mobility and semionic statistics. Finally, we identify the generalized discrete symmetries of the R2TC, which are much more complex than typical 1-form symmetries. They include conventional and unconventional 1-form symmetries, such as framed 1-form symmetries and what we call sublattice 1-form symmetries. Using these, we interpret the R2TC's unique properties (UV/IR mixing, position-dependent braiding, etc.) from the modern perspective of generalized spontaneous symmetry breaking and 't Hooft anomalies.

cond-mat.str-el↗
arXiv2022

Dipole condensates in tilted Bose-Hubbard chains

We study the quantum phase diagram of a Bose-Hubbard chain whose dynamics conserves both boson number and boson dipole moment, a situation which can arise in strongly tilted optical lattices. The conservation of dipole moment has a dramatic effect on the phase diagram, which we analyze by combining a field theory analysis with DMRG simulations. Unlike the conventional Bose-Hubbard model, the phase diagram contains no compressible phases, and is instead dominated by various types of exotic dipolar condensates. We suggest ways by which these condensates can be identified in near-term cold atom experiments.

cond-mat.quant-gas↗
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↗