arXiv subjects

Yun-Tak Oh

Publications and source records attributed to Yun-Tak Oh.

18 recordsLinked to original sources

arXiv2026

New directions in dynamical expectation estimation

Computing dynamical expectation values typically relies on approximations optimized for the state or observable separately, without accounting for how their errors combine in the final expression. This work explores an alternative approach in which each approximation is guided by both the state and the observable, accounting for how they jointly determine the target expectation value. This idea is implemented through a sweep algorithm with coupled loss functions for forward state and backward observable updates. Exact error relations provide an analytical rationale for how the proposed losses can improve the accuracy. Numerical tests on 30-qubit random circuits show errors two to three orders of magnitude smaller than those of variational state compression at equal bond dimensions. These results motivate further exploration of joint state and observable approximation for dynamical expectation value estimation.

quant-ph↗

arXiv2026

Topological phase transition of deformed ${\mathbb Z}_3$ toric code

We investigate topological phase transitions in a family of deformed $\mathbb Z_3$ toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the $Q=3$ Potts model for single-parameter deformations and to a three-state Ashkin--Teller-like (AT$_3$) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric ($e$) anyons are confined or condensed. These phases are separated by critical structures with central charges $c=4/5$, $8/5$, and isolated $c=1$ antiferromagnetic (AFM) endpoints. A normalized finite-distance $e$-anyon pair-state norm provides a Fredenhagen--Marcu-type check of the confinement boundary, while the topological data of the quantum double $D(\mathbb Z_3)$ imply a topological entanglement entropy $γ=\log3$ throughout the gapped toric-code phase. Relative to the $\mathbb Z_2$ case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent $U(1)$ one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.

quant-ph↗

arXiv2026

Reachability Constraints in Variational Quantum Circuits: Optimization within Polynomial Group Module

This work identifies a necessary condition for any variational quantum approach to reach the exact ground state. Briefly, the norms of the projections of the input and the ground state onto each group module must match, implying that module weights of the solution state have to be known in advance in order to reach the exact ground state. An exemplary case is provided by matchgate circuits applied to problems whose solutions are classical bit strings, since all computational basis states share the same module-wise weights. Combined with the known classical simulability of quantum circuits for which observables lie in a small linear subspace, this implies that certain problems admit a classical surrogate for exact solution with each step taking $O(n^5)$ time. The Maximum Cut problem serves as an illustrative example.

quant-ph↗

arXiv2026

Spin-orbit-induced Instability and Finite-Temperature Stabilization of a Triangular-lattice Supersolid

Geometrically frustrated triangular-lattice magnets provide fertile ground for realizing intriguing quantum phases such as spin supersolids. A common expectation is that spin-orbit coupling (SOC), which breaks continuous spin rotational symmetry, destabilizes these phases by gapping their low-energy modes. Revisiting this assumption, we map out the SOC-field phase diagram of a frustrated triangular-lattice magnet using spin-wave theory and infinite density-matrix renormalization group (iDMRG) simulations. We find that while infinitesimally weak SOC indeed drives a zero-temperature instability of the supersolid by opening a gap, certain supersolid states remain thermodynamically stable at non-zero temperatures. This reveals a previously unrecognized mechanism in which thermal fluctuations counteract SOC to stabilize supersolidity. The resulting finite-temperature supersolids retain key responses, including a giant magnetocaloric effect, highlighting their potential relevance to real materials. At larger SOC, the system transitions into distinct magnetic orders, including a skyrmion lattice, completing a unified phase diagram.

cond-mat.str-el↗

arXiv2025

Nested Shadows of Anyons:A Framework for Identifying Topological Phases

The 1-form symmetries in two-dimensional topological systems are ``shadowed'' as global symmetries in their one-dimensional quantum transfer matrices. In this work, we introduce a distinct shadow effect arising from the pair-creation of anyons, which manifests as a local symmetry of the quantum transfer matrix. The interplay between these two shadow effects provides a powerful framework for characterizing topological phases without extensive numerical simulations. Specifically, we derive the phase diagram of the filtered toric code state and precisely identify phase boundaries using the nested shadows of anyons. Additionally, we reveal that a class of topological states host gapless edge modes protected by 1-form symmetry rather than global symmetry. Finally, we apply our approach to the three-dimensional toric code and X-cube states, uncovering a nontrivial path in phase space that connects them through a subdimensional critical point, which is highly challenging to detect numerically due to the complexity of simulating three-dimensional systems.

cond-mat.str-el↗

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↗

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

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↗

arXiv2019

Ferromagnetic nodal-line metal in monolayer {\em h}-InC

Based on first-principles calculations, we predict a new two-dimensional ferromagnetic material that exhibits exotic Fermi surface topology. We show that monolayer hexagonal indium carbide ({\em h}-InC) is thermodynamically and dynamically stable, and it energetically favors the ferromagnetic ordering of spins. The perfectly planar geometry in two dimensions, together with ferromagnetism, gives rise to a unique opportunity to encounter intriguing electronic properties, captured in the Fermi surface and band topology. We show that multiple nodal lines coexist in momentum space, accompanied by the electron and hole pockets that touch each other linearly at the nodal lines. Inclusion of spin-orbit coupling enriches the magnetic and electronic properties of {\em h}-InC. Spin-orbit coupling leads to an easy-plane type magnetocrystalline anisotropy, and the nodal lines can be tuned into topological nodal points, contingent upon the magnetization direction. Symmetry analysis and a tight-binding model are provided to explain the nodal structure of the bands. Our findings suggest {\em h}-InC as a new venue for supporting carbon-based magnetism and exotic band topology in two dimensions.

cond-mat.mtrl-sci↗

arXiv2019

Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions

Previously known three-dimensional Dirac semimetals (DSs) occur in two types -- topological DSs and nonsymmorphic DSs. Here we present a novel three-dimensional DS that exhibits both features of the topological and nonsymmorphic DSs. We introduce a minimal tight-binding model for the space group 100 that describes a layered crystal made of two-dimensional planes in the $p4g$ wallpaper group. Using this model, we demonstrate that double glide-mirrors allow a noncentrosymmetric three-dimensional DS that hosts both symmetry-enforced Dirac points at time-reversal invariant momenta and twofold-degenerate Weyl nodal lines on a glide-mirror-invariant plane in momentum space. The proposed DS allows for rich topological physics manifested in both topological surface states and topological phase diagrams, which we discuss in detail. We also perform first-principles calculations to predict that the proposed DS is realized in a set of existing materials BaLa$X$B$Y_5$, where $X$ = Cu or Au, and $Y$ = O, S, or Se.

cond-mat.mes-hall↗

arXiv2017

Proposal of a spin-one chain model with competing dimer and trimer interactions

A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the Affleck-Kennedy-Lieb-Tasaki model and contains both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.

cond-mat.str-el↗

arXiv2016

Type-II Weyl cone transitions in driven semimetals

Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocket-like Fermi surfaces, can be induced in driven Dirac semimetals and line node semimetals. Under a circularly polarized drive, both semimemtal systems immediately generate Weyl node pairs whose types can be further controlled by the driving amplitude and direction. The resultant phase diagrams demonstrate experimental feasibilities.

cond-mat.mes-hall↗

arXiv2016

Adiabatic Green's function technique and the transient behavior in time-dependent fermion-boson coupled models

The Lang-Firsov Hamiltonian, a well-known solvable model of interacting fermion-boson system with sideband features in the fermion spectral weight, is generalized to have the time-dependent fermion-boson coupling constant. We show how to derive the two-time Green's function for the time-dependent problem in the adiabatic limit, defined as the slow temporal variation of the coupling over the characteristic oscillator period. The idea we use in deriving the Green's function is akin to the use of instantaneous basis states in solving the adiabatic evolution problem in quantum mechanics. With such "adiabatic Green's function" at hand we analyze the transient behavior of the spectral weight as the coupling is gradually tuned to zero. Time-dependent generalization of a related model, the spin-boson Hamiltonian, is analyzed in the same way. In both cases the sidebands arising from the fermion-boson coupling can be seen to gradually lose their spectral weights over time. Connections of our solution to the two-dimensional Dirac electrons coupled to quantized photons are discussed.

cond-mat.mes-hall↗

arXiv2015

Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-Skyrmion scattering

We construct Holstein-Primakoff Hamiltonian for magnons in arbitrary slowly varying spin background, for a microscopic spin Hamiltonian consisting of ferromagnetic spin exchange,Dzyaloshinskii-Moriya exchange, and the Zeeman term. The Gross-Pitaevskii-type equation for magnon dynamics contains several background gauge fields pertaining to local spin chirality, inhomogeneous potential, and anomalous scattering that violates the boson number conservation. Non-trivial corrections to previous formulas derived in the literature are given. Subsequent mapping to hydrodynamic fields yields the continuity equation and the Euler equation of the magnon fluid dynamics. Magnon wave scattering off a localized Skyrmion is examined numerically based on our Gross-Pitaevskii formulation. Dependence of the effective flux experienced by the impinging magnon on the Skyrmion radius is pointed out, and compared with analysis of the same problem using the Landau-Lifshitz-Gilbert equation.

cond-mat.mes-hall↗

arXiv2013

Fate of Topology in Spin-1 Spinor Bose-Einstein Condensate

One of the excitements generated by the cold atom systems is the possibility to realize, and explore, varied topological phases stemming from multi-component nature of the condensate. Popular examples are the antiferromagnetic (AFM) and the ferromagnetic (FM) phases in the three-component atomic condensate with effective spin-1, to which different topological manifolds can be assigned. It follows, from consideration of homotopy, that different sorts of topological defects will be stable in each manifold. For instance, Skyrmionic texture is believed to be a stable topological object in two-dimensional AFM spin-1 condensate. Countering such common perceptions, here we show on the basis of a new wave function decomposition scheme that there is no physical parameter regime wherein the temporal dynamics of spin-1 condensate can be described solely within AFM or FM manifold. Initial state of definite topological number prepared entirely within one particular phase must immediately evolve into a mixed state. Accordingly, the very notion of topology and topological stability within the sub-manifold of AFM or FM become invalid. Numerical simulation reveals the linear Zeeman effect to be an efficient catalyst to extract the alternate component from an initial topological object prepared entirely within one particular sub-manifold, serving as a potential new tool for "topology engineering" in multi-component Bose-Einstein condensates.

cond-mat.quant-gas↗